CA2042154A1 - Cone beam scanning trajectories for three-dimensional computerized tomography data acquisition where object is larger than the field of view - Google Patents
Cone beam scanning trajectories for three-dimensional computerized tomography data acquisition where object is larger than the field of viewInfo
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- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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- A61B6/02—Devices for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
- A61B6/03—Computerised tomographs
- A61B6/032—Transmission computed tomography [CT]
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- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/02—Devices for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
- A61B6/027—Devices for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis characterised by the use of a particular data acquisition trajectory, e.g. helical or spiral
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/40—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment with arrangements for generating radiation specially adapted for radiation diagnosis
- A61B6/4064—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment with arrangements for generating radiation specially adapted for radiation diagnosis specially adapted for producing a particular type of beam
- A61B6/4085—Cone-beams
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Abstract
RD-19682 CONE BEAM SCANNING TRAJECTORIES FOR THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY DATA ACQUISITION WHERE OBJECT IS LARGER THAN THE FIELD OF VIEW A configuration for three-dimensional cone beam computerized tomography imaging which minimizes the incompleteness of the data set and, at the same time, avoids corrupted data and resulting artifacts when only a portion of an object is imaged, the object being of greater axial extent compared to a cylindrical field of view. At least two circular source scanning trajectories are defined centered on a rotation axis and lying respectively in two endplanes defining the axial extent of the field of view. At least one cone beam x-ray source and at least one corresponding two-dimen-sional array detector are employed to scan the object along the source scanning trajectories, while acquiring cone beam projection data only from rays passing through the field of view. Preferably, at least one additional circular source scanning trajectory is defined, centered on the rotation axis and lying in a plane intermediate the two endplanes.
Description
~4~54 ~D-19682 T~EE-nIME~7sI
rJT~lTI~ J--g3~ 5~L~=3 ~HA~ FIEI.~ ~F VIEW
Ba~k~Q~nçLof th~ Inv~n~iQn The present inven~ion relates generally to three-dimensional (3D) computerized tomography (CT) and, more par-ticularly, to methods and systems for minimizing the amount of missing data and, at the same time, avoiding corrupted data and resulting artifacts in image reconstruction when a cone beam configuration is used to image a portion of an object which is larger than the field of view.
In conventional computerized tomography ~or both medical and industrial applications, an x-ray fan beam and a linear array detector are employed. Two-dimensional (2D) imaging is achieved. While the data set is complete and image quality is correspondingly high, only a single slice of an object is imaged at a time. When a 3D image is required, a "stack of slices" approach is employed. Acquiring a 3D
data set one 2D slice at a time is inherently slow. More-over, in medical applications, motion artifacts occur becauseadjacent slices are not imaged simultaneously. Also, dose utilization is less than optimal, because the distance between slices is typically less than the x-ray collimator aperture, resulting in double exposure to many parts of the body.
One approach to acquiring a 3D data set simultane-ously is described in the literature: Richard A. Robb, Arnold H. Lent, Barry K. Gilbert, and Aloysius Chu, "The Dynamic Spatial Reconstructor", J. Med. Syst., Vol. 4, No. 2, pp. 253-288 (1980). The Dynamic Spatial Reconstructor employs twenty-eight x-ray sources and twenty-eight x-ray : : :
imaging systems in a synchronous scanning system to acquire data for a conventional l'stack o~ slices" reconstruction all at once. The actual geometry is a stack of twenty-eight cone beams scanning twenty-eight respective cylindrical volumes, 5 with area detectors employed to acquire 240 adjacent video lines of data for each slice. However, the data is analyzed as though it is from a stack of fan beam projections, stacked in an axial direction, using conventional 2D reconstruction algorithms Consistent with this approach, in the Dynamic 10 Spatial Reconstructor the divergence of the x-ray beam above and below ~he central slice of each cylindrical volume is only ~ 4 .
In a system employing true cone ~eam geometry, a cone beam x-ray source and a 2D area detector are employed.
15 An object is scanned, preferably over a 360' angular range, either by moving the x-ray source in a scanning circle around the object, while keeping the 2D area detector fixed with reference to the source, or by rotating the object while the source and detector remain stationary. In either case, it is 20 relative movemen~ between the source and object which effects scanning. Compared to the conventional 2D "stack of slices"
approach to achieve 3D imaging, the cone beam geometry has the potential to achieve rapid 3D imaging of both medical and industrial objects, with improved dose utilization.
The cone beam geometry for 3D imaging has been dis-cussed extensively in the literature, as represented by the following: M. Schlindwein, "Interactive three-Dimensional ReconstructLon from Twin-Cone Beam Pro~ections", IEEE Trans.
Nucl.Sci., Vol. NS-25, No. 5, pp. 1135-1143 (October 1978);
30 Gerald N. Minerbo, "Convolutional Reconstruction ~rom Cone-Beam Projection Data", IEEE Trans. Nucl. Sci., Vol. NS-26, No. 2,, pp. 2682-2689 ~April 1979); Heang K. Tuy, ''An Inversion Formula for Cone-Beam P~econstruction", SIAM J.
Math., Vol. 43, No. 3, pp. 546-552 (June 1983); L.A. ~ -:
,. .
. . .
.
rJT~lTI~ J--g3~ 5~L~=3 ~HA~ FIEI.~ ~F VIEW
Ba~k~Q~nçLof th~ Inv~n~iQn The present inven~ion relates generally to three-dimensional (3D) computerized tomography (CT) and, more par-ticularly, to methods and systems for minimizing the amount of missing data and, at the same time, avoiding corrupted data and resulting artifacts in image reconstruction when a cone beam configuration is used to image a portion of an object which is larger than the field of view.
In conventional computerized tomography ~or both medical and industrial applications, an x-ray fan beam and a linear array detector are employed. Two-dimensional (2D) imaging is achieved. While the data set is complete and image quality is correspondingly high, only a single slice of an object is imaged at a time. When a 3D image is required, a "stack of slices" approach is employed. Acquiring a 3D
data set one 2D slice at a time is inherently slow. More-over, in medical applications, motion artifacts occur becauseadjacent slices are not imaged simultaneously. Also, dose utilization is less than optimal, because the distance between slices is typically less than the x-ray collimator aperture, resulting in double exposure to many parts of the body.
One approach to acquiring a 3D data set simultane-ously is described in the literature: Richard A. Robb, Arnold H. Lent, Barry K. Gilbert, and Aloysius Chu, "The Dynamic Spatial Reconstructor", J. Med. Syst., Vol. 4, No. 2, pp. 253-288 (1980). The Dynamic Spatial Reconstructor employs twenty-eight x-ray sources and twenty-eight x-ray : : :
imaging systems in a synchronous scanning system to acquire data for a conventional l'stack o~ slices" reconstruction all at once. The actual geometry is a stack of twenty-eight cone beams scanning twenty-eight respective cylindrical volumes, 5 with area detectors employed to acquire 240 adjacent video lines of data for each slice. However, the data is analyzed as though it is from a stack of fan beam projections, stacked in an axial direction, using conventional 2D reconstruction algorithms Consistent with this approach, in the Dynamic 10 Spatial Reconstructor the divergence of the x-ray beam above and below ~he central slice of each cylindrical volume is only ~ 4 .
In a system employing true cone ~eam geometry, a cone beam x-ray source and a 2D area detector are employed.
15 An object is scanned, preferably over a 360' angular range, either by moving the x-ray source in a scanning circle around the object, while keeping the 2D area detector fixed with reference to the source, or by rotating the object while the source and detector remain stationary. In either case, it is 20 relative movemen~ between the source and object which effects scanning. Compared to the conventional 2D "stack of slices"
approach to achieve 3D imaging, the cone beam geometry has the potential to achieve rapid 3D imaging of both medical and industrial objects, with improved dose utilization.
The cone beam geometry for 3D imaging has been dis-cussed extensively in the literature, as represented by the following: M. Schlindwein, "Interactive three-Dimensional ReconstructLon from Twin-Cone Beam Pro~ections", IEEE Trans.
Nucl.Sci., Vol. NS-25, No. 5, pp. 1135-1143 (October 1978);
30 Gerald N. Minerbo, "Convolutional Reconstruction ~rom Cone-Beam Projection Data", IEEE Trans. Nucl. Sci., Vol. NS-26, No. 2,, pp. 2682-2689 ~April 1979); Heang K. Tuy, ''An Inversion Formula for Cone-Beam P~econstruction", SIAM J.
Math., Vol. 43, No. 3, pp. 546-552 (June 1983); L.A. ~ -:
,. .
. . .
.
