Abstract:
For the purpose of providing a backprojection method and an X-ray CT apparatus by which backprojection processing can be simplified and sped up, instead of obtaining backprojection pixel data D 2 (x, y) directly from projection data D 0 (view, ch), axially projected data D 1 (view, pt) are obtained from projection data D 0 (view, ch) by projecting them onto a straight line, and then backprojection pixel data D 2  are obtained from the axially projected data D 1.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    The present invention relates to a backprojection method and an X-ray CT (computed tomography) apparatus, and more particularly to a backprojection method and an X-ray CT apparatus by which backprojection processing can be simplified and sped up.  
           [0002]    The current mainstream X-ray CT apparatus implements a filtered backprojection technique involving processes of data collection, preprocessing, filtering, backprojection processing, and post-processing to thereby reconstruct an image.  
           [0003]    Conventional backprojection processing is disclosed in, for example, Japanese Patent Application Laid Open No. H8-187241 and U.S. Pat. No. 5,414,622.  
           [0004]    In such backprojection processing, projection data D 0 (view, ch) obtained by a fan beam represented by a view angle view and a detector channel ch is subjected to a calculation for projecting the projection data D 0 (view, ch) onto coordinates (x, y) of a pixel constituting a reconstruction region to obtain backprojection pixel data D 2 (x, y), and the backprojection pixel data D 2 (x, y) for all views employed in image reconstruction are added to obtain backprojection data D 3 (x, y).  
           [0005]    In the conventional backprojection processing, a calculation for obtaining the backprojection pixel data D 2 (x, y) from the projection data D 0 (view, ch) must be conducted for, for example, 512×512 pixels, in which the projection data D 0 (view, ch) line up along arc-shaped geometrical positions corresponding to an arc-like shape of the detector, and the backprojection pixel data D 2 (x, y) line up along geometrical positions on rectangular coordinates of a reconstruction region. This raises the problems that the processing is intricate and time-consuming.  
         SUMMARY OF THE INVENTION  
         [0006]    It is therefore an object of the present invention is to provide a backprojection method and an X-ray CT apparatus by which backprojection processing can be simplified and sped up.  
           [0007]    The present invention, in accordance with its first aspect, provides a backprojection method characterized in comprising the steps of: obtaining axially projected data D 1  by projecting projection data D 0 (view, ch) obtained by a fan beam represented by a view angle view and a detector channel ch onto a straight projection axis; then, obtaining backprojection pixel data D 2  by projecting said axially projected data D 1  onto pixels constituting a reconstruction region; and obtaining backprojection data D 3  by adding the backprojection pixel data D 2  for all views employed in image reconstruction on a pixel-to-pixel basis.  
           [0008]    In the backprojection method of the first aspect, instead of obtaining the backprojection pixel data D 2  directly from the projection data D 0 (view, ch), axially projected data D 1 (view, pt) is obtained from the projection data D 0 (view, ch), and then backprojection pixel data D 2 (x, y) is obtained from the axially projected data D 1 . The symbol pt represents a coordinate on the projection axis.  
           [0009]    Although the calculation for obtaining the axially projected data D 1 (view, pt) lining up along geometrical positions on a straight projection axis from the projection data D 0 (view, ch) lining up along arc-shaped geometrical positions corresponding to an arc-like shape of the detector has a processing load per datum identical to that of a conventional calculation for obtaining backprojection pixel data D 2 (x, y) from the projection data D 0 (view, ch), the number of data is no more than about 8,000, for example, which is only {fraction (1/30)} of that of the conventional 512×512 pixels. On the other hand, although the calculation for obtaining the backprojection pixel data D 2  from the axially projected data D 1  requires calculations for 512×512 pixels as in the prior art, the calculation for obtaining the backprojection pixel data D 2 (x, y) lining up on rectangular coordinates from the axially projected data D 1 (view, pt) lining up along a straight line needs only simple processing involving mere sampling at a regular pitch and multiplication by a distance factor. Thus, as a whole, the backprojection processing can be simplified and sped up.  
           [0010]    The present invention, in accordance with its second aspect, provides the backprojection method of the aforementioned configuration, characterized in that when a direction of a center axis of the fan beam at view=0° is represented by a y-direction and a direction orthogonal to the y-direction and parallel to a fan beam plane is represented by an x-direction, said projection axis is defined as a straight line passing through a center of reconstruction and parallel to the x-direction for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity; and said projection axis is defined as a straight line passing through the center of reconstruction and parallel to the y-direction for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity.  
           [0011]    Note that view=−45° and view=315° are separately expressed herein for convenience of representation, but they are the same and represent the same view in reality.  
           [0012]    When data is projected onto a straight projection axis, accuracy increases as the angle formed between the projection direction line and the projection axis approaches 90°, and accuracy decreases as the angle approaches 0°.  
           [0013]    In the backprojection method of the second aspect, since the angle formed between the projection direction line and the projection axis never falls below about 45°, reduction in accuracy is prevented.  
