Abstract:
A CT image generation device for analyzing projection information acquired by scanning a scan subject with X-rays over a scan plane, and generating an image of the scan subject; wherein the CT image generation device comprises: a versatile processing unit for establishing a plurality of coordinate systems on the scan plane; a coordinate decision unit for selecting a coordinate system to be used in distance drive back projection or distance drive forward projection, from the plurality of coordinate systems on the basis of a projection angle; a distance drive processing unit for carrying out distance drive back projection or distance drive forward projection on the basis of the selected coordinate system, in accordance with the projection angle; and an image information processing unit for generating the image of the scan subject, on the basis of image information acquired by carrying out distance drive back projection in relation to projection information.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a CT image generation device, a CT image generating method, and a CT image generation system, particularly to a CT image generating method and a CT image generation system that use projection and back projection to reconstruct CT images. 
       BACKGROUND ART 
       [0002]    Technologies of computed tomography (CT) have been broadly used for medical examinations. CT images have been used as bases for disease diagnoses for thirty years. Improvement of CT image quality and reduction of image artifacts (artifacts) are conventional, important issues in studies of CT image reconstruction algorithms and clinics. 
         [0003]    Typically, the CT image reconstruction algorithms include a filtered back projection algorithm, an image iterative reconstructive algorithm, and an algebraic image reconstruction algorithm. The filtered back projection algorism is a main stream of CT image reconstructions, and has been widely used in current CT products. In the filtered back projection algorithm, the filtered back projection is performed to projection data acquired by actual scans to acquire image data. 
         [0004]    However, in the filtered back projection algorithm, it is assumed that the projection data for image reconstruction is not affected by noise, but the noise always actually exists in association with the projection data. Since the noise is remarkable particularly in low radiation dose scans, it is difficult to acquire high-definition CT images. However, the clinical application range of CT has spread with development of clinical medical examinations, and CT has reached an extremely higher level than before. Under the background of such a new situation, high image quality is newly desired in consideration of the safety at the time of CT usage in the industry. Therefore, it is difficult for the filtered back projection algorithm to meet the new demand, and the filtered back projection algorithm is used for medium or low level clinical applications in many cases. 
         [0005]    The iterative reconstructive algorithm is attracting attention in high-level clinical applications with respect to the above new demand. In the image iterative reconstructive algorithm, image artifacts due to electronic noise and other physical factors are processed properly. Thus, image information can be secured, and radiation dose can be reduced during examinations. However, it was not widely used in actual CT products due to huge calculation amount and high calculation cost. With rapid development of computer technology, the iterative reconstructive algorithm can be applied to the actual products. CT image quality is improved, and image artifacts are reduced, and at the same time, radiation dose necessary for projection can be reduced. With development of medicine and health promotion, the influence of X-ray radiation on human bodies during CT diagnoses is considered more important. Thus, there has been a trend toward low dose CT in the development of CT. Therefore, the iterative reconstructive algorithm has attracted more attention, and is an important subject of research. The iterative reconstructive algorithm mainly includes an iterative projection and back projection process looped multiple times. 
         [0006]    In the conventional filtered back projection algorithm, the main process is a back projection process, and when the back projection method such as the conventional pixel-driven type (Pixel-Driven) is used, the model error is large. Therefore, new back projection methods are being studied to reduce artifacts and improve image quality. 
         [0007]    On the other hand, in the iterative reconstructive algorithm that has attracted attention, the conventional projection and back projection method based on the ray-driven type (Ray-Driven) and pixel-driven type (Pixel-Driven), the model error is large, and when it is applied to the projection and back projection process in the iterative reconstructive algorithm, it is difficult for the algorithm to converge accurately. 
         [0008]    Based on the above situation, many new projection and back projection methods have been studied and proposed, and are used in the conventional filtered back projection algorithm, particularly in the iterative reconstruction algorithm that has attracted attention. The most typical methods include the distance-driven type (Distance-Driven) and separable footprint (Separable Footprint) method. In the distance-driven type, two midline intersections of a pixel block are projection points, and higher model accuracy can be acquired than in the ray-driven type and pixel-driven type. 
         [0009]    However, in the distance-driven projection and back projection method, the following technical problem is present. The model error is still large in some angular ranges of the projection/back projection to still affect the image quality after the reconstruction remarkably. 
       SUMMARY OF THE INVENTION 
     Technical Problem 
       [0010]    Based on the above technical problem in the conventional technology, an object of the present invention is to provide a CT image generation device and method and a CT image generation system in which a model error of projection and back projection can be reduced and which is available also in an iterative reconstructive algorithm and a filtered back projection algorithm to reduce artifacts. 
       Solution to Problem 
       [0011]    For solving the above technical problem in the conventional technology, the present invention provides a CT image generation device. The CT image generation device analyzes projection information acquired by scanning a scan target on a scan plane to generate an image of the scan target, and includes: a general-purpose processing unit that establishes multiple coordinate systems on the scan plane; a coordinate determination unit that selects a coordinate system used in a distance-driven back projection or distance-driven forward projection from the multiple coordinate systems on the basis of a projection angle; a distance-driven processing unit that performs the distance-driven back projection or distance-driven forward projection on the basis of the selected coordinate system in accordance with a projection angle; and an image information processing unit that generates an image of the scan target on the basis of image information acquired by performing the distance-driven back projection to projection information. 
         [0012]    The present invention further provides a CT image generation method. The image generation method is a CT image generation method that analyzes projection information acquired by scanning a scan target on the scan plane by use of X-rays to generate an image of the scan target, and includes: a general-purpose processing step for establishing multiple coordinate systems on the scan plane; a coordinate determination step for selecting a coordinate system used in the distance-driven back projection or distance-driven forward projection from the multiple coordinate systems on the basis of a projection angle; a distance-driven processing step for performs the distance-driven back projection or distance-driven forward projection on the basis of the selected coordinate system in accordance with a projection angle; and an image information processing step for generating an image of the scan target on the basis of image information acquired by performing the distance drive back projection to the projection information. 
