The present invention relates to an image reconstructing method and an X-ray CT (Computed Tomography) apparatus, and particularly to a method of reconstructing an image on the basis of projection data obtained by a helical scan with a tilted scan surface, using a multi-row detector, and an X-ray CT apparatus therefor.
In an X-ray CT apparatus, a helical scan with a scan surface tilted is conventionally effective as a method for imaging a depressed bareface of a subject in avoidance of exposure of its crystalline lens to radiation. When projection data are collected by the helical scan with the tilted scan surface through the use of a multi-row detector, and an image is reconstructed based on it, a tilt correction is effected on the projection data and image reconstruction is carried out using the tilt-corrected projection data (refer to, for example, the following patent document 1).
[Patent Document 1] Japanese Unexamined Patent Publication No. 2003-61948 (7th to 8th pages and FIGS. 6 through 14).
The more the number of sequences of a multi-row detector increases, the more the X ray becomes pronounced in the property of a cone beam. Therefore, a contradiction between projection data related to an image reconstruction area cannot be ignored. Thus, it is not possible to prevent archfacts from occurring in a reconstructed image under the utilization of a tilt correction alone.
Therefore, an object of the present invention is to realize an image reconstructing method which obtains an image good in quality where a helical scan with a scan surface being tilted is performed using a cone beam, and an X-ray CT apparatus therefor.
According to a first aspect, the present invention provides an image reconstructing method comprising the steps of, upon reconstructing an image using a multi-row detector having a plurality of detector sequences and on the basis of projection data D0 collected by a helical scan with a scan surface being tilted: effecting a tilt correcting process for correcting variations every views, in positions of respective channels of the detector sequences with respect to a linear travel axis due to the inclination of the scan surface, on the projection data D0; then projecting respective pixels in an X-ray penetration direction along lines parallel to an X axis or a Y axis on a reconstruction plane (XY plane) to determine the corresponding projection data D0 and defining the same as backprojected pixel data D2 of respective pixels constituting the reconstruction plane; and adding the backprojected pixel data D2 of all views used in image reconstruction in association with the pixels to determine backprojected data D3.
According to a second aspect, the present invention provides an image reconstructing method wherein the projection data D0 are fan-para converted from projection data D0f corresponding to collected fan data to projection data D0p corresponding to parallel data in advance and are based on the projection data D0p corresponding to the parallel data.
According to a third aspect, the present invention provides an image reconstructing method comprising the steps of, upon reconstructing an image using a multi-row detector having a plurality of detector sequences and on the basis of projection data D0 collected by a helical scan with a scan surface being tilted: effecting a tilt correcting process for correcting variations every views, in positions of respective channels of the detector sequences with respect to a linear travel axis due to the inclination of the scan surface, on the projection data D0; determining data D1 plane-projected onto the plane of projection on the basis of the tilt-corrected projection data D0; then projecting, in an X-ray penetration direction, the data D1 plane-projected on respective pixels constituting a plurality of lines which are placed on a reconstruction area with plural pixel intervals defined thereamong and extend in the direction parallel to the projection plane to thereby determine backprojected pixel data D2 of the respective pixels constituting the lines on the reconstruction area; and interpolating among the plurality of lines to determine backprojected pixel data D2 of respective pixels among the lines on the reconstruction area; and adding the backprojected pixel data D2 of all views employed in image reconstruction in association with the pixels to determine backprojected data D3.
According to a fourth aspect, the present invention provides an image reconstructing method comprising the steps of, upon reconstructing an image using a multi-row detector having a plurality of detector sequences and on the basis of projection data D0 collected by a helical scan with a scan surface being tilted: effecting a tilt correcting process for correcting variations every views, in positions of respective channels of the detector sequences with respect to a linear travel axis due to the inclination of the scan surface, on the projection data D0; determining data D1 plane-projected onto lines on a projection plane, corresponding to a plurality of lines which are placed on a reconstruction area with plural pixel intervals defined thereamong and extend in the direction parallel to the projection plane, on the basis of the tilt-corrected projection data D0; determining backprojected pixel data D2 of respective pixels on the reconstruction area on the basis of the plane-projected data D1 located on the lines on the projection plane; and adding the backprojected pixel data D2 of all views used in image reconstruction in association with the pixels to determine backprojected data D3.
According to a fifth aspect, the present invention provide an image reconstructing method wherein in the image reconstructing method having the above configuration, the number of the lines ranges from 1/64 to ½ of the number of the pixels in the reconstruction area as viewed in the direction orthogonal to the lines.
According to a sixth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, when the direction orthogonal to a rotating plane of an X-ray tube or the multi-row detector is defined as a z direction, the direction of a center axis of an X-ray beam at view=0° is defined as a y direction, and the direction orthogonal to the z direction and the y direction is defined as an x direction, an xz plane passing through the center of rotation is configured as the projection plane in −45°≦view<45°0 or a view angular range containing even a periphery with this view as a principal part, and 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part, and a yz plane passing through the center of rotation is configured as the projection plane in 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part, and 225≦view<315° or a view angular range containing even a periphery with this view as a principal part.
According to a seventh aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, one plane-projected data D1 is determined from the plurality of projection data D0 by an interpolation/extrapolation process.
According to an eighth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, addresses and interpolation/extrapolation factors for the plurality of projection data D0 for determining one plane-projected data D1 are tabulated.
According to a ninth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, one plane-projected data D1 is determined from the plurality of projection data D0 by an interpolation/extrapolation process, addresses and interpolation/extrapolation factors for the plurality of projection data D0 for determining one plane-projected data D1 are arranged in table form in any one of −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part, 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part, 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part, and 225°≦view<315° or a view angular range containing even a periphery with this view as a principal part, and the table is utilized in other view angular ranges.
According to a tenth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, the interpolation/extrapolation process includes a 0-order interpolation/extrapolation process or a primary interpolation/extrapolation process.