2~
Feldkamp, L.C. Davis, and J.W. Kress, ~Practical Cone-Beam Algorithm", J. Opt. Soc. Am. A., Vol. 1, No. 6, pp. 612-619 (June 1984); Bruce D. Smith, ~Image Reconstruction ~rom Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods", IEEE Trans. Med. Imag., Vol. MI-44, pp. 14-25 (March 1985); and Hui Hu, Robert A. Kruger, and Grant T. Gullberg, "Quantitative Cone-Beam Construction", SPIE Medical Imaging III: Image Processing, Vol. 1092, pp.
492-501 (1989).
A typical scanning and data acquisition configura-tion employing cone-beam geometry is depicted in FIG. 1. An object 20 is positioned within a field of view between a cone beam x-ray point source 22 and a 2D detector array 24, which provides cone beam projection data. An axis of rotation 26 passes through the field of view and object 20. For purposes of analysis, a midplane 28 is defined which contains the x-ray point source 22 and is perpendicular to the axis of rota-tion 26. By convention, the axis of rotation 26 is referred to as ~he z-axis, and the intersection of the axis of rota-tion 26 and the midplane 28 is taken as the origin of coordi-nates. x and y axes lie in the midplane 28 as indicated, and the (x,y,z) coordinate system rotates with the source 22 and detector 24. For scanning the object 20 at a plurality of angular positions, the source 22 moves relative to the object 20 and the field of view along a circular scanning trajectory 30 lying in the midplane 28, while the detector 24 remains fixed with respect to the source 22.
Thus, in the configuration of FIG. 1, data are acquired at a number of angular positions around the object by scanning the source and detector along the single circular scanning trajectory 30 ~or equivalently rotating the object ~hlle the source and detector remain st=tionar~
Feldkamp, L.C. Davis, and J.W. Kress, ~Practical Cone-Beam Algorithm", J. Opt. Soc. Am. A., Vol. 1, No. 6, pp. 612-619 (June 1984); Bruce D. Smith, ~Image Reconstruction ~rom Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods", IEEE Trans. Med. Imag., Vol. MI-44, pp. 14-25 (March 1985); and Hui Hu, Robert A. Kruger, and Grant T. Gullberg, "Quantitative Cone-Beam Construction", SPIE Medical Imaging III: Image Processing, Vol. 1092, pp.
492-501 (1989).
A typical scanning and data acquisition configura-tion employing cone-beam geometry is depicted in FIG. 1. An object 20 is positioned within a field of view between a cone beam x-ray point source 22 and a 2D detector array 24, which provides cone beam projection data. An axis of rotation 26 passes through the field of view and object 20. For purposes of analysis, a midplane 28 is defined which contains the x-ray point source 22 and is perpendicular to the axis of rota-tion 26. By convention, the axis of rotation 26 is referred to as ~he z-axis, and the intersection of the axis of rota-tion 26 and the midplane 28 is taken as the origin of coordi-nates. x and y axes lie in the midplane 28 as indicated, and the (x,y,z) coordinate system rotates with the source 22 and detector 24. For scanning the object 20 at a plurality of angular positions, the source 22 moves relative to the object 20 and the field of view along a circular scanning trajectory 30 lying in the midplane 28, while the detector 24 remains fixed with respect to the source 22.
Thus, in the configuration of FIG. 1, data are acquired at a number of angular positions around the object by scanning the source and detector along the single circular scanning trajectory 30 ~or equivalently rotating the object ~hlle the source and detector remain st=tionar~
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However, there are two limitations of the prior art single circular scanning trajectory approach which ar~
addressed by the present invention. The first limitation is that the data set acquired is incomplete for 3D image recon-struction. The second limitation occurs when the field ofview to be imaged is smaller than the entire object, a common situation in both industrial and medical applications. In this situation, some measured projections contain information from both the field of view of interest and from other regions of the object outside the field of view. The image of the field of view of interest is therefore corrupted by data resulting from overlying material.
Regarding the incomplete data set limitation, Smith, 1985, above, has shown that a cone beam data set is complete if there is a point from the x-ray source scanning trajectory on each plane passing through the object of inter-est ~with the assumptions that the detector is locked in position relative to the source and large enough to span tne object under inspection). A configuration suggested by Minerbo (1979, above) and Tuy (1983, above), which Smith points out satisfies his condition for data completeness, is to employ two circular source scanning trajectories which are perpendicular to each other. Such a scanning configuration is however difficult to implement as a practical mattcr.
Moreover, it presumes that the object fits within the scan-ning trajectories, and does not address the situation where an object is larger than the field of view.
Accordingly, it is an object of the invention to provide a configuration for cone beam 3D CT imaging which both eliminates the problem of contributions to projections from regions outside the field of view, and minimi~es the : ': . :' '. : :' ~ ' - , . . :
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2~ 5 ~ RD -19 6 8 2 incompleteness of the data set to the point where very high quality images can be achieved.
It is another object of the invention to provide methods and systems for fast data acquisition to minimize motion artifacts, particularly in medical imaging applica-tions.
These and other objects are achieved by the present invention, which is applicable to scanning and data acquisi-tion for three-dimensional computerized tomography (CT) imag-ing of a portion of an object within a cylindrical field ofview radially centered on a rotation axis and having an axial extent defined by two endplanes perpendicular to the rotation axis, where the object is of greater axial extent than the field of view.
Briefly, a method in accordance with the invention includes the steps of defining at least two circular source scanning trajectories centered on the rotation axis and lying respectively in the two endplanes, and employing at least one cone beam x-ray source and at least one corresponding two-dimensional array detector positioned with reference to the source and with reference to the field of view to scan the object at a plurality of relative angular positions along the source scanning trajectories to acquire cone beam projection data, while acquiring data only from rays passing through the field of view.
Preferably~ at least one additional circular source scanning trajectory is defined, centered on the rotation axis and lying ln a plane intermediate the two endplanes. The method then includes the step of scanning the object at a plurality of angular positions along the additional source scanning trajectory to acquire cone beam projection data from rays passing through the field of view.
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Z ~ 4 ~ ~ 5 ~ RD-196~2 Thus, in accordance with the invention, only data from the field of view is acquired. In any individual scan, this results in less available data (more missing data) than would be achieved if the scan were not limited to data from S only the field of view. However, when several scans are com-bined, the resulting available data set is larger than would be achieved in any single scan of the object, and the problem of overlying material is completely avoided. The number of source scanning trajectories chosen is a tradeoff of mechani-cal complexity, scanning time, and the amount of missing datathat can be tolerated in a specific imaging application.
In à more particular aspect, the method includes providing at least two scan heads corresponding to the two source scanning trajectories, each scan head including a cone beam x-ray source and a two-dimensional array detector posi-tioned with reference to the x ray source of the particular scan head and field of view for obtaining cone beam projec-tion data, and employing the two scan heads to simultaneously scan the object along the two source scanning trajectories.
Where a~ least one additional circular source scan-ning trajectory has been defined, the method further includes providing a separate scan head corresponding to each of the source scanning trajectories, each of the scan heads then including a cone beam x-ray source and a two-dimensional array detector positioned with reference to the x-ray source of the particular scan head in the field of view for obtain-ing cone beam projection data, and employing all the scan heads to simultaneously scan the object along the source ~` scanning trajectories.
The additional source scanning trajectory may be locatad in a plane where it is desired to obtain exact two-dimensional computerized tomography data. ;~
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In accordance with another aspect of the invention, a system is provided which includes at least one cone beam x-ray source and at least one two-dimensional array detector corresponding to the source and positioned with reference to the source and the field of view for obtaining cone beam pro-jection data from rays passing through the field of view.
The system additionally includes a scanning element for effecting relative motion between the source and the object, the source moving relative to the object along at least two circular source scanning trajectories centered on the rota-tion axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays passing through the field of view with the source at a plurality of angular positions on the source scanning trajectories.
Preferably, the scanning element effects relative motion between the source and the object along an additional circu-lar source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes.
In accordance with another aspect of the invention, a system includes a pair of cone beam x-ray sources and a pair of two-dimensional array detectors respectively corre-sponding to the sources and positioned with reference to the sources and the field of view for obtalning cone beam projec-tion data from x-rays passing through the field of view. The system additionally includes a scanning element for effecting relative motion between the sources and the object, the sources moving relative to the object along a corresponding pair of circular source scanning trajectories entered on the rotation axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays pass-ing through the field of view with the sources at a plurality of angular positions on the source scanning trajectories.
:
, . ~ :
~' '` ~ ' ~ ' '. ` ' Preferably, the system includes at least one addi-tional cone beam x-ray source and at least one additional two-dimensional array detector cor~esponding to the addi-tional source and positioned with reference to the additional source of obtaining cone beam projection data from rays pass-ing through the field of view. ~he scanning element also effects relative motion between the additional source and the object, the additional source moving relative to the object along an additional circular source scanning trajectory cen-tered on the rotation axis and lying in a plane intermediatethe two endplanes.
In those embodiments of the invention where a plu-rality of scan heads are employed to simultaneously scan the object along a plurality of source scanning trajectories, the cone beam x-ray sources of the scan heads are angularly off-set so as to reduce interference caused by x-rays from one source interacting with the detector corresponding to the other source.