           [0014]    The present invention, in accordance with its third aspect, provides the backprojection method of the aforementioned configuration, characterized in that one axially projected datum D 1  is obtained by interpolation calculation from a plurality of projection data D 0 .  
           [0015]    The number of projection data D 0  and the positional intervals thereof at one view angle are determined by the detector. Specifically, the number of projection data D 0  is “the number of channels of the detector (e.g., 1,000)”, and the positional intervals of the projection data D 0  are “the channel pitch of the detector (e.g., 1 mm)”.  
           [0016]    In the backprojection method of the third aspect, since one axially projected datum D 1  is obtained by interpolation calculation from a plurality of projection data D 0 , the number of the axially projected data D 1  (e.g., 3,500 per view angle) and the data intervals thereof (e.g., 1 mm) on the projection axis can be selected without limitation by the number and position intervals of the projection data D 0 .  
           [0017]    The present invention, in accordance with its fourth aspect, provides the backprojection method of the aforementioned configuration, characterized in that addresses of the plurality of projection data D 0  and interpolation factors for obtaining the one axially projected datum D 1  are set in a table.  
           [0018]    Although the addresses of the plurality of projection data D 0  and interpolation factors for obtaining the one axially projected datum D 1  may be calculated each time the one axially projected datum D 1  is to be obtained, the time of the calculation is an overhead.  
           [0019]    In the backprojection method of the fourth aspect, this overhead is eliminated by calculating beforehand the addresses of the plurality of projection data D 0  and interpolation factors and setting them in a table.  
           [0020]    The present invention, in accordance with its fifth aspect, provides the backprojection method of the aforementioned configuration, characterized in further comprising the steps of: obtaining one axially projected datum D 1  by interpolation calculation from a plurality of projection data D 0 ; setting in a table addresses of the plurality of projection data D 0  and interpolation factors for obtaining the one axially projected datum D 1  for any one of a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity; and using said table for other view angle ranges.  
           [0021]    Considering a case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the X-ray tube, detector and projection axis is rotated by 180° around the center of reconstruction for a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the X-ray tube, detector and projection axis for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity. Therefore, the addresses of the projection data D 0  and the interpolation factors for obtaining one axially projected datum D 1  can be used in common in these view angle ranges.  
           [0022]    Moreover, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the X-ray tube, detector and projection axis is rotated by −90° around the center of reconstruction for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the X-ray tube, detector and projection axis for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the addresses of the projection data D 0  and the interpolation factors for obtaining one axially projected datum D 1  can be used in common in these view angle ranges.  
           [0023]    Furthermore, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the X-ray tube, detector and projection axis is rotated by 90° around the center of reconstruction for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the X-ray tube, detector and projection axis for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the addresses of the projection data D 0  and the interpolation factors for obtaining one axially projected datum D 1  can be used in common in these view angle ranges.  
           [0024]    In the backprojection method of the fifth aspect, since a table used for any one of a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity is used in common for other view angle ranges, the storage capacity required for the table is reduced.  
           [0025]    The present invention, in accordance with its sixth aspect, provides the backprojection method of the aforementioned configuration, characterized in that the backprojection pixel data D 2  are obtained by transformation calculation from the axially projected data D 1 .  
           [0026]    The number of the axially projected data D 1  is, for example, 8,000, and the number of the backprojection pixel data D 2  is, for example, 512×512. Therefore, the effect of speedup is larger in simplifying the calculation for obtaining the backprojection pixel data D 2  from the axially projected data D 1  than in simplifying the calculation for obtaining the axially projected data D 1  from the projection data D 0 .  
           [0027]    In the backprojection method of the sixth aspect, since the backprojection pixel data D 2  is obtained from the one axially projected datum D 1 , transformation calculation simpler than the interpolation calculation, involving only sampling at a regular pitch and multiplication by a distance factor is merely required, thus enhancing the effect of speedup.  
           [0028]    The present invention, in accordance with its seventh aspect, provides the backprojection method of the aforementioned configuration, characterized in that parameters for said transformation calculation are set in a table.  
           [0029]    Although the parameters for the transformation calculation may be calculated each time the one backprojection pixel datum D 2  is to be obtained, the time of the calculation is an overhead.  
           [0030]    In the backprojection method of the seventh aspect, this overhead is eliminated by calculating beforehand the parameters for the transformation calculation and setting them in a table.  
           [0031]    The present invention, in accordance with its eighth aspect, provides the backprojection method of the aforementioned configuration, characterized in further comprising the steps of: obtaining one backprojection pixel datum D 2  by transformation calculation from one axially projected datum D 1 ; setting in a table parameters for the transformation calculation for any one of a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity; and using said table for other view angle ranges.  
           [0032]    Considering a case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the projection axis and reconstruction region is rotated by 180° around the center of reconstruction for a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the projection axis and reconstruction region for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity. Therefore, the parameters for the transformation calculation for obtaining the backprojection pixel data D 2  from the axially projected data D 1  can be used in common in these view angle ranges.  
           [0033]    Moreover, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the projection axis and reconstruction region is rotated by −90° around the center of reconstruction for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the projection axis and reconstruction region for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the parameters for the transformation calculation for obtaining the backprojection pixel data D 2  from the axially projected data D 1  can be used in common in these view angle ranges.  