According to an eleventh aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, one backprojected pixel data D2 is determined by a weight adding process of the plurality of plane-projected data D1.
According to a twelfth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, the weight of the weight adding process is determined according to a distance from an X-ray focal point to each plane-projected data D1.
According to a thirteenth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, the weight of the weight adding process is determined according to a distance from the X-ray focal point to each of the pixels in the reconstruction area.
According to a fourteenth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, the weight of the weight adding process is common to the respective pixels lying in the reconstruction area and the pixels lying on the straight lines parallel to the projection plane.
According to a fifteenth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, a start address, a sampling pitch and the number of samplings are determined and the plane-projected data D1 are sampled to select the plane-projected data D1 for effecting the weight adding process on the respective pixels lying in the reconstruction area and the pixels lying on the straight lines parallel to the projection plane.
According to a sixteenth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, the weight of the weight adding process, the start address, the sampling pitch and the number of the samplings are determined in advance and tabulated.
According to a seventeenth aspect, the present invention provides an image reconstructing method wherein in the image reconstructing method having the above configuration, a result obtained by multiplying backprojected pixel data D2 of a given view and backprojected pixel data D2 of an opposite view by weighting factors ωa and ωb (where ωa+ωb=1) corresponding to angles formed by the straight lines connecting the respective pixels of the reconstruction area at both views and the X-ray focal point and the plane containing the reconstruction area and by adding the same together is set as backprojected pixel data D2 of a given view.
According to an eighteenth aspect, the present invention provides an X-ray CT apparatus comprising an X-ray tube; a multi-row detector opposite to the X-ray tube and having a plurality of detector sequences; linear movement control means for relatively moving the X-ray tube and the multi-row detector linearly with a subject along a linear travel axis; rotation control means for rotating at least one of the X-ray tube and the multi-row detector about a rotational axis; tilt control means for tilting an angle of a scan surface formed by the rotation with respect to the linear travel axis to an angular slope other than 90°; scan control means for collecting projection data D0, using the multi-row detector and by a helical scan with a scan surface being tilted; and image reconstructing means for reconstructing an image, based on the projection data D0, wherein the image reconstructing means includes tilt correcting means for effecting a tilt correcting process for correcting variations every views, in positions of respective channels of the detector sequences with respect to the linear travel axis due to the inclination of the scan surface, on the projection data D0, backprojected pixel data calculating means for then projecting respective pixels in an X-ray penetration direction along lines parallel to an X axis or a Y axis on a reconstruction plane (XY plane) to determine the corresponding projection data D0 and thereby determining backprojected pixel data D2 of respective pixels constituting the reconstruction plane; and backprojected data calculating means for adding the backprojected pixel data D2 of all views used in image reconstruction in association with the pixels to determine backprojected data D3.
According to a nineteenth aspect, the present invention provides an X-ray CT apparatus further comprising fan-para converting means for determining projection data D0p corresponding to parallel data from projection data D0f corresponding to fan data, wherein in the X-ray CT apparatus having the above configuration, the scan control means collects the projection data DOf corresponding to the fan data, and the tilt correcting means effects a tilt correcting process on the projection data D0p corresponding to the parallel data.
According to a twentieth aspect, the present invention provides an X-ray CT apparatus comprising an X-ray tube; a multi-row detector opposite to the X-ray tube and having a plurality of detector sequences; linear movement control means for relatively moving the X-ray tube and the multi-row detector linearly with a subject along a linear travel axis; rotation control means for rotating at least one of the X-ray tube and the multi-row detector about a rotational axis; tilt control means for tilting an angle of a scan surface formed by the rotation with respect to the linear travel axis to an angular slope other than 90°; scan control means for collecting projection data D0, using the multi-row detector and by a helical scan with a scan surface being tilted; and image reconstructing means for reconstructing an image, based on the projection data D0, wherein the image reconstructing means includes tilt correcting means for effecting a tilt correcting process for correcting variations every views, in positions of respective channels of the detector sequences with respect to the linear travel axis due to the inclination of the scan surface, on the projection data D0, plane-projected data calculating means for determining data D0 plane-projected onto the plane of projection on the basis of the tilt-corrected projection data D0, backprojected pixel data calculating means for projecting, in an X-ray penetration direction, the plane-projected data D1 onto respective pixels constituting a plurality of lines which are placed on a reconstruction area with plural pixel intervals defined thereamong and extend in the direction parallel to the projection plane to thereby determine backprojected pixel data D2 of the respective pixels constituting the lines on the reconstruction area, and interpolating among the plurality of lines to determine backprojected pixel data D2 of respective pixels among the lines on the reconstruction area, and backprojected data calculating means for adding the backprojected pixel data D2 of all views employed in image reconstruction in association with the pixels to determine backprojected data D3.
According to a twenty-first aspect, the present invention provides an X-ray CT apparatus comprising an X-ray tube; a multi-row detector opposite to the X-ray tube and having a plurality of detector sequences; linear movement control means for relatively moving the X-ray tube and the multi-row detector linearly with a subject along a linear travel axis; rotation control means for rotating at least one of the X-ray tube and the multi-row detector about a rotational axis; tilt control means for tilting an angle of a scan surface formed by the rotation with respect to the linear travel axis to an angular slope other than 90°; scan control means for collecting projection data D0, using the multi-row detector and by a helical scan with a scan surface being tilted; and image reconstructing means for reconstructing an image, based on the projection data D0, wherein the image reconstructing means includes tilt correcting means for effecting a tilt correcting process for correcting variations every views, in positions of respective channels of the detector sequences with respect to the linear travel axis due to the inclination of the scan surface, on the projection data D0, plane-projected data calculating means for determining data D1 plane-projected onto lines on a projection plane, corresponding to a plurality of lines which are placed on a reconstruction area with plural pixel intervals defined thereamong and extend in the direction parallel to the projection plane, on the basis of the tilt-corrected projection data D0, backprojected pixel data calculating means for determining backprojected pixel data D2 of respective pixels on the reconstruction area on the basis of the plane-projected data D1, and backprojected data calculating means for adding the backprojected pixel data D2 of all views used in image reconstruction in association with the pixels to determine backprojected data D3.