Brief Descrie~ion Qf the D~a~i~gs While the novel features of the invention are set forth with particularity in the appended claims, the inven-tion, both as to organization and content, will be better understood and appreciated, along with other objects and fea-tures thereof, from the following detailed description taken in conjunction with the drawings, in which:
25FIG. 1, referred to hereinabove, represents conven-tional cone beam scanning geometry for 3D CT;
FIGS, 2a, 2b, 2c, 2d, 2e and 2f are diagrams depicting the Radon transform approach to 3D CT imaging; ~:
FIG 3 is a representation of the 3D Radon transform of an object at a given point;
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FIGS. 4a and 4b depict Radon space filling in the case of 2D parallel beam CT;
- FIGS. Sa and 5b depict Radon space filling in the case of 2D fan beam CT;
FIGS. ~a and 6b depict Radon space filling in the case of 3D parallel beam CT;
FIGS. 7a and 7b depict Radon space ~illing in the case of 3D cone beam CT;
FIG. 8 depicts a prior art circular scanning tra~
jectory corresponding to ~IG. 1;
FIG. 9 depicts regions of available data and miss-ing data in Radon space when the prior art scanning configu-ration of FIGS. 1 and 8 is employed;
FIG. 10 depicts a configuration wherein an x-ray source and a two-dimensional area detector scan a cylindrical field of view which is a subsection of a larger cylindrical object wherein measured projections are corrupted by contri-butions from sections of the object outside the field of view;
FIG. 11 depicts a similar configuration, wherein data is acquixed over a subset of the cylindrical field of view;
FIG. 12 is a top view of a system embodying the scanning configuration of the invention;
FIG. 13 is a side view of a system embodying the scanning configuration of the invention, modified for pur-poses of illustration to better represent the vertical offset between the several circular scanning trajectories; and .
.
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FIG. 14 depicts regions of available data and miss-ing data in Radon space when the ~canning configuration of FIGS. 12 and 13 is employed.
Detailed Descrl~tiQn Since the present invention is in part directed to reducing the data set incompleteness in the prior art cone beam scanning geometry of FIG. 1, what is meant by data set incompleteness will next be defined and described, followed by a description of methods and systems in accordance with the invention.
Data set completeness can be defined most clearly and rigorously in terms of the Radon transform approach to 3D
imaging, represented in FIGS. 2a through 2f. The object it-self is defined in terms of its x-ray attenuation coefficient f(x,y,z) (FIG. 2a). The measured cone beam projection data then corresponds to a line integral of this function over the radial direction ~ f(r,~,zO)dr (FIG. 2b). The line inte-grals of the detector data (also known as detector integrals) are given by ¦X(~)d~-¦¦f(r,~,z)dr d~ ~FIG. 2c). In the paral-lel beam case, these detector integrals are simply equal to the Radon transform of the object. In the cone beam case,however, the Radon transform is given instead by ¦¦f(r,~,zO)r dr d~ (FIG. 2d). The additional factor of r in the Radon transform integral results from the Jacobian of the co-ordinate transformation from Cartesian to polar coordinates.
As depicted in FIGS. 2e and 2f, an inverse Radon transform procedure reconstructs a 3D CT image from the detector inte-grals. Since direct inverse Radon transformation requires planar integrals of the object as inputt an intermediate step ` of converting cone beam detector integrals to planar inte-.~
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grals ~ay be employed, although a variety of reconstruction techniques are available, as is apparent from the literature.
It is significant to note that the data set is com-plete if it provides data at every point in Radon trans~orm space; i.e., Radon space is filled with data over the region of support corresponding to the field of view in real space within which the object of interest fits. Therefore, the filling of Radon space by various scanning configurations is of significant interest. ~In addition, it can be shown that if detector integral space is filled over the region of sup-port for the object, the data set is complete.) As depic~ed in FIG. 3, the Radon transform of an object at a point xO~yO~ZO is given by the area integral of the x-ray attenuation coefficient over the plane passing through 15 Xo~yo~zo that is perpendicular to the line from the origin to xO~yO~ 7O, and can be expressed as xO~yo~zo)=lJf(x~y~z) da plane In 2D, the situation is similar, except that the integral is over a line, not over a plane.
Any scanning and data acquisition configuration provides data over some volume of Radon space. Described next with reference to ~IGS. 4a through 7b are regions in Radon space which are filled and which are not for various 2D
and 3D scanning configurations.
FIGS. 4a and 4b represent Radon space filling for 2D parallel beam CT. The x-ray paths for two view angles are shown in FIG. 4a, and the resulting points in Radon space are shown in FIG. 4b. For each point in RadoD space, a line is extended from the origin to the point of interest, and the x ray intensity is integrated over a line passing through tha~
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point and perpendicular to the line to that point ~rom the origin. Such points are shown in FIG. 4b for each ray depicted in FIG. 4a, for each of two view angles.
The situation ~or ~an beam data acquisition is sim-ilar (FIGS. 5a and 5b), but here the ray paths diverge from the x-ray source, and the geometry is slightly more compli-cated. The procedure is the same, however. ~y way of exam-ple, the extreme right-hand ray o~ the fan beam is analyzed in FIG. Sb. The perpendicular line to the ray is labeled "s". It may be noted that the point of Radon space of inter-est forms a right triangle with the origin and the x-ray source point.. (It is the same point ~hat would be determined in parallel beam geometry for a view angle orientation of one-half the fan angle.) This is generally true for any point in Radon space acquired with the detector in this posi-tion. Therefore, by geometry, the points in Radon space lie on the arc of a circle whose diameter is the source to center of rotation distance. Similar arcs are constructed for each view angle position around the object. It can be appreciated from this construct that complete data is provided by rotat-ing source and detector around the object through an angle of 180- plus the fan angle.
The parallel beam case for 3D is represented in FI~S. 6a and 6b. Here, the x-ray attenuation measurement corresponds to integration in the ~ direction, and line inte-grals o~ the detector data are taken at other orientations in the detector plane to fill in Radon space on a singIe plane pa~sing through the object. For example, the point in Radon space at x=O,y=yO corresponds to the detector integral over points in the detector a distance yO above the x,z plane.
Points of~ axis in Radon space correspond to detector inte-grals along straight lines with various slopes in detector . spa~e. For example, the point at x=c,y=c in Radon space cor- -responds to detector integrals along lines with slope -45 `: :
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with respect to the x axis and a distance ~ from the ori-gin.
The particularly relevant cone beam case in 3D is similarly represented in FIGS. 7a and 7b. Corresponding to FIGS. 7a and 7b are prior art FIG. 1, described hereinabove;
prior art FIG. 8, which depicts a single circular source scanning trajectory 32 around a cylindrical field of view 34 within which an object to be scanned fits; and prior art FIG.
9, which depicts in cross-section the intersection of a vol-ume 36 in Radon space comprising the region of support forthe field of view 34 with a toric volume 38 representing the region in Radon space for which data are available. In FIG.
9, the diameter of each side of the toric volume 38 is equal to the source to axis of rotation distance D. For purposes of comparison with the Radon space region of support volume 36, superimposed in phantom in FIG. 9 is the real space ~ield of view 34.
In FIGS. 7a and 7b, the exemplary point shown in Radon space corresponds to the detector integral along the top line of the detector data. The geometry i~ similar to the fan beam case in 2D. The points in Radon space for all detector line integrals at a single view angle correspond to a section of a sphere with diameter equal to the source to center of rotation distance. A new spherical shell of data is created at each view angle, and for a 360- scan, the available data falls inside the toric volume 38 (FIG. 9).
Thus, as represented in FIG. 9, in Radon space data for reconstruction are available at those points within the region of support volume 36 where the region of support vol-ume 36 intersects the toric volume 38, as indicated by theword "data". As indicated by the words "missing data", data are absent for points on the top and bottom of the ~adon space region of support volume 36 because these points corre-, , ~ . . ~: ., .
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spond to planes parallel and near parallel to the x,y plane and data for these planes are not available because of the cone beam nature of the x-ray source. The region of missing data narrows as z approaches the midplane, and for z=0 (on the midplane~, all the required data are available.
As shown by Smith, 1985, above, a cone beam data set is complete if there is a point from the x-ray source scanning trajectory on each plane passing through the object of interest. (The detector is assumed to be locked in posi-tion relative to the source and large enough to span theobject under inspection.) Relating this to FIG. 8 where the circular source scanning trajectory 32 surrounds the exem-plary field of view 34, by Smith's criterion the trajectory 32 is incomplete because a number of horizontal and near-hor-izontal planes pass through the region of support of theobject (i.e. the field of view 34) without intersecting the source scanning trajectory 32. These planes are exactly those that correspond to the missing data in Radon space in FIG. 9. When applying Smith's criterion, it may be noted that, for large z, the number of planes through the object not intersecting the source scanning trajectory is relatively large, and the number decreases as z decreases. This same behavior is noted in Radon space, as shown in FIG. 9. It may also be noted that vertical planes passing through the object do intersect the scanning trajectory, and that, as the diame-ter of the trajectory increases relative to the diameter of the object, the amount of missing data (the number of planes that do not intersect the scanning trajectory) decreases.