           [0034]    Furthermore, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the projection axis and reconstruction region is rotated by 90° around the center of reconstruction for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the projection axis and reconstruction region for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the parameters for the transformation calculation for obtaining the backprojection pixel data D 2  from the axially projected data D 1  can be used in common in these view angle ranges.  
           [0035]    In the backprojection method of the eighth aspect, since a table used for any one of a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity is used in common for other view angle ranges, the storage capacity required for the table is reduced (for example, to ¼ in a 360° full scan).  
           [0036]    The present invention, in accordance with its ninth aspect, provides the backprojection method of the aforementioned configuration, characterized in further comprising the steps of: separately conducting addition of the backprojection pixel data D 2  for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity and for a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, and addition of the backprojection pixel data D 2  for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity and for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity; and obtaining the backprojection data D 3  by finally adding the sums from the additions.  
           [0037]    When the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, the processing is easier by a method involving the step of obtaining the backprojection pixel data D 2  with the fixed y-coordinate and varying x-coordinate, and repeating the step with the varying y-coordinate. On the other hand, when the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, the processing is easier by a method involving the step of obtaining the backprojection pixel data D 2  with the fixed x-coordinate and varying y-coordinate, and repeating the step with the varying x-coordinate. However, this requires separate algorithms for these methods.  
           [0038]    In the backprojection method of the ninth aspect, since addition of the backprojection pixel data D 2  for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity and for a view angle range of 135≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, i.e., addition when the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, is conducted separately from addition of the backprojection pixel data D 2  for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity and for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity, i.e., addition when the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, confusion of data is avoided when x and y are switched, and the algorithm can be used in common. It should be noted that when the backprojection data D 3 (x, y) is obtained by finally adding the sums from these additions, it is necessary to transform coordinates so that x and y match in the two sums.  
           [0039]    The present invention, in accordance with its tenth aspect, provides an X-ray CT apparatus characterized in comprising: an X-ray tube; a detector for detecting X-rays of a fan beam; scanning means for collecting projection data D 0 (view, ch) represented by a view angle view and a detector channel ch while rotating at least one of said X-ray tube and said detector around a subject to be imaged; axially projected data calculating means for obtaining axially projected data D 1  by projecting said projection data D 0 (view, ch) onto a straight projection axis; backprojection pixel data calculating means for obtaining backprojection pixel data D 2  by projecting said axially projected data Dr onto pixels constituting a reconstruction region; and backprojection data calculating means for obtaining backprojection data D 3  by adding the backprojection pixel data D 2  for all views employed in image reconstruction on a pixel-to-pixel basis.  
           [0040]    In the X-ray CT apparatus of the tenth aspect, the backprojection method of the first aspect can be suitably implemented.  
           [0041]    The present invention, in accordance with its eleventh aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that when a direction of a center axis of the fan beam at view=0° is represented by a y-direction and a direction orthogonal to the y-direction and parallel to a fan beam plane is represented by an x-direction, said axially projected data calculating means defines said projection axis as a straight line passing through a center of reconstruction and parallel to the x-direction for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity; and defines said projection axis as a straight line passing through the center of reconstruction and parallel to the y-direction for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity.  
           [0042]    In the X-ray CT apparatus of the eleventh aspect, the backprojection method of the second aspect can be suitably implemented.  
           [0043]    The present invention, in accordance with its twelfth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said axially projected data calculating means obtains one axially projected datum D 1  by interpolation calculation from a plurality of projection data D 0 .  
           [0044]    In the X-ray CT apparatus of the twelfth aspect, the backprojection method of the third aspect can be suitably implemented.  
           [0045]    The present invention, in accordance with its thirteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said axially projected data calculating means uses a table in which addresses of the plurality of projection data D 0  and interpolation factors for obtaining the one axially projected datum D 1  are set.  
           [0046]    In the X-ray CT apparatus of the thirteenth aspect, the backprojection method of the fourth aspect can be suitably implemented.  
           [0047]    The present invention, in accordance with its fourteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said axially projected data calculating means obtains one axially projected datum D 1  by interpolation calculation from a plurality of projection data D 0 ; sets in a table addresses of the plurality of projection data D 0  and interpolation factors for obtaining the one axially projected datum D 1  for any one of a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity; and uses said table for other view angle ranges.  
           [0048]    In the X-ray CT apparatus of the fourteenth aspect, the backprojection method of the fifth aspect can be suitably implemented.  
           [0049]    The present invention, in accordance with its fifteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said pixel projection data calculating means obtains the backprojection pixel data D 2  by transformation calculation from the axially projected data D 1 .  
           [0050]    In the X-ray CT apparatus of the fifteenth aspect, the backprojection method of the sixth aspect can be suitably implemented.  
           [0051]    The present invention, in accordance with its sixteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said pixel projection data calculating means uses a table in which parameters for said transformation calculation are set.  