According to a twenty-second aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the number of the lines ranges from 1/64 to ½ of the number of the pixels in the reconstruction area as viewed in the direction orthogonal to the lines.
According to a twenty-third aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, when the direction orthogonal to a rotating plane of the X-ray tube or the multi-row detector is defined as a z direction, the direction of a center axis of an X-ray beam at view=0° is defined as a y direction, and the direction orthogonal to the z direction and the y direction is defined as an x direction, the plane-projected data calculating means sets an xz plane passing through the center of rotation as the projection plane in −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part, and 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part, and sets a yz plane passing through the center of rotation as the projection plane in 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part, and 225°≦view<315° or a view angular range containing even a periphery with this view as a principal part.
According to a twenty-fourth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the plane-projected data calculating means determines one plane-projected data D1 from the plurality of projection data D0 by an interpolation/extrapolation process.
According to a twenty-fifth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the plane-projected data calculating means uses a table to which addresses and interpolation/extrapolation factors for the plurality of projection data D0 for determining one plane-projected data D1 are set.
According to a twenty-sixth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the plane-projected data calculating means determines one plane-projected data D1 from the plurality of projection data D0 by an interpolation/extrapolation process, tabulates addresses and interpolation/extrapolation factors for the plurality of projection data D0 for determining one plane-projected data D1 in any one of −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part, 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part, 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part, and 225°≦view<315° or a view angular range containing even a periphery with this view as a principal part, and makes use of the resultant table in other view angular ranges.
According to a twenty-seventh aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the interpolation/extrapolation process includes a 0-order interpolation/extrapolation process or a primary interpolation/extrapolation process.
According to a twenty-eighth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, one backprojected pixel data D2 is determined by a weight adding process of the plurality of plane-projected data D1.
According to a twenty-ninth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the weight of the weight adding process is determined according to a distance from each of the pixels in the reconstruction area to each plane-projected data D1.
According to a thirtieth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the weight of the weight adding process is determined according to a distance from each of the pixels in the reconstruction area to the X-ray focal point.
According to a thirty-first aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the weight of the weight adding process is common to the respective pixels lying in the reconstruction area and the pixels lying on the straight lines parallel to the projection plane.
According to a thirty-second aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, a start address, a sampling pitch and the number of samplings are determined, and the plane-projected data D1 are sampled to continuously select the plane-projected data D1 for effecting the weight adding process on the respective pixels lying in the reconstruction area and the pixels lying on the straight lines parallel to the projection plane.
According to a thirty-third aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the weight of the weight adding process, the start address, the sampling pitch and the number of the samplings are determined in advance and tabulated.
According to a thirty-fourth aspect, the present invention provides an X-ray CT apparatus wherein in the X-ray CT apparatus having the above configuration, the weight of the weight adding process is determined according to an angle formed by a straight line connecting each pixel of a reconstruction area at a given view and an X-ray focal point and a plane containing the reconstruction area, and an angle formed by a straight line connecting each pixel of the reconstruction area at an opposite view and an X-ray focal point and a plane containing the reconstruction area.
In the image reconstructing method according to the first aspect, a tilt correcting process for correcting variations every views, in positions of respective channels of detector sequences with respect to a linear travel axis due to the inclination of a scan surface is effected on the projection data D0. Then, respective pixels are projected in an X-ray penetration direction along lines parallel to an X axis or a Y axis on a reconstruction plane (XY plane) to determine the corresponding projection data D0, thereby determining backprojected pixel data D2 of respective pixels constituting the reconstruction plane. Thus, reconstruction can be performed at high speed using projection data properly corresponding to an X-ray beam transmitted through a reconstruction area.
In the image reconstructing method according to the second aspect, projection data D0p corresponding to parallel data are determined from projection data D0f corresponding to fan data without directly determining plane-projected data D1 from the projection data D0f corresponding to the fan data, and the plane-projected data D1 are determined from the projection data D0p corresponding to the parallel data.
When the plane-projected data D1 are determined directly from the projection data D0f corresponding to the fan data here, it was necessary to take into consideration the distance from an X-ray focal point to a channel corresponding to each projection data D0f and the distance from the X-ray focal point to a projection position on a projection plane. That is, there was a need to multiply the data by distance factors. Since, however, there is no need to perform multiplication of the distance factors where the plane-projected data D1 are determined from the projection data D0p corresponding to the parallel data, computing can be simplified. It was not possible to make a contrivance to handle the opposite view in the case of the projection data D0f corresponding to the fan data. However, the projection data D0p corresponding to the parallel data make it easy to handle the opposite view. Therefore, the utilization of the opposite view shifted by a−¼ channel and the original view shifted by a+¼ channel in combination makes it possible to enhance resolution in a channel direction, reduce the number of views at backprojection to ½ and lessen a calculated amount.
In the image reconstructing method according to the third aspect, plane-projected data D1 are determined from tilt-corrected projection data D0, and the plane-projected data D1 are projected onto a reconstruction area in an X-ray penetration direction to determine backprojected pixel data D2. Thus, reconstruction can be done at high speed using projection data properly associated with an X-ray beam transmitted through the reconstruction area.
Incidentally, while the reconstruction area is of a plane, a multi-row detector is located in an arcuate spatial position. When data located in the arcuate form are directly projected onto a reconstruction area corresponding to lattice coordinates, a coordinate transformation process becomes complicated and hence a calculated amount is needed. Further, when this processing is done over all pixels of the reconstruction area, an enormous amount of calculation is required. That is, the direct determination of the projection data D0 from the backprojected pixel data D2 makes processing complicated and also lengthens a processing time interval.