Considering now in particular the problem of data corruption by overlying material in the situation where an object to be imaged is of greater axial extent than a field of view, in FIG. 10, depicted is a cylindrical field of view 50 radially centered on a z-axis or rotation axis 52, and having an axial extent defined by two endplanes 54 and 56 ' . ' :
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perpendicular to the rotation axis 52. An object 58 to be imaged is of greater axial extent that the field of view 50.
Thus, only that portion of the object 58 lying within the field of view 50 is to be imaged.
In FIG. 10, an x-ray source 60 and a two-dimen-sional detector 62 are scanning the field of view 50. The extreme rays 64 and 66 are required to acquire data over the entire field of view 50 of interest. it can be seen that rays near the ends of the cylindrical field of view 50 pene-10 trate through portions 68 and 70 of the object 58 outside the field of view 50. This overlying material 68 and 70 then corrupts the projections acquired by the area detector 62 which projections, in the reconstruction algorithm, are assumed to contain contributions from the field of view 50 only. A reconstructed image therefore contains contributions from regions outside the field of view, and artifacts result.
One approach to the problem of data corruption due to overlying material is depicted in FIG. 11, which is comparable to FIG. 10 except that the x-ray cone angle is reduced so that data is acquired only over a subset of the cylindrical field of view 50. However, this configuration results in a significant loss of data, since regions 72 and ` 74 just inside the ends of the cylindrical field of view 50 are not sampled by projection data at all. This result exacerbates the missing data problem which is already present in 3D CT image reconstruction as described hereinabove.
It may be noted that approaches intermediate those of FIGS. 10 and 11 are known in the prior art. For example, Feldkamp et al., 1984, above, describe a reconstruction technique which corresponds to a scanning configuration wherein the outer rays of the x-ray cone beam pass through the field of view at the rotation axis.
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P~D-19682 FIGS. 12 and 13 depict a scanning configuration in accordance with the invention. In particular, FIG. 12 is a top view, while FIG. 13 is a side view modified for purposes of illustration by repositioning the x-ray source so as to more clearly depict the vertical offset. In the top view of FIG. 12, the various circular source scanning trajectories are superimposed and lie on a single circle 80. The cylindrical field of view 50 is defined by a radius r, and has an axial extent between the two endplanes 54.
Corresponding to the configuration of FIG. 11, above, an x-ray source S1 scans along a circular scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes 54. Corresponding to the source S1 is a detector D1, which is sized to acquire cone beam projection data from rays passing through the field of view 50, but not from rays outside the field of view.
In accordance with the invention, two further cir-cular source scanning trajectories are defined lying in the endplanes 54 and 56, along which sources S2 and S3 scan.
Detectors D2 and D3 correspond to the source S2 and S3.
Scanning effected by source S2 and its corresponding detector D2 does an excellent job of filling a missing data at the top of the cylindrical field of view 50, while scanning by the source S3 and detector D3 does an excellent job of filling in missing data at the bottom of the cylindrical field of view 50. All of the scans acquire data only over projection paths completely included in the cylindrical field of view 50.
It will be appreciated that each of the detectors D1, D2 and D3 is fixed in position relative to its corre-sponding source S1, S2 and S3. Each of the sources S1, S2and S3 and its corresponding detector D1, D2 and D3 may be viewed as a scan head. Scanning is accomplished in a conven-tional manner by moving the sources along the respective ... . ..
.
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- scanning circles relative to the object an the field of view 50. Since it is rel.ative movement which effects scanning, either the object and with it the field of view 50 can be rotated while the sources and detectors remain stationary, or the object and field of view 50 can remain stationary while the sources and detector move. By way of example, in FIG. 13 a generalized scanning element 82 is connected to the object in order to move the object as required, while the sources and detectors remain stationary.
As may be seen particularly in FIG. 12, in order to reduce interference of X-rays from one source interacting with the detector corresponding to another source, the sources are angularly offset. In the particular configura-tion shown, the angular offset is 120-. Other angular off-sets may be employed, chosen for purposes of sca~ter reduc-tion, mechanical convenience, or other system considerations.
It will be appreciated that the various scans at different locations need not be made simultaneously.
Simultaneous scanning may be required in medical applications to reduce or eliminate motion artifacts, but are less neces-sary in industrial applications where a part to be inspected can be securely fixtured into position. Thus, it will be appreciated that one scan head comprising a single x-ray source and a single detector may be repositioned to effect scanning allowing each of the scanning circles, or a plural-ity of scan heads may be employed. Where only a single scan head ls employed, a preferred scanning element 82 is a two-axis CNC part manipulator, the two axes being a vertical translation axis and a rotation axis.
It will further be appreciated that scanning along various numbers of circular source scanning trajectories can be dofie in accordance with the invention. Scanning along the two circular source scanning trajectorie~ lying in the end-,. ,. , . . .:
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planes 54 and 56, that is with sources S2 and S3 and corre-sponding detectors D2 and D3, reduces hardware costs and com-plexity, but requires image reconstruction with l~ss avail-able data. Scanning along three trajectories as depicted is particularly attractive, because scan 1 provides exact data on the midplane at the center of the field of view 50, while scans 2 and 3 provide exact data on midplanes at the top and bottom of the object field of view. Scanning along four or more source trajectories (simultaneously) increases hardware costs and complexity, but reduces the missing data even more and, perhaps more importantly, allows selection of the posi-tion of the midplane locations where the reconstruction is exact.
FIG. 14 depicts Radon space filling as is achieved with the illustrated embodiment wherein scanning is along three circular source scanning trajectories. FIG. 14 depicts in cross-section the Radon space region of support 36 corre-sponding to a cylindrical field of view, as in FIG. 9.
Superimposed in FIG. 14 are three available data circles re-spectively defining additional toric volumes 86 and 88 corre-sponding to the scans of sources S2 and S3 along the trajec tories lying within the endplanes 59 and 56. Again, avail-able data and missing data areas are indicated.
In FIG. 14, it may be noted that the Radon space region 36 which must be filled for the cylindrical field of view dips down at the poles, just as do the regions of avail-able data. Thus, the shapes of the available data and the region of support are well matched for a cylindrical field of view.
While the invention is described and claimed herein in terms of acquiring data only from rays passing through the field of view, it will be appreciated that the detectors may, as an incidental matter, acquire data from rays passing .
' ' ".' "'" ' ' ~ RD-19682 through regions outside the field of view. However, this particular data is discarded at some point and not employed for reconstruction. The particular point where the data is discar~ed is arbitrary. Preferably, the area detectors are optimally sized to match the field of view and the source scanning geometry so that no detector area is ~wasted~.
However, in practical systems, it is not always possible to optimally size the area detectors. Accordingly, the termi-nology employed herein with reference to acquiring data only from rays passing through the field of view is intended to be given a reasonable interpretation, and does not preclude incidentally requiring data outside the field of view, which data is subsequently discarded.
While specific embodiments of the invention have been illustrated and described herein, it is realized that modifications and changes will occur to those skilled in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit and scope of the invention.
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However, there are two limitations of the prior art single circular scanning trajectory approach which ar~
addressed by the present invention. The first limitation is that the data set acquired is incomplete for 3D image recon-struction. The second limitation occurs when the field ofview to be imaged is smaller than the entire object, a common situation in both industrial and medical applications. In this situation, some measured projections contain information from both the field of view of interest and from other regions of the object outside the field of view. The image of the field of view of interest is therefore corrupted by data resulting from overlying material.
Regarding the incomplete data set limitation, Smith, 1985, above, has shown that a cone beam data set is complete if there is a point from the x-ray source scanning trajectory on each plane passing through the object of inter-est ~with the assumptions that the detector is locked in position relative to the source and large enough to span tne object under inspection). A configuration suggested by Minerbo (1979, above) and Tuy (1983, above), which Smith points out satisfies his condition for data completeness, is to employ two circular source scanning trajectories which are perpendicular to each other. Such a scanning configuration is however difficult to implement as a practical mattcr.
Moreover, it presumes that the object fits within the scan-ning trajectories, and does not address the situation where an object is larger than the field of view.
Accordingly, it is an object of the invention to provide a configuration for cone beam 3D CT imaging which both eliminates the problem of contributions to projections from regions outside the field of view, and minimi~es the : ': . :' '. : :' ~ ' - , . . :
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2~ 5 ~ RD -19 6 8 2 incompleteness of the data set to the point where very high quality images can be achieved.