           [0052]    In the X-ray CT apparatus of the sixteenth aspect, the backprojection method of the seventh aspect can be suitably implemented.  
           [0053]    The present invention, in accordance with its seventeenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said pixel projection data calculating means obtains one backprojection pixel datum D 2  by transformation calculation from one axially projected datum D 1 ; sets in a table parameters for the transformation calculation for any one of a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity, a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity; and uses said table for other view angle ranges.  
           [0054]    In the X-ray CT apparatus of the seventeenth aspect, the backprojection method of the eighth aspect can be suitably implemented.  
           [0055]    The present invention, in accordance with its eighteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said backprojection data calculating means separately conducts addition of the backprojection pixel data D 2  for a view angle range of −45°≦view&lt;45° or a view angle range mainly including the range and also including its vicinity and for a view angle range of 135°≦view&lt;225° or a view angle range mainly including the range and also including its vicinity, and addition of the backprojection pixel data D 2  for a view angle range of 45°≦view&lt;135° or a view angle range mainly including the range and also including its vicinity and for a view angle range of 225°≦view&lt;315° or a view angle range mainly including the range and also including its vicinity; and obtains the backprojection data D 3  by finally adding the sums from the additions.  
           [0056]    In the X-ray CT apparatus of the eighteenth aspect, the backprojection method of the ninth aspect can be suitably implemented.  
           [0057]    According to the backprojection method and X-ray CT apparatus of the present invention, since axially projected data D 1 (view, pt) are first obtained from projection data D 0 (view, ch), and then backprojection pixel data D 2 (x, y) are obtained from the axially projected data D 1 (view, pt), instead of obtaining the backprojection pixel data D 2 (x, y) directly from the projection data D 0 (view, ch), the backprojection processing can be simplified and sped up.  
           [0058]    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. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0059]    [0059]FIG. 1 is a block diagram showing an X-ray CT apparatus in accordance with a first embodiment of the present invention.  
         [0060]    [0060]FIG. 2 shows an exemplary lookup table for calculating axially projected data.  
         [0061]    [0061]FIG. 3 shows an exemplary lookup table for calculating backprojection pixel data.  
         [0062]    [0062]FIG. 4 is a general flow chart of operation of the X-ray CT apparatus.  
         [0063]    [0063]FIG. 5 is a flow chart of backprojection processing in accordance with the first embodiment.  
         [0064]    [0064]FIG. 6 is a diagram for explaining processing for obtaining axially projected data from projection data in a range of −45°≦view&lt;45°.  
         [0065]    [0065]FIG. 7 is a diagram for explaining processing for obtaining axially projected data from projection data at view=45°−Δview.  
         [0066]    [0066]FIG. 8 is a diagram for explaining processing for obtaining axially projected data from projection data at view=45°.  
         [0067]    [0067]FIG. 9 is a diagram for explaining processing for obtaining backprojection pixel data from axially projected data in a range of −45°≦view&lt;45°.  
         [0068]    [0068]FIG. 10 is a diagram for explaining processing for adding backprojection pixel data in ranges of −45°≦view&lt;45° and 135°≦view&lt;225°.  
         [0069]    [0069]FIG. 11 is a diagram for explaining processing for obtaining axially projected data from projection data in a range of 45°≦view&lt;135°.  
         [0070]    [0070]FIG. 12 is a diagram for explaining processing for obtaining backprojection pixel data from axially projected data in a range of 45°≦view&lt;135°.  
         [0071]    [0071]FIG. 13 is a diagram for explaining processing for adding backprojection pixel data in ranges of 45°≦view&lt;135° and 225°≦view&lt;315°.  
         [0072]    [0072]FIG. 14 is a flow chart of backprojection processing in accordance with a second embodiment.  
         [0073]    [0073]FIG. 15 is a flow chart continued from FIG. 14.  
         [0074]    [0074]FIG. 16 is a diagram for explaining processing for adding backprojection pixel data in ranges of −45°≦view&lt;45° and 135°≦view&lt;225°.  
         [0075]    [0075]FIG. 17 is a diagram for explaining processing for adding backprojection pixel data in ranges of 45°≦view&lt;135° and 225°≦view&lt;315°.  
         [0076]    [0076]FIG. 18 is a diagram for explaining 90° rotation processing of data.  
         [0077]    [0077]FIG. 19 shows an exemplary lookup table for calculating axially projected data in accordance with a third embodiment. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0078]    The present invention will now be described in more detail with reference to embodiments shown in the accompanying drawings. It should be noted that the present invention is not limited to the embodiments.  
         [0079]    First Embodiment  
         [0080]    [0080]FIG. 1 is a block diagram of the configuration of an X-ray CT apparatus in accordance with a first embodiment of the present invention.  
         [0081]    The X-ray CT apparatus  100  comprises an operator console  1 , an imaging table  10 , and a scan gantry  20 .  
         [0082]    The operator console  1  comprises an input device  2  for accepting inputs by a human operator, a central processing apparatus  3  for executing backprojection processing in accordance with the present invention, a data collection buffer  5  for collecting projection data acquired at the scan gantry  20 , a CRT  6  for displaying an X-ray CT image reconstructed from the projection data, and a storage device  7  for storing programs, data, and X-ray CT images.  