In contrast, in the image reconstructing method according to the third aspect, plane-projected data D1 are determined from projection data D0 without directly determining backprojected pixel data D2 from the projection data D0, and the backprojected pixel data D2 are determined from the plane-projected data D1. When data located in the plane is projected onto a reconstruction area corresponding to lattice coordinates here, the processing is done by primary or linear transformation (affine transformation) capable of realizing the processing by data sampling with an equi-sampling pitch. Thus, the simplification and speeding-up of the processing are enabled looking overall. Incidentally, the plane-projected data D1 may preferably be set to intervals sufficiently close in a channel direction of at least a detector.
Further, when backprojected pixel data D2 are determined from plane-projected data D1, only backprojected pixel data D2 on respective pixels constituting lines which are placed on a reconstruction area with plural pixel intervals defined thereamong and extend in the direction parallel to the plane of projection are determined, and an interpolation process is applied among the lines arranged at plural pixel intervals. Therefore, a processing time interval can be shortened as compared with the case in which the backprojected pixel data D2 on all the pixels constituting the reconstruction area are determined from the plane-projected data D1. Incidentally, if the number of lines at the plural pixel intervals is properly selected, then deterioration in image quality can be suppressed to a negligible degree.
In the image reconstructing method according to the fourth aspect, plane-projected data D1 are determined from tilt-corrected projection data D0, and the plane-projected data D1 are projected on a reconstruction area in an X-ray penetration direction to determine backprojected pixel data D2. Thus, reconstruction can be carried out at high speed using projection data properly corresponding to an X-ray beam transmitted through the reconstruction area.
Incidentally, while the reconstruction area is of a plane, a multi-row detector is located in an arcuate spatial position. When data located in the arcuate form are directly projected on a reconstruction area corresponding to lattice coordinates, a coordinate transformation process becomes complicated and hence a calculated amount is needed. Further, when this processing is done over all pixels of the reconstruction area, an enormous amount of calculation is required. That is, the direct determination of the projection data D0 from the backprojected pixel data D2 makes processing complicated and also lengthens a processing time interval.
In contrast, in the image reconstructing method according to the fourth aspect, plane-projected data D1 are determined from projection data D0 without directly determining backprojected pixel data D2 from the projection data D0, and the backprojected pixel data D2 are determined from the plane-projected data D1. When data located in the plane is projected onto a reconstruction area corresponding to lattice coordinates here, the processing is done by primary or linear transformation (affine transformation) capable of realizing the processing by data sampling with an equi-sampling pitch. Thus, the simplification and speeding-up of the processing are enabled looking overall. Incidentally, the plane-projected data D1 may preferably be set to intervals sufficiently close in a channel direction of at least a detector.
Further, when the plane-projected data D1 are determined, unnecessary computing can be omitted upon determining data D1 plane-projected on lines on the plane of projection, corresponding to a plurality of lines which are placed on a reconstruction area with plural pixel intervals defined thereamong and extend in the direction parallel to the plane of projection. Therefore, a processing time interval can be shortened. Incidentally, if the number of lines placed at the plural pixel intervals is selected properly, then deterioration in the image quality can be suppressed to a negligible degree.
In the image reconstructing method according to the fifth aspect, the number of the lines at the plural pixel intervals is set so as to range from 1/64 to ½ of the number of pixels of a reconstruction area as viewed in the direction normal to each line, so that the shortening effect of processing time and deterioration in image quality can be suitably kept in balance.
In the image reconstructing method according to the sixth aspect, the angle which an xz plane or a yz plane corresponding to the plane of projection forms with a projection-directed line is not smaller than about 45°. Therefore, a reduction in the accuracy of calculation can be suppressed to within an allowable range.
Incidentally, view=−45° and view=315° are actually equal and the same view although they are described in different expressions for convenience of expression in the present specification. When data are projected onto the plane of projection, the accuracy becomes high as the angle formed by its projection-directed line and the plane of projection approaches 90°, whereas the accuracy becomes low as the angle approaches 0°.
In the image reconstructing method according to the seventh aspect, one plane-projected data D1 is determined from a plurality of projection data D0 by an interpolation process. Therefore, the density of the plane-projected data D1 can be made high sufficiently as compared with a pixel density of a reconstruction area. Thus, the process of projecting the plane-projected data D1 onto the corresponding reconstruction area as seen in an X-ray penetration direction to determine backprojected pixel data D2 is intended for the most proximity affine transformation process, i.e., sampling process alone, and hence the interpolation process can be eliminated, thereby making it possible to achieve simplification and speeding up of processing. However, the interpolation process may be done if desired.
In the image reconstructing method according to the eighth aspect, addresses and interpolation/extrapolation factors for a plurality of projection data D0 are calculated in advance and set to a table, so that the overhead can be eliminated. That is, processing can be speeded up by tabulation. Incidentally, the addresses and interpolation/extrapolation factors for the plurality of projection data D0 for determining one plane-projected data D1 may be calculated every attempt to determine one plane-projected data D1. However, the time required for its calculation results in overhead.
When a geometrical relationship among an X-ray tube, a detector and a projection axis in 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part is rotated by 180° about the center of rotation where an xz plane passing through the center of rotation is configured as the plane of projection, it coincides with a geometrical relationship among the X-ray tube, the detector and the projection axis in −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part. Thus, addresses and interpolation/extrapolation factors for projection data D0 for determining one plane-projected data D1 can be shared between the two.
When a geometrical relationship among the X-ray tube, the detector and the projection axis in 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part is rotated by −90° about the center of rotation where a yz plane passing through the center of rotation is configured as the plane of projection, it coincides with a geometrical relationship among the X-ray tube, the detector and the projection axis in −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part where the xz plane passing through the center of rotation is set as the plane of projection. Thus, addresses and interpolation/extrapolation factors for projection data D0 for determining one plane-projected data D1 can be shared between the two.