It is another object of the invention to provide methods and systems for fast data acquisition to minimize motion artifacts, particularly in medical imaging applica-tions.
These and other objects are achieved by the present invention, which is applicable to scanning and data acquisi-tion for three-dimensional computerized tomography (CT) imag-ing of a portion of an object within a cylindrical field ofview radially centered on a rotation axis and having an axial extent defined by two endplanes perpendicular to the rotation axis, where the object is of greater axial extent than the field of view.
Briefly, a method in accordance with the invention includes the steps of defining at least two circular source scanning trajectories centered on the rotation axis and lying respectively in the two endplanes, and employing at least one cone beam x-ray source and at least one corresponding two-dimensional array detector positioned with reference to the source and with reference to the field of view to scan the object at a plurality of relative angular positions along the source scanning trajectories to acquire cone beam projection data, while acquiring data only from rays passing through the field of view.
Preferably~ at least one additional circular source scanning trajectory is defined, centered on the rotation axis and lying ln a plane intermediate the two endplanes. The method then includes the step of scanning the object at a plurality of angular positions along the additional source scanning trajectory to acquire cone beam projection data from rays passing through the field of view.
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Z ~ 4 ~ ~ 5 ~ RD-196~2 Thus, in accordance with the invention, only data from the field of view is acquired. In any individual scan, this results in less available data (more missing data) than would be achieved if the scan were not limited to data from S only the field of view. However, when several scans are com-bined, the resulting available data set is larger than would be achieved in any single scan of the object, and the problem of overlying material is completely avoided. The number of source scanning trajectories chosen is a tradeoff of mechani-cal complexity, scanning time, and the amount of missing datathat can be tolerated in a specific imaging application.
In à more particular aspect, the method includes providing at least two scan heads corresponding to the two source scanning trajectories, each scan head including a cone beam x-ray source and a two-dimensional array detector posi-tioned with reference to the x ray source of the particular scan head and field of view for obtaining cone beam projec-tion data, and employing the two scan heads to simultaneously scan the object along the two source scanning trajectories.
Where a~ least one additional circular source scan-ning trajectory has been defined, the method further includes providing a separate scan head corresponding to each of the source scanning trajectories, each of the scan heads then including a cone beam x-ray source and a two-dimensional array detector positioned with reference to the x-ray source of the particular scan head in the field of view for obtain-ing cone beam projection data, and employing all the scan heads to simultaneously scan the object along the source ~` scanning trajectories.
The additional source scanning trajectory may be locatad in a plane where it is desired to obtain exact two-dimensional computerized tomography data. ;~
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In accordance with another aspect of the invention, a system is provided which includes at least one cone beam x-ray source and at least one two-dimensional array detector corresponding to the source and positioned with reference to the source and the field of view for obtaining cone beam pro-jection data from rays passing through the field of view.
The system additionally includes a scanning element for effecting relative motion between the source and the object, the source moving relative to the object along at least two circular source scanning trajectories centered on the rota-tion axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays passing through the field of view with the source at a plurality of angular positions on the source scanning trajectories.
Preferably, the scanning element effects relative motion between the source and the object along an additional circu-lar source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes.
In accordance with another aspect of the invention, a system includes a pair of cone beam x-ray sources and a pair of two-dimensional array detectors respectively corre-sponding to the sources and positioned with reference to the sources and the field of view for obtalning cone beam projec-tion data from x-rays passing through the field of view. The system additionally includes a scanning element for effecting relative motion between the sources and the object, the sources moving relative to the object along a corresponding pair of circular source scanning trajectories entered on the rotation axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays pass-ing through the field of view with the sources at a plurality of angular positions on the source scanning trajectories.
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~' '` ~ ' ~ ' '. ` ' Preferably, the system includes at least one addi-tional cone beam x-ray source and at least one additional two-dimensional array detector cor~esponding to the addi-tional source and positioned with reference to the additional source of obtaining cone beam projection data from rays pass-ing through the field of view. ~he scanning element also effects relative motion between the additional source and the object, the additional source moving relative to the object along an additional circular source scanning trajectory cen-tered on the rotation axis and lying in a plane intermediatethe two endplanes.
In those embodiments of the invention where a plu-rality of scan heads are employed to simultaneously scan the object along a plurality of source scanning trajectories, the cone beam x-ray sources of the scan heads are angularly off-set so as to reduce interference caused by x-rays from one source interacting with the detector corresponding to the other source.
Brief Descrie~ion Qf the D~a~i~gs While the novel features of the invention are set forth with particularity in the appended claims, the inven-tion, both as to organization and content, will be better understood and appreciated, along with other objects and fea-tures thereof, from the following detailed description taken in conjunction with the drawings, in which:
25FIG. 1, referred to hereinabove, represents conven-tional cone beam scanning geometry for 3D CT;
FIGS, 2a, 2b, 2c, 2d, 2e and 2f are diagrams depicting the Radon transform approach to 3D CT imaging; ~:
FIG 3 is a representation of the 3D Radon transform of an object at a given point;
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FIGS. 4a and 4b depict Radon space filling in the case of 2D parallel beam CT;
- FIGS. Sa and 5b depict Radon space filling in the case of 2D fan beam CT;
FIGS. ~a and 6b depict Radon space filling in the case of 3D parallel beam CT;
FIGS. 7a and 7b depict Radon space ~illing in the case of 3D cone beam CT;
FIG. 8 depicts a prior art circular scanning tra~
jectory corresponding to ~IG. 1;
FIG. 9 depicts regions of available data and miss-ing data in Radon space when the prior art scanning configu-ration of FIGS. 1 and 8 is employed;
FIG. 10 depicts a configuration wherein an x-ray source and a two-dimensional area detector scan a cylindrical field of view which is a subsection of a larger cylindrical object wherein measured projections are corrupted by contri-butions from sections of the object outside the field of view;
FIG. 11 depicts a similar configuration, wherein data is acquixed over a subset of the cylindrical field of view;
FIG. 12 is a top view of a system embodying the scanning configuration of the invention;
FIG. 13 is a side view of a system embodying the scanning configuration of the invention, modified for pur-poses of illustration to better represent the vertical offset between the several circular scanning trajectories; and .
.
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FIG. 14 depicts regions of available data and miss-ing data in Radon space when the ~canning configuration of FIGS. 12 and 13 is employed.
Detailed Descrl~tiQn Since the present invention is in part directed to reducing the data set incompleteness in the prior art cone beam scanning geometry of FIG. 1, what is meant by data set incompleteness will next be defined and described, followed by a description of methods and systems in accordance with the invention.
Data set completeness can be defined most clearly and rigorously in terms of the Radon transform approach to 3D
imaging, represented in FIGS. 2a through 2f. The object it-self is defined in terms of its x-ray attenuation coefficient f(x,y,z) (FIG. 2a). The measured cone beam projection data then corresponds to a line integral of this function over the radial direction ~ f(r,~,zO)dr (FIG. 2b). The line inte-grals of the detector data (also known as detector integrals) are given by ¦X(~)d~-¦¦f(r,~,z)dr d~ ~FIG. 2c). In the paral-lel beam case, these detector integrals are simply equal to the Radon transform of the object. In the cone beam case,however, the Radon transform is given instead by ¦¦f(r,~,zO)r dr d~ (FIG. 2d). The additional factor of r in the Radon transform integral results from the Jacobian of the co-ordinate transformation from Cartesian to polar coordinates.
As depicted in FIGS. 2e and 2f, an inverse Radon transform procedure reconstructs a 3D CT image from the detector inte-grals. Since direct inverse Radon transformation requires planar integrals of the object as inputt an intermediate step ` of converting cone beam detector integrals to planar inte-.~
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grals ~ay be employed, although a variety of reconstruction techniques are available, as is apparent from the literature.
It is significant to note that the data set is com-plete if it provides data at every point in Radon trans~orm space; i.e., Radon space is filled with data over the region of support corresponding to the field of view in real space within which the object of interest fits. Therefore, the filling of Radon space by various scanning configurations is of significant interest. ~In addition, it can be shown that if detector integral space is filled over the region of sup-port for the object, the data set is complete.) As depic~ed in FIG. 3, the Radon transform of an object at a point xO~yO~ZO is given by the area integral of the x-ray attenuation coefficient over the plane passing through 15 Xo~yo~zo that is perpendicular to the line from the origin to xO~yO~ 7O, and can be expressed as xO~yo~zo)=lJf(x~y~z) da plane In 2D, the situation is similar, except that the integral is over a line, not over a plane.
Any scanning and data acquisition configuration provides data over some volume of Radon space. Described next with reference to ~IGS. 4a through 7b are regions in Radon space which are filled and which are not for various 2D
and 3D scanning configurations.