         [0083]    The table apparatus  10  comprises a cradle  12  for laying thereon a subject and transporting the subject into/out of a bore (internal cavity portion) of the scan gantry  20 . The cradle  12  is driven by a motor incorporated in the table apparatus  10 .  
         [0084]    The scan gantry  20  comprises an X-ray tube  21 , an X-ray controller  22 , a collimator  23 , a detector  24 , a DAS (data acquisition system)  25 , a rotation controller  26  for rotating the X-ray tube etc. around the body axis of the subject, and a control interface  29  for communicating control signals etc. with the operator console  1  and imaging table  10 .  
         [0085]    [0085]FIG. 2 is a conceptual diagram of a lookup table  31  stored in the storage device  7  for axial projection.  
         [0086]    In the lookup table  31 , a coordinate pt of axially projected data D 1  on a projection axis for each view angle view in a view angle range of −45°≦view&lt;45° (or a view angle range mainly including the range and also including its vicinity), an address of projection data D 0 , i.e., a channel index ch(pt), for obtaining the axially projected data D 1 (view, pt), and interpolation factors k 1 (pt) and k 2 (pt) for two-point interpolation are calculated beforehand and stored.  
         [0087]    The symbol Δview is a step angle for the view angle (i.e., the view angle difference between adjacent views), and is “0.36°”, for example. The symbol Pe is the maximum of pt, and is “8,000”, for example.  
         [0088]    [0088]FIG. 3 is a conceptual diagram of a lookup table  32  stored in the storage device  7  for transformation calculation.  
         [0089]    In the lookup table  32 , a y-coordinate y of backprojection pixel data D 2  for each view angle view in a view angle range of −45°≦view&lt;45° (or a view angle range mainly including the range and also including its vicinity), a distance factor R(y) as a parameter of the transformation calculation for obtaining one backprojection pixel datum D 2 (I, x) from one axially projected datum D 1 , a sampling pitch Δpt, the number of sampling points str_pt, a start address str_x and an end address end_x are calculated beforehand and stored. These parameters will be described later with reference to FIG. 11.  
         [0090]    The symbol Ye is the maximum of the y-coordinate in a reconstruction region Rf, as shown in FIG. 6.  
         [0091]    [0091]FIG. 4 is a flow chart showing the general flow of the operation of the X-ray CT apparatus  100 .  
         [0092]    In Step S 1 , projection data D 0 (view, ch) represented by the view angle view and the detector channel ch are collected while rotating the X-ray tube  21  and detector  24  around the subject to be imaged.  
         [0093]    In Step S 2 , preprocessing (e.g., offset correction, DAS gain correction, and sensitivity correction) is performed on the projection data D 0 (view, ch).  
         [0094]    In Step S 3 , filtering is performed on the preprocessed projection data D 0 (view, ch). Specifically, the data is Fourier-transformed, is filtered (subjected to a reconstruction function), and is inversely Fourier-transformed.  
         [0095]    In Step S 4 , backprojection processing is performed on the filtered projection data D 0 (view, ch) in accordance with the present invention to obtain backprojection data D 3 (x, y). The backprojection processing is described below with reference to FIG. 5.  
         [0096]    In Step S 5 , post-processing is performed on the backprojection data D 3 (x, y) to produce a CT image.  
         [0097]    [0097]FIG. 5 is a detailed flow chart of the backprojection processing (S 4 ).  
         [0098]    In Step R 1 , one view angle view is taken as a view angle of interest from a plurality of views needed in image reconstruction.  
         [0099]    In Step R 2 , if the view angle of interest view is −45°≦view&lt;45° or 135°≦view&lt;225°, the process goes to R 3 ; otherwise (i.e., if it is 45°≦view&lt;135° or 225°≦view&lt;315°, goes to Step R 6 .  
         [0100]    In Step R 3 , a lookup table  31  corresponding to a view angle view is referred to, to first obtain a channel index ch( 0 ) corresponding to pt=0, and then retrieve the filtered projection data D 0 (view, ch( 0 )+1) and D 0 (view, ch( 0 )) for two-point interpolation. In addition, interpolation factors k 1 ( 0 ) and k 2 ( 0 ) are read out. Then, axially projected data D 1 (view,  0 ) is calculated according to the following equation, and is stored in the storage device  7 :  
           D   1 ( view ,  0 )= k   1 ( 0 )× D   0 ( view,ch ( 0 )+1)+ k   2 ( 0 )× D   0 ( view,ch ( 0 )).  
         [0101]    Similarly, axially projected data D 1 (view, pt) are calculated for pt=1−Pe according to the following equation:  
           D   1 ( view,pt )= k   1 ( pt )× D   0 ( view,ch ( pt )+1)+ k   2 ( pt )× D   0 ( view,ch ( pt )).  
         [0102]    If ch(pt) is not defined for a certain pt, this pt is skipped and the next pt is taken.  
         [0103]    Moreover, for 135°≦view&lt;225°, a lookup table  31  corresponding to a view angle view=view−180° is referred to.  