When a geometrical relationship among the X-ray tube, detector and projection axis in 225°≦view<315° or a view angular range containing even a periphery with this view as a principal part is rotated by 90° about the center of rotation where the yz plane passing through the center of rotation is configured as the plane of projection, it coincides with a geometrical relationship among the X-ray tube, the detector and the projection axis in −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part where the xz plane passing through the center of rotation is set as the plane of projection. Thus, addresses and interpolation/extrapolation factors for projection data D0 for determining one plane-projected data D1 can be shared between the two.
In the image reconstructing method according to the ninth aspect, a table used in any one of −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part, 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part, 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part, and 225°≦view<315° or a view angular range containing even a periphery with this view as a principal part can be shared even in other view angular ranges. It is therefore possible to reduce memory capacity necessary for the table.
In the image reconstructing method according to the tenth aspect, an interpolation/extrapolation process can be simply handled because a 0-order interpolation/extrapolation process (i.e., adoption of proximity data) and a primary interpolation/extrapolation process (i.e., interpolation/extrapolation using two proximity data) are included.
In the image reconstructing method according to the eleventh aspect, the weight addition of plural data of the same view or opposite view near a reconstruction area is applicable. In the image reconstructing method according to the twelfth aspect, backprojected pixel data D2 can be properly determined. This is because data D1 in which the distance from an X-ray focal point to plane-projected data D1 is short, are generally considered to include information about respective pixels more properly as compared with data D1 long in distance.
In the image reconstructing method according to the thirteenth aspect, backprojected pixel data D2 can be determined more properly. This is because the distance from an X-ray focal point to a detector is constant and hence data D1 at the time that the distance from each of pixels of a reconstruction area to the X-ray focal point is long, are considered to be near the detector in distance and to include information about respective pixels more properly as compared with data D1 at the time that the distance is short.
In the image reconstructing method according to the fourteenth aspect, the weight is used in common and processing can be simplified. The weight of a weight adding process can be defined as the ratio between the distance from an X-ray focal point to plane-projected data D1 and the distance from the X-ray focal point to each of pixels of a reconstruction area. In this case, the ratio becomes identical in value between each of the pixels of the reconstruction area and each of pixels located on straight lines parallel to the plane of projection.
In the image reconstructing method according to the fifteenth aspect, plane-projected data D1 for determining backprojected pixel data D2 can be selected by a simple process. This is because plane-projected data D1 for determining backprojected pixel data D2 about respective pixels of a reconstruction area and pixels located on straight lines parallel to the plane of projection exist on the lines on the plane of projection. Thus, if a start address, a sampling pitch and the number of samplings are fixed, then the data can be selected by simple processing.
In the image reconstructing method according to the sixteenth aspect, processing can be speeded up by tabulation. In the image reconstructing method according to the seventeenth aspect, backprojected pixel data D2 can be determined more properly. This is because information about respective pixels are generally considered to be contained more properly as the angle which a straight line connecting each pixel of a reconstruction area and an X-ray focal point forms with a plane containing the reconstruction area, approaches 90°.
The X-ray CT apparatus according to the eighteenth aspect is capable of suitably implementing the image reconstructing method according to the first aspect. The X-ray CT apparatus according to the nineteenth aspect is capable of suitably implementing the image reconstructing method according to the second aspect. The X-ray CT apparatus according to the twentieth aspect is capable of suitably implementing the image reconstructing method according to the third aspect. The X-ray CT apparatus according to the twenty-first aspect is capable of suitably implementing the image reconstructing method according to the fourth aspect. The X-ray CT apparatus according to the twenty-second aspect is capable of suitably implementing the image reconstructing method according to the fifth aspect. The X-ray CT apparatus according to the twenty-third aspect is capable of suitably implementing the image reconstructing method according to the sixth aspect. The X-ray CT apparatus according to the twenty-fourth aspect is capable of suitably implementing the image reconstructing method according to the seventh aspect.
The X-ray CT apparatus according to the twenty-fifth aspect is capable of suitably implementing the image reconstructing method according to the eighth aspect. The X-ray CT apparatus according to the twenty-sixth aspect is capable of suitably implementing the image reconstructing method according to the ninth aspect. The X-ray CT apparatus according to the twenty-seventh aspect is capable of suitably implementing the image reconstructing method according to the tenth aspect. The X-ray CT apparatus according to the twenty-eighth aspect is capable of suitably implementing the image reconstructing method according to the eleventh aspect. The X-ray CT apparatus according to the twenty-ninth aspect is capable of suitably implementing the image reconstructing method according to the twelfth aspect.
The X-ray CT apparatus according to the thirtieth aspect is capable of suitably implementing the image reconstructing method according to the thirteenth aspect. The X-ray CT apparatus according to the thirty-first aspect is capable of suitably implementing the image reconstructing method according to the fourteenth aspect. The X-ray CT apparatus according to the thirty-second aspect is capable of suitably implementing the image reconstructing method according to the fifteenth aspect. The X-ray CT apparatus according to the thirty-third aspect is capable of suitably implementing the image reconstructing method according to the sixteenth aspect. The X-ray CT apparatus according to the thirty-fourth aspect is capable of suitably implementing the image reconstructing method according to the seventeenth aspect.
Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings.
Best modes for carrying out the invention will be explained below with reference to the accompanying drawings. Incidentally, the present invention is not limited to the best modes for carrying out the invention. A block diagram of an X-ray CT apparatus is shown in
As shown in
The table device 8 includes a cradle 8c which places a subject thereon and a transfer controller 8a for moving the cradle 8c in a z-axis direction and a y-axis direction. Incidentally, a y axis is defined as a vertical direction and a z axis is defined as the longitudinal direction of the cradle 8c. An axis orthogonal to the y axis and the z axis is defined as an x axis. A body axis of the subject is placed in the z-axis direction.