FIGS. 4a and 4b represent Radon space filling for 2D parallel beam CT. The x-ray paths for two view angles are shown in FIG. 4a, and the resulting points in Radon space are shown in FIG. 4b. For each point in RadoD space, a line is extended from the origin to the point of interest, and the x ray intensity is integrated over a line passing through tha~
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point and perpendicular to the line to that point ~rom the origin. Such points are shown in FIG. 4b for each ray depicted in FIG. 4a, for each of two view angles.
The situation ~or ~an beam data acquisition is sim-ilar (FIGS. 5a and 5b), but here the ray paths diverge from the x-ray source, and the geometry is slightly more compli-cated. The procedure is the same, however. ~y way of exam-ple, the extreme right-hand ray o~ the fan beam is analyzed in FIG. Sb. The perpendicular line to the ray is labeled "s". It may be noted that the point of Radon space of inter-est forms a right triangle with the origin and the x-ray source point.. (It is the same point ~hat would be determined in parallel beam geometry for a view angle orientation of one-half the fan angle.) This is generally true for any point in Radon space acquired with the detector in this posi-tion. Therefore, by geometry, the points in Radon space lie on the arc of a circle whose diameter is the source to center of rotation distance. Similar arcs are constructed for each view angle position around the object. It can be appreciated from this construct that complete data is provided by rotat-ing source and detector around the object through an angle of 180- plus the fan angle.
The parallel beam case for 3D is represented in FI~S. 6a and 6b. Here, the x-ray attenuation measurement corresponds to integration in the ~ direction, and line inte-grals o~ the detector data are taken at other orientations in the detector plane to fill in Radon space on a singIe plane pa~sing through the object. For example, the point in Radon space at x=O,y=yO corresponds to the detector integral over points in the detector a distance yO above the x,z plane.
Points of~ axis in Radon space correspond to detector inte-grals along straight lines with various slopes in detector . spa~e. For example, the point at x=c,y=c in Radon space cor- -responds to detector integrals along lines with slope -45 `: :
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with respect to the x axis and a distance ~ from the ori-gin.
The particularly relevant cone beam case in 3D is similarly represented in FIGS. 7a and 7b. Corresponding to FIGS. 7a and 7b are prior art FIG. 1, described hereinabove;
prior art FIG. 8, which depicts a single circular source scanning trajectory 32 around a cylindrical field of view 34 within which an object to be scanned fits; and prior art FIG.
9, which depicts in cross-section the intersection of a vol-ume 36 in Radon space comprising the region of support forthe field of view 34 with a toric volume 38 representing the region in Radon space for which data are available. In FIG.
9, the diameter of each side of the toric volume 38 is equal to the source to axis of rotation distance D. For purposes of comparison with the Radon space region of support volume 36, superimposed in phantom in FIG. 9 is the real space ~ield of view 34.
In FIGS. 7a and 7b, the exemplary point shown in Radon space corresponds to the detector integral along the top line of the detector data. The geometry i~ similar to the fan beam case in 2D. The points in Radon space for all detector line integrals at a single view angle correspond to a section of a sphere with diameter equal to the source to center of rotation distance. A new spherical shell of data is created at each view angle, and for a 360- scan, the available data falls inside the toric volume 38 (FIG. 9).
Thus, as represented in FIG. 9, in Radon space data for reconstruction are available at those points within the region of support volume 36 where the region of support vol-ume 36 intersects the toric volume 38, as indicated by theword "data". As indicated by the words "missing data", data are absent for points on the top and bottom of the ~adon space region of support volume 36 because these points corre-, , ~ . . ~: ., .
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spond to planes parallel and near parallel to the x,y plane and data for these planes are not available because of the cone beam nature of the x-ray source. The region of missing data narrows as z approaches the midplane, and for z=0 (on the midplane~, all the required data are available.
As shown by Smith, 1985, above, a cone beam data set is complete if there is a point from the x-ray source scanning trajectory on each plane passing through the object of interest. (The detector is assumed to be locked in posi-tion relative to the source and large enough to span theobject under inspection.) Relating this to FIG. 8 where the circular source scanning trajectory 32 surrounds the exem-plary field of view 34, by Smith's criterion the trajectory 32 is incomplete because a number of horizontal and near-hor-izontal planes pass through the region of support of theobject (i.e. the field of view 34) without intersecting the source scanning trajectory 32. These planes are exactly those that correspond to the missing data in Radon space in FIG. 9. When applying Smith's criterion, it may be noted that, for large z, the number of planes through the object not intersecting the source scanning trajectory is relatively large, and the number decreases as z decreases. This same behavior is noted in Radon space, as shown in FIG. 9. It may also be noted that vertical planes passing through the object do intersect the scanning trajectory, and that, as the diame-ter of the trajectory increases relative to the diameter of the object, the amount of missing data (the number of planes that do not intersect the scanning trajectory) decreases.
Considering now in particular the problem of data corruption by overlying material in the situation where an object to be imaged is of greater axial extent than a field of view, in FIG. 10, depicted is a cylindrical field of view 50 radially centered on a z-axis or rotation axis 52, and having an axial extent defined by two endplanes 54 and 56 ' . ' :
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perpendicular to the rotation axis 52. An object 58 to be imaged is of greater axial extent that the field of view 50.
Thus, only that portion of the object 58 lying within the field of view 50 is to be imaged.
In FIG. 10, an x-ray source 60 and a two-dimen-sional detector 62 are scanning the field of view 50. The extreme rays 64 and 66 are required to acquire data over the entire field of view 50 of interest. it can be seen that rays near the ends of the cylindrical field of view 50 pene-10 trate through portions 68 and 70 of the object 58 outside the field of view 50. This overlying material 68 and 70 then corrupts the projections acquired by the area detector 62 which projections, in the reconstruction algorithm, are assumed to contain contributions from the field of view 50 only. A reconstructed image therefore contains contributions from regions outside the field of view, and artifacts result.
One approach to the problem of data corruption due to overlying material is depicted in FIG. 11, which is comparable to FIG. 10 except that the x-ray cone angle is reduced so that data is acquired only over a subset of the cylindrical field of view 50. However, this configuration results in a significant loss of data, since regions 72 and ` 74 just inside the ends of the cylindrical field of view 50 are not sampled by projection data at all. This result exacerbates the missing data problem which is already present in 3D CT image reconstruction as described hereinabove.
It may be noted that approaches intermediate those of FIGS. 10 and 11 are known in the prior art. For example, Feldkamp et al., 1984, above, describe a reconstruction technique which corresponds to a scanning configuration wherein the outer rays of the x-ray cone beam pass through the field of view at the rotation axis.
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P~D-19682 FIGS. 12 and 13 depict a scanning configuration in accordance with the invention. In particular, FIG. 12 is a top view, while FIG. 13 is a side view modified for purposes of illustration by repositioning the x-ray source so as to more clearly depict the vertical offset. In the top view of FIG. 12, the various circular source scanning trajectories are superimposed and lie on a single circle 80. The cylindrical field of view 50 is defined by a radius r, and has an axial extent between the two endplanes 54.
Corresponding to the configuration of FIG. 11, above, an x-ray source S1 scans along a circular scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes 54. Corresponding to the source S1 is a detector D1, which is sized to acquire cone beam projection data from rays passing through the field of view 50, but not from rays outside the field of view.
In accordance with the invention, two further cir-cular source scanning trajectories are defined lying in the endplanes 54 and 56, along which sources S2 and S3 scan.
Detectors D2 and D3 correspond to the source S2 and S3.
Scanning effected by source S2 and its corresponding detector D2 does an excellent job of filling a missing data at the top of the cylindrical field of view 50, while scanning by the source S3 and detector D3 does an excellent job of filling in missing data at the bottom of the cylindrical field of view 50. All of the scans acquire data only over projection paths completely included in the cylindrical field of view 50.
It will be appreciated that each of the detectors D1, D2 and D3 is fixed in position relative to its corre-sponding source S1, S2 and S3. Each of the sources S1, S2and S3 and its corresponding detector D1, D2 and D3 may be viewed as a scan head. Scanning is accomplished in a conven-tional manner by moving the sources along the respective ... . ..
.
.. . .. . .. .
;-.
.
- scanning circles relative to the object an the field of view 50. Since it is rel.ative movement which effects scanning, either the object and with it the field of view 50 can be rotated while the sources and detectors remain stationary, or the object and field of view 50 can remain stationary while the sources and detector move. By way of example, in FIG. 13 a generalized scanning element 82 is connected to the object in order to move the object as required, while the sources and detectors remain stationary.
As may be seen particularly in FIG. 12, in order to reduce interference of X-rays from one source interacting with the detector corresponding to another source, the sources are angularly offset. In the particular configura-tion shown, the angular offset is 120-. Other angular off-sets may be employed, chosen for purposes of sca~ter reduc-tion, mechanical convenience, or other system considerations.
It will be appreciated that the various scans at different locations need not be made simultaneously.