         [0104]    [0104]FIG. 6 is an explanatory diagram showing details of Step R 3 .  
         [0105]    Step R 3  is calculation processing for obtaining axially projected data D 1 (view, pt) lining up along a projection axis represented by a straight line y=Ye/2 parallel to the x-axis direction of a reconstruction plane and passing through a center of reconstruction IC, from projection data D 0 (view, ch) lining up at arc-shaped geometrical positions corresponding to the arc-like shape of the detector  24 . The symbol Ye designates the maximum of the y-coordinate of the reconstruction region Rf The position of the axially projected data D 1 (view,  0 ) is defined by the position of the channel index ch( 0 ) of the detector at a view angle view=45°−Δview, as shown in FIG. 7. Note that view=0° when the center axis direction of the fan beam is parallel to the y-axis direction, and the view angle step is represented by Δview.  
         [0106]    On the other hand, the position of the axially projected data D 1  (view, Pe) is defined by the position of the channel index ch( 1 , 000 ) of the detector at a view angle view=−45°, as shown in FIG. 8. Note that the detector  24  has 1,000 channels here.  
         [0107]    As can be seen from FIGS.  6 - 8 , one view has a projection axis portion contained in the fan beam and a projection axis portion not contained in the fan beam. No value of ch(pt) is set in the lookup table  31  for pt corresponding to a projection axis portion not contained in the fan beam.  
         [0108]    Returning to FIG. 5, in Step R 4 , a lookup table  32  corresponding to a view angle view is referred to, to first obtain Δpt, str_pt and str_x for y=0, set x=str_x, and then retrieve axially projected data D 1  (view, str_pt) from the storage device  7 . In addition, a distance factor R(y) is read out. Then, backprojection pixel data D 2 (view, str_x,  0 ) is calculated according to the following equation:  
           D   2 ( view,str   —   x , 0 )= R ( 0 )× D   1 ( view,str   —   pt ).  
         [0109]    The data is added to D 2 (x, y) stored in the storage device  7 :  
           D2        (     str_x   ,              0     )       =       ∑   view                               D2        (     view   ,              str_x   ,              0     )                  .                                          
 
         [0110]    Similarly, backprojection pixel data D 2 (view, x,  0 ) are calculated for x=str_x+1−end_x, and added to the backprojection pixel data D 2 (x,  0 ) stored in the storage device  7  according to the following equations:  
           D   2 ( view,x , 0 )= R ( 0 )× D   1 ( view,str   —   pt +( x−str   —   x )Δ pt ), and  
         [0111]    [0111]         D2        (     x   ,              0     )       =       ∑   view                               D2        (     view   ,              x   ,              0     )       .                               
         [0112]    Next, backprojection pixel data D 2 (view, x, y) are similarly calculated for y=1−Ye, and added to the backprojection pixel data D 2 (x, y) stored in the storage device  7  according to the following equations:  
         D2        (     view   ,              x   ,              y     )       =       R        (   y   )       ×     D1   (       view   ,              sir_pt     +       (     x   -   str_x     )        Δ                 pt       )     ,              and               D2        (     x   ,              y     )       =       ∑   view                               D2        (     view   ,              x   ,              y     )                  .                             
 
         [0113]    For 135°≦view&lt;225°, a lookup table  32  corresponding to a view angle view=view−180° is referred to.  
         [0114]    Then, the process goes to Step R 5 .  
         [0115]    [0115]FIG. 9 is an explanatory diagram showing details of Step R 4 .  
         [0116]    Backprojection pixel data D 2  is calculated along a straight line parallel to the x-axis from the axially projected data D 1  on the projection axis y=Ye/2, and this process is repeated for Y=0−Ye.  
         [0117]    [0117]FIG. 10 is a conceptual diagram of a backprojection pixel data storage section  70  in the storage device  7 .  
         [0118]    The backprojection pixel data D 2  is added along a straight line parallel to the x-axis, and this process is repeated for Y=0−Ye.  
         [0119]    In Step R 6 , if the view angle falls within 45°≦view&lt;135°, a lookup table  31  corresponding to a view angle view=view−90° is referred to, and if the view angle falls within 225°≦view&lt;315°, a lookup table  31  corresponding to a view angle view=view−270° is referred to. Then, axially projected data D 1 (view, pt) are calculated for pt=0−Pe similarly to Step R 3  according to the following equation:  
           D   1 ( view,pt )= k   1 ( pt )× D   0 ( view,ch ( pt )+1)+ k   2 ( pt )× D   0 ( view,ch ( pt )).  
         [0120]    If ch(pt) is not defined for a certain pt, this pt is skipped and the next pt is taken.  
         [0121]    [0121]FIG. 11 is an explanatory diagram showing details of Step R 6 .  
         [0122]    Step R 6  corresponds to calculation for obtaining axially projected data D 1 (view, pt) lining up along a projection axis represented by a straight line x=Xe/2 parallel to the y-axis direction and passing through the center of reconstruction IC, from projection data D 0 (view, ch) lining up at arc-shaped geometrical positions corresponding to the arc-like shape of the detector  24 . The symbol Xe designates the maximum of the x-coordinate of the reconstruction region Rf.  