The scanning gantry 9 is provided with an X-ray controller 10, an X-ray tube 11, a collimator 12, a multi-row detector 13 having a plurality of detector sequences, a data acquisition unit 14, a rotation controller 15 for rotating the X-ray tube 11 and the multi-row detector 13 or the like about an isocentre ISO, and a tilt controller 16 for making the slope of an angle of a scan surface. The tilt controller 16 controls the slope of the scanning gantry 9.
In Step S1, a pre-treatment (offset correction, logarithmic correction, X-ray dose correction and sensitivity correction) is effected on the projection data D0(view, δ, j, i). In Step S2, a tilt correcting process is performed on the projection data D0(view, δ, j, i). The tilt correcting process will be explained again later.
In Step S3, a filter process is effected on the projection data D0(view, δ, j, i) subjected to the tilt correcting process. That is, a Fourier transform is performed on the projection data, each of which is followed by being multiplied by a filter (reconstruction function) to perform an inverse Fourier transform thereof. In Step S4, a three-dimensional back projecting process according to the present invention is effected on the projection data D0(view, δ, j, i) subjected to the filter process to determine backprojected data D3(x, y). The three-dimensional back projecting process will be explained again later. In Step S5, a post-treatment is effected on the backprojected data D3(x, y) to obtain a CT image.
The tilt correcting process will be explained.
In Step T2, data lying in a range in which data exist over all views as seen in a view direction under a post-movement data array, are cut out. A specific example of the data cutting-out process will be explained later. In Step T3, dummy data is added to the cut-out data to fix up a data range. A specific example of the dummy data adding process will be explained later. In Step T4, the data are converted to data in which channel positions of all views are aligned with one another. A specific example of the data converting process will be explained later.
The specific examples will next be described. Now consider that a helical scan is rotated by substantially 2π over all views (corresponding to one cycle) and linearly moved by a slice width under the rotation of 2π (helical pitch=1), a tilt angle is defined θ and the distance from an intersecting point (isocenter ISO) of a linear travel axis and a rotational axis to a scan surface corresponding to a jth detector sequence is defined as Lj. A view angle at the time that the multi-row detector 13 is located directly below is defined as φ=0, and a view number is defined as pvn=1.
hj(pvn,i)=h(0,i)+j—delt—iso—max·sin{2π(pvn−1)/VWN}
Incidentally, the view angle φ=2π(pvn−1)/VWN
j—delt—iso—max=Lj·tan θ
−1_delt_iso_max·sin{2π(pvn−1)/VWN}
In a post-movement data array shown in
1_delt_iso_max·sin{2π(pvn−1)/VWN}
In a post-movement data array shown in
A data cut-out range is generally expressed in the following manner. That is, when a channel-to-channel distance is defined as DMM and Roundup{ } is defined as a round function, the data cut-out range extends from a (Roundup{Lj·tan θ/DMM}+1)th channel of a pvnth view of a jth detector sequence to an (I-Roundup{Lj·tan θ/DMM}−1)th channel.
When the data are moved in the direction of a small channel number as shown in
delt—iso=delt—iso—max·sin{2π(pvn-1)/VWN}
int—delt—iso=abs{int{delt—iso/DMM}}
ratio=abs{delt—iso/DMM}−int—delt—iso
dest{i−int—delt—iso}=src{i}·(1−ratio)+src{i+1}·ratio
On the other hand, when the data are moved in the direction of a large channel number, the linear interpolating process results in the following equation:
dest{i+int—delt—iso}=src{i}·(1−ratio)+src{i+1}·ratio
The three-dimensional back projecting process will be explained.
In Step R2, backprojected pixel data D2(view, x, y) are obtained from the data D1(view, qt, pt) plane-projected onto the plane of projection. This process will be described later with reference to
In Step R3, views corresponding to 360° are added to the backprojected pixel data D2(view, x, y) in association with pixels, or views corresponding to “180°+fan angle” are added thereto to obtain backprojected data D3(x, y). This process will be explained later with reference to
FIGS. 17(a) and 17(b) show the layout of the X-ray tube 21 and the multi-row detector 24 at view=0° and δ=0°. A plane pp of projection at this time is an xz plane that passes through the center of rotation ISO. The xz plane is inclined to the linear travel axis. The axis of rotation of a scan is placed on the xz plane.
Projection data D0(view=0, δ=0, j, i) obtained at respective channels of the multi-row detector 24 are multiplied by distance coefficients and laid out at positions where the respective channels are plane-projected onto the projection plane pp as viewed in an X-ray penetration direction, followed by interpolating processing in a channel direction to thereby make data densities high sufficiently, whereby plane-projected data D1′(view=0, δ=0, j, pt) are obtained as shown in
Incidentally, when the distance from an X-ray focal point of the X-ray tube 21 to each channel of the multi-row detector 24 is defined as r0, and the distance from the X-ray tube 21 to the position of projection on the projection plane pp is defined as r1, the distance coefficient is given as (r1/r0)2. Z0 shown in
FIGS. 18(a) and 18(b) show the layout of the X-ray tube 21 and the multi-row detector 24 at view=0° and δ=360° (i.e., after one rotation from δ=0°). When projection data D0(view=0, δ=360, j, i) obtained at this time are plane-projected onto the projection plane pp, plane-projected data D1′(view=0, δ=360, j, pt) are obtained as shown in
Next, such plane-projected data D1′(0, 0, j, i), D1′(0, 360, j, i) and D1′(0, 720, j, i) as shown in
As compared with view=0°, the first channel side of the multi-row detector 24 approaches the projection plane pp and the Ith channel side becomes distant from the projection plane pp. Therefore, the plane-projected data D1′(30, 0, j, pt), D1′(30, 360, j, pt) and D1′(30, 720, j, pt) become wide on the first channel side, whereas they become narrow on the Ith channel side. Incidentally, Z30 indicates origin coordinates indicative of a spatial position of plane-projected data D1′(30, 0, 1, 0).