Simultaneous scanning may be required in medical applications to reduce or eliminate motion artifacts, but are less neces-sary in industrial applications where a part to be inspected can be securely fixtured into position. Thus, it will be appreciated that one scan head comprising a single x-ray source and a single detector may be repositioned to effect scanning allowing each of the scanning circles, or a plural-ity of scan heads may be employed. Where only a single scan head ls employed, a preferred scanning element 82 is a two-axis CNC part manipulator, the two axes being a vertical translation axis and a rotation axis.
It will further be appreciated that scanning along various numbers of circular source scanning trajectories can be dofie in accordance with the invention. Scanning along the two circular source scanning trajectorie~ lying in the end-,. ,. , . . .:
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,: , ' "
5~
planes 54 and 56, that is with sources S2 and S3 and corre-sponding detectors D2 and D3, reduces hardware costs and com-plexity, but requires image reconstruction with l~ss avail-able data. Scanning along three trajectories as depicted is particularly attractive, because scan 1 provides exact data on the midplane at the center of the field of view 50, while scans 2 and 3 provide exact data on midplanes at the top and bottom of the object field of view. Scanning along four or more source trajectories (simultaneously) increases hardware costs and complexity, but reduces the missing data even more and, perhaps more importantly, allows selection of the posi-tion of the midplane locations where the reconstruction is exact.
FIG. 14 depicts Radon space filling as is achieved with the illustrated embodiment wherein scanning is along three circular source scanning trajectories. FIG. 14 depicts in cross-section the Radon space region of support 36 corre-sponding to a cylindrical field of view, as in FIG. 9.
Superimposed in FIG. 14 are three available data circles re-spectively defining additional toric volumes 86 and 88 corre-sponding to the scans of sources S2 and S3 along the trajec tories lying within the endplanes 59 and 56. Again, avail-able data and missing data areas are indicated.
In FIG. 14, it may be noted that the Radon space region 36 which must be filled for the cylindrical field of view dips down at the poles, just as do the regions of avail-able data. Thus, the shapes of the available data and the region of support are well matched for a cylindrical field of view.
While the invention is described and claimed herein in terms of acquiring data only from rays passing through the field of view, it will be appreciated that the detectors may, as an incidental matter, acquire data from rays passing .
' ' ".' "'" ' ' ~ RD-19682 through regions outside the field of view. However, this particular data is discarded at some point and not employed for reconstruction. The particular point where the data is discar~ed is arbitrary. Preferably, the area detectors are optimally sized to match the field of view and the source scanning geometry so that no detector area is ~wasted~.
However, in practical systems, it is not always possible to optimally size the area detectors. Accordingly, the termi-nology employed herein with reference to acquiring data only from rays passing through the field of view is intended to be given a reasonable interpretation, and does not preclude incidentally requiring data outside the field of view, which data is subsequently discarded.
While specific embodiments of the invention have been illustrated and described herein, it is realized that modifications and changes will occur to those skilled in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit and scope of the invention.
--19-- :
,. : - : . : . :: ~, . ~
, . . . . . . . .
Claims (12)
1. A scanning and data acquisition method for three-dimensional computerized tomography (CT) imaging of a portion of an object within a cylindrical field of view radi-ally centered on a rotation axis and having an axial extent defined by two endplanes perpendicular to the rotation axis, the object being of greater axial extent than the field of view, said method comprising;
defining at least two circular source scanning tra-jectories centered on the rotation axis and lying respec-tively in the two endplanes; and employing at least one cone beam x-ray source and at least one corresponding two-dimensional array detector positioned with reference to the source and with reference to the field of view to scan the object at a plurality of rela-tive angular positions along the source scanning trajectories to acquire cone beam projection data, while acquiring data only from rays passing through the field of view.
defining at least two circular source scanning tra-jectories centered on the rotation axis and lying respec-tively in the two endplanes; and employing at least one cone beam x-ray source and at least one corresponding two-dimensional array detector positioned with reference to the source and with reference to the field of view to scan the object at a plurality of rela-tive angular positions along the source scanning trajectories to acquire cone beam projection data, while acquiring data only from rays passing through the field of view.
2. A method in accordance with Claim 1, which fur-ther comprises:
defining at last one additional circular source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes; and scanning the object at a plurality of angular posi-tions along the additional source scanning trajectory to acquire cone beam projection data from rays passing through the field of view.
defining at last one additional circular source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes; and scanning the object at a plurality of angular posi-tions along the additional source scanning trajectory to acquire cone beam projection data from rays passing through the field of view.
3. A method in accordance with Claim 1, which com-prises:
providing at least two scan heads corresponding to the two source scanning trajectories, each scan head includ-ing a cone beam x-ray source and a two-dimensional array de-tector positioned with reference to the X-ray source of the particular scan head and the field of view for obtaining cone beam projection data; and employing the two scan heads to simultaneously scan the object along the two source scanning trajectories.
providing at least two scan heads corresponding to the two source scanning trajectories, each scan head includ-ing a cone beam x-ray source and a two-dimensional array de-tector positioned with reference to the X-ray source of the particular scan head and the field of view for obtaining cone beam projection data; and employing the two scan heads to simultaneously scan the object along the two source scanning trajectories.
4. A method in accordance with Claim 2, which com-prises:
providing a separate scan head corresponding to each of the source scanning trajectories, each of the scan heads including a cone beam x-ray source and a two-dimen-sional array detector positioned with reference to the x-ray source of the particular scan head and the field of view for obtaining cone beam projection data; and employing the scan heads to simultaneously scan the object along the source scanning trajectories.
providing a separate scan head corresponding to each of the source scanning trajectories, each of the scan heads including a cone beam x-ray source and a two-dimen-sional array detector positioned with reference to the x-ray source of the particular scan head and the field of view for obtaining cone beam projection data; and employing the scan heads to simultaneously scan the object along the source scanning trajectories.
5. A method in accordance with Claim 2, which com-prises locating the additional source scanning trajectory in a plane where it is desired to obtain exact two-dimensional computerized tomography data.
6. A scanning and data acquisition system for three-dimensional computerized tomography (CT) imaging of a portion of an object within a cylindrical field of view radi-ally centered on a rotation axis and having an axial extent defined by two endplanes perpendicular to the rotation axis, the object being of greater axial extent than the field of view, said system comprising:
at least one cone beam x-ray source;
at least one two-dimensional array detector corre-sponding to said source and positioned with reference to said source and the field of view for obtaining cone beam projec-tion data from rays passing through the field of view; and a scanning element for effecting relative motion between said at least one source and the object, said source moving relative to the object along at least two circular source scanning trajectories centered on the rotation axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays passing through the field of view with said source at a plurality of angular positions on the scanning trajectories.
at least one cone beam x-ray source;
at least one two-dimensional array detector corre-sponding to said source and positioned with reference to said source and the field of view for obtaining cone beam projec-tion data from rays passing through the field of view; and a scanning element for effecting relative motion between said at least one source and the object, said source moving relative to the object along at least two circular source scanning trajectories centered on the rotation axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays passing through the field of view with said source at a plurality of angular positions on the scanning trajectories.
7. A system in accordance with Claim 6, wherein said scanning element effects relative motion between said at least one source and the object along an additional circular source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two endplanes.
8. A scanning and data acquisition system for three-dimensional computerized tomography (CT) imaging of a portion of an object within a cylindrical field of view radi-ally centered on a rotation axis and having an axial extent defined by two endplanes perpendicular to the rotation axis, the object being of greater axial extent than the field of view, said system comprising:
a pair of cone beam x-ray sources;
a pair of two-dimensional array detectors respec-tively corresponding to said sources and positioned with ref-erence to said sources and the field of view for obtaining cone beam projection data from x-rays passing through the field of view; and a scanning element for effecting relative motion between said sources and the object, said sources moving rel-ative to the object along a corresponding pair of circular source scanning trajectories centered on the rotation axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays passing through the field of view with said sources at a plurality of angular po-sitions on the scanning trajectories.
a pair of cone beam x-ray sources;
a pair of two-dimensional array detectors respec-tively corresponding to said sources and positioned with ref-erence to said sources and the field of view for obtaining cone beam projection data from x-rays passing through the field of view; and a scanning element for effecting relative motion between said sources and the object, said sources moving rel-ative to the object along a corresponding pair of circular source scanning trajectories centered on the rotation axis and lying respectively in the two endplanes, so as to acquire cone beam projection data only from rays passing through the field of view with said sources at a plurality of angular po-sitions on the scanning trajectories.
9. A system in accordance with Claim 8, which fur-ther comprises:
at least one additional cone beam x-ray source; and at least one additional two dimensional array detector corresponding to said additional source and posi-tioned with reference to said additional source for obtalning cone beam projection data from rays passing through the field of view; and wherein said scanning element effects relative motion between said additional source and the object, said addi-tional source moving relative to the object along an addi-tional circular source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two end-planes.
at least one additional cone beam x-ray source; and at least one additional two dimensional array detector corresponding to said additional source and posi-tioned with reference to said additional source for obtalning cone beam projection data from rays passing through the field of view; and wherein said scanning element effects relative motion between said additional source and the object, said addi-tional source moving relative to the object along an addi-tional circular source scanning trajectory centered on the rotation axis and lying in a plane intermediate the two end-planes.