         [0123]    Returning to FIG. 5, in Step R 9 , if the view angle falls within 45°≦view&lt;135°, a lookup table  32  corresponding to a view angle view=view −90° is referred to, and if the view angle falls within 225°≦view&lt;315°, a lookup table  32  corresponding to a view angle view=view −270° is referred to. At that time, interpretation of y into x, R(y) into R(x), str_x into stray, and end_x into end_y is conducted, and backprojection pixel data D 2 (view, x, y) are calculated for x=0−x=Xe and for y=str_y−end_y, and added to the backprojection pixel data D 2 (x, y) stored in the storage device  7  according to the following equations:  
           D   2 ( view,x,y )= R ( y )× D   1 ( view,str   —   pt +( y−str   —   y )Δ pt ), and          D2        (     x   ,              y     )       =       ∑   view                               D2        (     view   ,              x   ,              y     )                  .                               
         [0124]    Then, the process goes to Step R 5 .  
         [0125]    [0125]FIG. 12 is an explanatory diagram showing details of Step R 9 .  
         [0126]    Backprojection pixel data D 2  is calculated along a straight line parallel to the y-axis from the axially projected data D 1  on the projection axis x=Xe/2, and this process is repeated for X=0−Xe.  
         [0127]    [0127]FIG. 13 is a conceptual diagram of the backprojection pixel data storage section  70  in the storage device  7 .  
         [0128]    The backprojection pixel data D 2  is added along a straight line parallel to the y-axis, and this process is repeated for X=0−Xe.  
         [0129]    Returning to FIG. 5, in Step R 5 , if Steps R 1 -R 9  have not been repeated for all views needed in image reconstruction, the process goes back to Step R 1 ; and if Steps R 1 -R 9  have been repeated for all views needed in image reconstruction, the process goes to Step R 12 .  
         [0130]    In Step R 12 , data acquired in the backprojection pixel data storage section  70  are output as backprojection data D 3 (x, y).  
         [0131]    The backprojection processing is then terminated.  
         [0132]    According to the X-ray CT apparatus  100  of the first embodiment, the backprojection processing can be simplified and sped up. Moreover, in Steps R 3 , R 4 , R 6  and R 9 , the lookup tables  31  and  32  can be used in common, although interpretation of view angles and parameters for the transformation calculation is needed. Furthermore, only one backprojection pixel data storage section  70  is needed, although interpretation of parameters is needed in Step R 9 . (Two backprojection pixel data storage sections are required in the second embodiment.)  
         [0133]    Second Embodiment  
         [0134]    In the second embodiment, addition of the backprojection pixel data D 2  for a view angle range of −45°≦view&lt;45° (or a view angle range mainly including the range and also including its vicinity) and for a view angle range of 135°≦view&lt;225° (or a view angle range mainly including the range and also including its vicinity) is conducted separately from addition of the backprojection pixel data D 2  for a view angle range of 45°≦view&lt;135° (or a view angle range mainly including the range and also including its vicinity) and for a view angle range of 225°≦view&lt;315° (or a view angle range mainly including the range and also including its vicinity), and the backprojection data D 3 (x, y) are obtained by finally adding the sums from the additions.  
         [0135]    [0135]FIGS. 14 and 15 are flow charts showing backprojection processing in accordance with the second embodiment.  
         [0136]    In Step R 1  in FIG. 14, one view angle view is taken as a view angle of interest from a plurality of views needed for image reconstruction.  
         [0137]    In Step R 2 , if the view angle of interest view is −45°≦view&lt;45° or 135°≦view&lt;225°, the process goes to R 3 ; otherwise (i.e., if it is 45°≦view&lt;135° or 225°≦view&lt;315°, goes to Step R 6 .  
         [0138]    In Step R 3 , a lookup table  31  corresponding to a view angle view is referred to, to calculate axially projected data D 1 (view, pt) for pt=0−Pe according to the following equation:  
           D   1 ( view,pt )= k   1 ( pt )× D   0 ( view,ch ( pt )+1)+ k   2 ( pt )× D   0 ( view,ch ( pt )).  
         [0139]    If ch(pt) is not defined for a certain pt, this pt is skipped and the next pt is taken.  
         [0140]    Moreover, for 135°≦view&lt;225°, a lookup table  31  corresponding to a view angle view=view−180° is referred to.  
         [0141]    In Step R 4 ′, a lookup table  32  corresponding to a view angle view is referred to, and backprojection pixel data D 2 (view, x, y) are calculated for a range y= 0 −y=Ye, and for x=str_x−end_x, and added to backprojection pixel data D 2 (x, y) stored in a first backprojection pixel data storage section  71  shown in FIG. 16 in the storage device  7 , according to the following equations:  
           D   2 ( view,x,y )= R ( y )× D   1 ( view,str   —   pt +( x−str   —   x )Δ pt ), and          D2        (     x   ,              y     )       =       ∑   view                               D2        (     view   ,              x   ,              y     )                  .                               