FIGS. 23(a) and 23(b) show the layout of the X-ray tube 21 and the multi-row detector 24 at view=90°. A projection plane pp at this time is a yz plane that passes through the center of rotation ISO. When obtained projection data D0(view=90, δ, j, i) are plane-projected onto the projection plane pp, plane-projected data D1′(view=90, δ, j, pt) are obtained as shown in
Thus, the xz plane that passes through the center of rotation ISO is defined as the projection plane pp in −45°≦view<45° or a view angular range containing even a periphery with this view as a principal part, and 135°≦view<225° or a view angular range containing even a periphery with this view as a principal part. The yz plane that passes through the center of rotation ISO is defined as the projection plane pp in 45°≦view<135° or a view angular range containing even a periphery with this view as a principal part, and 225°≦view<315° or a view angular range containing even a periphery with this view as a principal part.
It is preferable that when the plane-projected data D1′(view, δ, j, pt) are determined from the projection data D0(view, δ, j, i), such a plane-projecting lookup table 31 as shown in
The lookup table 31 shown in
The data D1 are expressed as follows:
D1(view,δj,pt)=k1×D0(view,δ,j,i)+k2×D0(view,δj,i+1).
Incidentally, Δview indicates a step angle (view angle difference between adjacent views) for each view angle. Δview results in “0.36°” in the case of 1000 views in total, for example.
The lookup table 31′ shown in
In the case of a helical scan, interpolation coefficients in a qt direction are also set to lookup tables similar to the lookup tables 31 and 31′. Similar interpolation/extrapolation is effected even in the qt direction. The interpolation in the qt direction is repeated in such rectangular areas Ra as shown in
Even other than the view angular range of −45°≦view<45° (or view angular range containing even the periphery with this view as the principal part) from geometrical similarity, the lookup tables 31 and 31′ in the view angular range of −45°≦view<45° (or view angular range containing even the periphery with this view as the principal part) can be appropriated.
As shown in
Incidentally, when the angle which a straight line connecting the focal point of the X-ray tube 21 and a pixel g(x, y) on a reconstruction area P at view=βa forms with a center axis Bc of an X-ray beam is defined as γ, and its opposite view is defined as view=βb, the following equation is established:
βb=βa+180°−2γ
Next, plane-projected data D1(0, qt_a, pt) corresponding to the coordinates (X0, Z0_a) is determined. Also plane-projected data D1(0, qt_b, pt) corresponding to the coordinates (X0, Z0_b) is determined. When the distance from the X-ray focal point of the X-ray tube 21 at view=0° to the plane-projected data D1(0, qt_a, pt) is set as r0—0a, and the distance from the X-ray focal point of the X-ray tube 21 to the pixel g(x, y) is assumed to be r0—1a, backprojected pixel data D2(0, x, y)_a at view=0° is determined from the following equation:
D2(0,x,y)_a=(r0—0a/r0—1a)2·D1(0,qt—a,pt)
When the distance from the X-ray tube 21 at an opposite view to the plane-projected data D1(0, qt_b, pt) is defined as r0—0b, and the distance from the X-ray tube 21 to the pixel g(x, y) is defined as r0—0b, backprojected pixel data D2(0, x, y)_b of the opposite view is determined from the following equation:
D2(0,x,y)—b=(r0—0/r0—1b)2·D1(0,qt—b,pt)
Next, the backprojected pixel data D2(0, x, y)_a and D2(0, x, y)_b are multiplied by cone beam reconstruction weighting factors ωa and ωb dependent on angles αa and αb shown in
D2(0,x,y)=ωa·D2(0,x,y)—a+ωb·D2(0,x,y)—b
Incidentally, the angle αa indicates an angle which an X ray that passes through the pixel g(x, y) at view=0° forms with a plane containing a reconstruction area P. Also the angle αb indicates an angle which an X ray that passes through the pixel g(x, y) at an opposite view forms with a plane containing a reconstruction area P. Further, the following equation is established:
ωa+ωb=1
Cone angle archfacts can be reduced by multiplying the data by the cone beam reconstruction weighting factors ωa and ωb and adding the same together. As the cone beam reconstruction weighting factors ωa and ωb, for example, ones determined from the following equations can be used.
When max[ ] is defined as a function that takes a large value, and ½ of a fan beam angle is defined as γmax, the following are expressed as follows:
ga=max[0,{(π/2+γ max)−|βa|}]·|tan(αa)|
gb=max[0,{π/2+γ max)−|βb|}]·|tan(αb)|
xa=2·gaq/(gaq+gbq)
xb=2·gbq/(gaq+gbq)
ωa=xa2·(3−2xa)
ωb=xb2·(3−2xb)
Weights R(y)_a=(r0—0a/r0—1a)2, start addresses str_x and str_qt, sampling pitches Δqt and Δpt, and the number of samplings n(y) are calculated and set to the lookup table 32 in advance as conversion computational parameters for determining one backprojected pixel data D2(view, x, y)_a from a y coordinate y (y coordinate of each line) of backprojected pixel data D2 and one plane-projected data D1(view, qt, pt), every view angles views in a view angular range of −45°≦view<45° (or view angular range containing even a periphery with the view as a principal part).
Even other than the view angular range of −45°≦view<45° (or view angular range containing even the periphery with this view as the principal part) from geometrical similarity, the lookup table 32 in the view angular range of −45°≦view<45° (or view angular range containing even the periphery with this view as the principal part) can be used.