10. A system in accordance with Claim 8, wherein said cone beam x-ray sources are angularly offset so aq to reduce interference caused by x-rays from one source inter-acting with the detector corresponding to the other source.
11. A system in accordance with Claim 9, wherein said cone beam x-ray sources are angularly offset so as to reduce interference caused by x-rays from one source inter-acting with the detector correspondins to another source.
12. The invention as defined in any of the preceding claims including any further features of novelty disclosed.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US577,163 | 1990-09-04 | ||
| US07/577,163 US5187659A (en) | 1990-09-04 | 1990-09-04 | Cone beam scanning trajectories for three-dimensional computerized tomography data acquisition where object is larger than the field of view |
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| CA2042154A1 true CA2042154A1 (en) | 1992-03-05 |
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| CA002042154A Abandoned CA2042154A1 (en) | 1990-09-04 | 1991-05-09 | Cone beam scanning trajectories for three-dimensional computerized tomography data acquisition where object is larger than the field of view |
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| EP (1) | EP0500857B1 (en) |
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| CA (1) | CA2042154A1 (en) |
| DE (1) | DE69115248T2 (en) |
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| US5365560A (en) * | 1991-07-29 | 1994-11-15 | General Electric Company | Method and apparatus for acquiring a uniform distribution of radon data sufficiently dense to constitute a complete set for exact image reconstruction of an object irradiated by a cone beam source |
| US5333164A (en) * | 1991-12-11 | 1994-07-26 | General Electric Company | Method and apparatus for acquiring and processing only a necessary volume of radon data consistent with the overall shape of the object for efficient three dimensional image reconstruction |
| US5390226A (en) * | 1992-07-02 | 1995-02-14 | General Electric Company | Method and apparatus for pre-processing cone beam projection data for exact three dimensional computer tomographic image reconstruction of a portion of an object |
| US5278884A (en) * | 1992-12-18 | 1994-01-11 | General Electric Company | Complete 3D CT data acquisition using practical scanning paths on the surface of a sphere |
| US5325296A (en) * | 1992-12-18 | 1994-06-28 | General Electric Company | Step size in complete data scanning path for three dimensional computerized tomography |
| US5390112A (en) * | 1993-10-04 | 1995-02-14 | General Electric Company | Three-dimensional computerized tomography scanning method and system for imaging large objects with smaller area detectors |
| US5390111A (en) * | 1993-11-12 | 1995-02-14 | General Electric Company | Method and system for processing cone beam data for reconstructing free of boundary-induced artifacts a three dimensional computerized tomography image |
| US5463666A (en) * | 1993-11-12 | 1995-10-31 | General Electric Company | Helical and circle scan region of interest computerized tomography |
| US5406479A (en) * | 1993-12-20 | 1995-04-11 | Imatron, Inc. | Method for rebinning and for correcting cone beam error in a fan beam computed tomographic scanner system |
| US5740224A (en) * | 1994-09-27 | 1998-04-14 | University Of Delaware | Cone beam synthetic arrays in three-dimensional computerized tomography |
| US5504792A (en) * | 1994-12-27 | 1996-04-02 | General Electric Company | Method and system for masking cone beam projection data generated from either a region of interest helical scan or a helical scan |
| US5559335A (en) * | 1994-12-28 | 1996-09-24 | The University Of Utah | Rotating and warping projector/backprojector for converging-beam geometries |
| US5559846A (en) * | 1995-09-22 | 1996-09-24 | General Electric Company | Technique for improving processor efficiency in CT imaging |
| US6084936A (en) * | 1998-07-10 | 2000-07-04 | General Electric Company | Almost-everywhere extrapolation from cone-beam data |
| DE10035138A1 (en) * | 2000-07-19 | 2002-01-31 | Philips Corp Intellectual Pty | Computer tomography method with conical radiation of an object |
| ATE376389T1 (en) * | 2002-02-15 | 2007-11-15 | Breakaway Imaging Llc | GANTRY RING WITH REMOVABLE SEGMENT FOR MULTI-DIMENSIONAL X-RAY IMAGING |
| JP2005519688A (en) * | 2002-03-13 | 2005-07-07 | ブレークアウェイ・イメージング・エルエルシー | Pseudo simultaneous multiplanar X-ray imaging system and method |
| AU2003224711A1 (en) * | 2002-03-19 | 2003-10-08 | Breakaway Imaging, Llc | Computer tomograph with a detector following the movement of a pivotable x-ray source |
| US7001045B2 (en) * | 2002-06-11 | 2006-02-21 | Breakaway Imaging, Llc | Cantilevered gantry apparatus for x-ray imaging |
| US6597756B1 (en) * | 2002-06-19 | 2003-07-22 | Ge Medical Systems Global Technology Company, Llc | Methods and apparatus for multi-slice image reconstruction |
| US7106825B2 (en) | 2002-08-21 | 2006-09-12 | Breakaway Imaging, Llc | Apparatus and method for reconstruction of volumetric images in a divergent scanning computed tomography system |
| ATE471110T1 (en) * | 2002-08-21 | 2010-07-15 | Breakaway Imaging Llc | SCAFFOLD POSITIONING DEVICE FOR X-RAY EQUIPMENT |
| CN100492411C (en) * | 2003-02-20 | 2009-05-27 | 皇家飞利浦电子股份有限公司 | Asymmetric cone beam |
| JP2005006772A (en) * | 2003-06-17 | 2005-01-13 | Ge Medical Systems Global Technology Co Llc | X-ray diagnostic equipment and ct image forming method |
| US6901132B2 (en) * | 2003-06-26 | 2005-05-31 | General Electric Company | System and method for scanning an object in tomosynthesis applications |
| US7403587B2 (en) * | 2003-09-05 | 2008-07-22 | Koninklijke Philips Electronics N.V. | Computer tomography method using a cone-shaped bundle of rays |
| US7142633B2 (en) * | 2004-03-31 | 2006-11-28 | General Electric Company | Enhanced X-ray imaging system and method |
| US7310407B2 (en) * | 2004-09-03 | 2007-12-18 | Juni Jack E | Nuclear medical imaging device |
| US7418076B2 (en) * | 2005-11-16 | 2008-08-26 | General Electric Company | System and method for cross table tomosynthesis imaging for trauma applications |
| US7460636B2 (en) * | 2006-10-26 | 2008-12-02 | Moshe Ein-Gal | CT scanning system with interlapping beams |
| WO2008122970A1 (en) * | 2007-04-10 | 2008-10-16 | Arineta Ltd. | X-ray tube plurality of targets and corresponding number of electron beam gates |
| EP2083695B1 (en) * | 2007-04-10 | 2013-01-09 | Arineta LTD. | Cone-beam ct |
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| JP7273272B2 (en) * | 2018-05-28 | 2023-05-15 | 国立研究開発法人理化学研究所 | Acquisition method, acquisition device, and control program for tomographic image data by angular offset |
| CN112964738B (en) * | 2021-01-29 | 2022-11-22 | 山东大学 | Industrial CT rapid scanning system and method |
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| DE2726635C3 (en) * | 1977-06-14 | 1981-05-27 | Philips Patentverwaltung Gmbh, 2000 Hamburg | Tomographic device for determining the absorption of radiation in a three-dimensional examination area |
| US4196352A (en) * | 1978-04-28 | 1980-04-01 | General Electric Company | Multiple purpose high speed tomographic x-ray scanner |
| FR2509053A1 (en) * | 1981-07-02 | 1983-01-07 | Inst Francais Du Petrole | DEVICE FOR DETECTING WATER INTAKE WITHIN A SEISMIC FLUTE |
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- 1991-05-09 CA CA002042154A patent/CA2042154A1/en not_active Abandoned
- 1991-08-29 WO PCT/US1991/006199 patent/WO1992003970A1/en active IP Right Grant
- 1991-08-29 EP EP91915438A patent/EP0500857B1/en not_active Expired - Lifetime
- 1991-08-29 DE DE69115248T patent/DE69115248T2/en not_active Expired - Fee Related
- 1991-08-29 JP JP3514561A patent/JPH04505575A/en active Pending
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| EP0500857A1 (en) | 1992-09-02 |
| WO1992003970A1 (en) | 1992-03-19 |
| US5187659A (en) | 1993-02-16 |
| DE69115248D1 (en) | 1996-01-18 |
| JPH04505575A (en) | 1992-10-01 |
| EP0500857B1 (en) | 1995-12-06 |
| DE69115248T2 (en) | 1996-08-22 |
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