         [0142]    For 135°≦view&lt;225°, a lookup table  32  corresponding to a view angle view=view−180° is referred to.  
         [0143]    The process then goes to Step R 5 .  
         [0144]    [0144]FIG. 16 is a conceptual diagram of the first backprojection pixel data storage section  71 .  
         [0145]    The backprojection pixel data D 2  is added along a straight line parallel to the x-axis, and this process is repeated for y=0−Ye.  
         [0146]    Returning to FIG. 14, in Step R 6 , if the view angle falls within 45°≦view&lt;135° a lookup table  31  corresponding to a view angle view=view −90° is referred to, and if the view angle falls within 225°≦view&lt;315°, a lookup table  31  corresponding to a view angle view=view−270° is referred to. Then, axially projected data D 1 (view, pt) are calculated for pt=0−Pe similarly to Step R 3  according to the following equation:  
           D   1 ( view,pt )= k   1 ( pt )× D   0 ( view,ch ( pt )+1)+ k   2 ( pt )× D   0 ( view,ch ( pt )).  
         [0147]    If ch(pt) is not defined for a certain pt, this pt is skipped and the next pt is taken.  
         [0148]    In Step R 7 , the current view is saved in view′.  
         [0149]    In Step R 8 , if the view angle falls within 45°≦view&lt;135°, the view angle is set to view=view−90°, and if the view angle falls within 225°≦view&lt;315°, the view angle is set to view=view−270°.  
         [0150]    In Step R 9 ′, a lookup table  32  corresponding to a view angle view is referred to, and backprojection pixel data D 2 (view, x, y) are calculated for a range y=0−y=Ye, and for x=str_x−end_x, and added to backprojection pixel data D 2 (x, y) stored in a second backprojection pixel data storage section  72  shown in FIG. 17 in the storage device  7  according to the following equations:  
           D   2 ( view′,x,y )= R ( y )× D   1 ( view′,str   —   pt +( x−str   —   x )Δ pt ), and          D2        (     x   ,              y     )       =       ∑     view   ′                                 D2        (       view   ′     ,              x   ,              y     )                  .                               
         [0151]    The process then goes to Step R 5 .  
         [0152]    [0152]FIG. 17 is a conceptual diagram of the second backprojection pixel data storage section  72 .  
         [0153]    The backprojection pixel data D 2  is added along a straight line parallel to the x-axis, and this process is repeated for y=0−Ye.  
         [0154]    Returning to FIG. 14, in Step R 5 , if Steps R 1 -R 9 ′ have not been repeated for all views needed in image reconstruction, the process goes back to Step R 1 ; and if Steps R 1 -R 9 ′ have been repeated for all views needed in image reconstruction, the process goes to Step R 10  in FIG. 15.  
         [0155]    In Step R 10  in FIG. 15, the data in the second backprojection pixel data storage section  72  is rotation-processed by 90°.  
         [0156]    In Step R 11 , the data in the second backprojection pixel data storage section  72  rotation-processed by 90° are added to the data in the first backprojection pixel data storage section  71 .  
         [0157]    In Step R 12 ′, data acquired in the pixel projection data storage section  71  are output as backprojection data D 3 (x, y).  
         [0158]    The backprojection processing is then terminated.  
         [0159]    According to the X-ray CT apparatus of the second embodiment, the backprojection processing can be simplified and sped up. Moreover, in Steps R 3 , R 4 ′, R 6  and R 9 ′, the lookup tables  31  and  32  can be used in common, although interpretation of view angles and parameters for the transformation calculation are needed. Furthermore, the need for interpretation of parameters in Step R 9 ′ is eliminated, although two backprojection pixel data storage sections  71  and  72  are required.  
         [0160]    Third embodiment  
         [0161]    While one axially projected datum D 1  is calculated by interpolation calculation from two projection data D 0  in the first and second embodiments, the one axially projected datum D 1  is calculated by interpolation calculation from three projection data D 0  in a third embodiment.  
         [0162]    In this case, a lookup table  31 ′ for axial projection as shown in FIG. 19 is employed, and the axially projected data D 1  are calculated according to the following equation:  
                 D1        (     view   ,              pt     )       =              k1        (   pt   )       ×     D0   (       view   ,                ch   (   pt   )       +   2     )                                  +            k2        (   pt   )         ×       D0        (       view   ,                ch        (   pt   )         +   1     )       .                   +            k3        (   pt   )         ×     D0        (     view   ,                ch        (   pt   )         )                                   
 
         [0163]    According to the X-ray CT apparatus of the third embodiment, the backprojection processing can be simplified and sped up. Moreover, accuracy is improved.  
         [0164]    Other Embodiments  
         [0165]    While two-point interpolation or three-point interpolation is employed in obtaining D 3  from D 0  in the preceding embodiments, interpolation by four or more points may be employed.  
         [0166]    Moreover, while a medical X-ray CT apparatus is considered in the preceding embodiments, the present invention can be applied to an industrial X-ray CT apparatus.  
         [0167]    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.