Weights R(y)_a about the pixel g(x, y) lying on the lines parallel to the x axis all assumes (r0—1a/r0—0a)2 and become common. Thus, the following equation is represented:
D2(view,x,y)—a=R(y)—×D1(view,str—qt+(x−str—x)Δqt,str—pt+(x−str—x)Δpt)
D3(x,y)=viewΣD2(view,x,y)
According to the X-ray CT apparatus 100 that performs such operation, data D1 plane-projected from projection data D0 are determined, and the plane-projected data D1 are projected onto a reconstruction area in an X-ray penetration direction to determine backprojected pixel data D2. Therefore, it is possible to perform reconstruction using projection data properly corresponding to an X beam transmitted through the reconstruction area. Thus, an image excellent in quality can be obtained. Looking overall, processing can be simplified and speeded up.
Further, when the backprojected pixel data D2 are determined from the plane-projected data D1, only backprojected pixel data D2 on respective pixels constituting lines L0 through L8 are determined and a process for interpolating among the lines is performed. Therefore, a processing time interval can be shortened as compared with the determination of the backprojected pixel data D2 on all pixels constituting the reconstruction area P from the plane-projected data D1.
Another example of the best mode for carrying out the present invention will be explained. As shown in
As shown in
Next, backprojected pixel data D2(view, x, y) are determined using a back projecting lookup table 32′ shown in
Interpolation coefficients km and km+1, weights S(y)=ωa×R(y)_a, a start address str_x, a sampling pitch Apt, and the number of samplings n(y) are calculated and set to the lookup table 32′ in advance as conversion computational parameters for determining one backprojected pixel data D2(view, x, y) from y coordinates y (y coordinates of all lines constituting reconstruction area P) of backprojected pixel data D2, and plane-projected data D1(view, Lm′, pt) and D1(view, Lm+1′, pt) of 2 lines, every view angles views in a view angular range of −45°≦view<45° (or view angular range containing even a periphery with the view as a principal part).
Even other than the view angular range of −45°≦view<45° (or view angular range containing even the periphery with this view as the principal part) from geometrical similarity, the lookup table 32 of the view angular range of −45°≦view<45° (or view angular range containing even the periphery with this view as the principal part) can be used.
As shown in
D2(view,x,y)=S(y)×{km×D1(view,Lm′,(x−str—x)Δpt)+km+1×D1(view,Lm+1′,(x−str—x) Δpt)}
According to this example, since only the plane-projected data D1(view, Lm′, pt) on the lines L0′ through L8′ are determined, a processing time interval can be shortened as compared with the case in which a large quantity of plane-projected data D1(view, qt, pt) are determined.
A further example of the best mode for carrying out the present invention will be explained.
In Step S12, a pre-treatment (offset correction, logarithmic correction, X-ray dose correction and sensitivity correction) is effected on the projection data D0f(view, δ, j, i) corresponding to the fan data. In Step S13, a fan-para converting process is effected on the pre-treated projection data D0f(view, δ, j, i) corresponding to the fan data to determine projection data D0p(view, δ, j, i) corresponding to parallel data. The present fan-para converting process will be described later with reference to
In Step S14, a tilt correcting process is performed. In Step S15, a filter process is effected on the tilt-processed projection data D0p(view, δ, j, i) about the parallel data. That is, a Fourier transform is performed on the projection data, each of which is followed by being multiplied by a filter (reconstruction function) to perform an inverse Fourier transform thereof.
In Step S16, a three-dimensional back projecting process is effected on the projection data D0p(view, δ, j, i) subjected to the filter process to determine backprojected data D3(x, y). The three-dimensional back projecting process will be explained later with reference to
Penetration paths of X rays incident to respective channels corresponding to the projection data D0p(view, δ, j, i) corresponding to the parallel data are parallel in a channel direction as indicated by broken lines in
Referring back to
If the view angles views are different by 180° in the projection data D0p(view, δ, j, i) corresponding to the parallel data, then they are brought to opposite views. Therefore, the projection data become easy to handle (e.g., it is easy to apply view weights of opposite views thereto). In contrast, even if view angles views are different by 180° in the case of the projection data D0f(view, δ, j, i) corresponding to the parallel data, they are not brought to opposite views except for a fan center. Therefore, their handling become complicated.
In Step F3, the projection data D0p(view, δ, i, j) corresponding to the parallel data are arranged according to an interpolation process as shown in
In Step R13, in a manner similar to the description of the above example, views corresponding to 360° are added to backprojected pixel data D2(view, x, y) in association with pixels, or views corresponding to “180°+fan angle” are added thereto to obtain backprojected data D3(x, y).
In the respective examples referred to above, the following selections are enabled.
(1) Although the above example has explained the case in which “the number of lines”/“the number of pixels in the reconstruction area P in the direction orthogonal to the lines” has been set to =9/512≈1/57, the number of the lines may be set to 8 to 256.
(2) Although the above example has been described under the assumption that 512 pixels are configured as the reconstruction area P, the present invention is applicable even to a 1024-pixel configuration and other number of pixels.
(3) Although the above example has been described assuming that the primary interpolation/extrapolation process is performed, a 0-order interpolation/extrapolation process (copy of most proximity data) or a secondary or more interpolation/extrapolation process (e.g., Hanning interpolation or Cubic interpolation) may be adopted.
(4) Although the above example has considered the interpolation using the two data D2 of the opposite view, helical interpolation using two data D2 of the same view may be adopted if an effective slice may become thick.
(5) Although such a view that the center axis Bc of the X-ray beam becomes parallel to the y axis, is assumed to be view=0° in the above example, an arbitrary angle may be set as view=0°.
(6) Although the medical X-ray CT apparatus has been supposed to be used in the above example, the present invention can be applied even to an industrial X-ray CT apparatus.
Many widely different embodiments of the invention may be configured without departing from the spirit and the scope of the present invention. It should be understood that the present invention is not limited to the specific embodiments described in the specification, except as defined in the appended claims.
Number | Date | Country | Kind |
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2004-030727 | Feb 2004 | JP | national |