         [0013]    According to the CT image generation device and method of the present invention, a model error in the distance-driven forward projection and back projection of the conventional technology can be reduced by performing the distance-driven forward projection and/or back projection by use of multiple image coordinate systems. Accordingly, reconstruction accuracy of the iterative reconstruction technology and filtered back projection technology is increased, artifacts of CT images are reduced, and an actual CT device and a simulation system of the CT device can be improved. 
         [0014]    In the CT image generation device of the present invention, included angles between respective coordinate axes of the multiple coordinate systems established on the scan plane by the general-purpose processing unit may be equal to each other. 
         [0015]    In the CT image generation method of the present invention, included angles between respective coordinate axes of the multiple coordinate systems established on the scan plane at the general-purpose processing step may be equal to each other. 
         [0016]    According to the above CT image generation device and method, as high accuracy as possible is achievable by a small number of coordinate systems by establishing multiple coordinate systems on the scan plane on the basis of even distribution. Accordingly, the processing load due to combination of coordinate systems can be reduced, and as high CT image reconstruction accuracy as possible is securable. 
         [0017]    In the CT image generation device of the present invention, the general-purpose processing unit may establish, on the scan plane, two coordinate systems whose coordinate axes form an included angle of 45 degrees. 
         [0018]    In the CT image generation method of the present invention, at the general-purpose processing step, two coordinate systems whose coordinate axes form an included angle of 45 degrees may be established on the scan plane. 
         [0019]    According to the above CT image generation device and method, by establishing two coordinate systems on the scan plane on the basis of even distribution, as high accuracy as possible is achievable by a small number of coordinate systems. Accordingly, the processing load due to combination of coordinate systems can be reduced, and high CT image reconstruction accuracy can be securable. 
         [0020]    In the CT image generation device of the present invention, the general-purpose processing unit may establish N-number (an integer equal to two or more) of coordinate systems on the scan plane on the basis of an accuracy requirement of the CT image generation device. 
         [0021]    In the CT image generation method of the present invention, N-number (an integer equal to two or more) of coordinate systems may be established on the basis of an accuracy requirement of the CT image generation device at the general-purpose processing step. 
         [0022]    According to the above CT image generation device and method, the number of coordinate systems is determined based on an accuracy requirement. Accordingly, as few coordinate systems as possible are selected on the premise that an accuracy requirement is met, the processing load due to the combination of coordinate systems is reduced, and required CT image reconstruction accuracy is securable. 
         [0023]    In the CT image generation device of the present invention, the coordinate determination unit may select a coordinate system whose coordinate axis and the projection angle form the smallest included angle from the multiple coordinate systems, and the selected coordinate system may be used in the distance-driven back projection or distance-driven forward projection. 
         [0024]    In the CT image generation method of the present invention, at the coordinate determination step, a coordinate system whose coordinate axis and the projection angle form the smallest included angle is selected from the multiple coordinate systems, and used in the distance-driven back projection or distance-driven forward projection. 
         [0025]    According to the above CT image generation device and method, the coordinate system whose coordinate axis and the projection angle form the smallest included angle is selected. Accordingly, the model error in the distance-driven forward projection and back projection can be minimized. 
         [0026]    In the CT image generation device of the present invention, in accordance with each projection angle on the projection plane, the coordinate determination unit selects a coordinate system from the multiple coordinate systems to perform the distance-driven back projection to projection information of the projection angle. On the basis of the coordinate system selected by the coordinate determination unit, the distance-driven processing unit performs the distance-driven back projection to projection information at each projection angle to acquire image information in each coordinate system. The image information processing unit may perform interpolation and addition to the image information in each coordinate system to acquire image information, and may generate an image of the scan target on the basis of the acquired image information. 
         [0027]    In the CT image generation method of the present invention, at the coordinate determination step, in accordance with each projection angle on the projection plane, a coordinate system is selected from the multiple coordinate systems to perform the distance-driven back projection to projection information on the projection angle. At the distance-driven processing step, in accordance with the coordinate system selected at the coordinate determination step, the image information in each coordinate system is acquired by performing the distance-driven back projection to the projection information at each projection angle. At the image information processing step, interpolation and addition are performed to the image information in each coordinate system to acquire image information, and an image of the scan target may be generated based on the acquired image information. 
         [0028]    According to the above CT image generation device and method, the model error in the distance-driven back projection of the conventional technology can be reduced by performing the distance-driven back projection by use of the multiple image coordinate systems. 
         [0029]    In the CT image generation device of the present invention, the image information processing unit performs interpolation to the image information to acquire image information in each coordinate system. In accordance with each projection angle on the projection plane, the coordinate determination unit selects a coordinate system from the multiple coordinate systems to perform the distance-driven forward projection to the image information at the projection angle. On the basis of the coordinate system selected by the coordinate determination unit, the distance-driven processing unit performs the distance-driven forward projection to the image information in the coordinate system at each projection angle to acquire projection information at the projection angle, and may collect the projection information at each projection angle to acquire the projection information. 
         [0030]    In the CT image generation method of the present invention, interpolation is performed to image information at the image information processing step to acquire image information in each coordinate system. At the coordinate determination step, in accordance with each projection angle on the projection plane, a coordinate system is selected from the multiple coordinate systems to perform the distance-driven projection to the image information at the projection angle. At the distance-driven processing step, on the basis of the coordinate system selected at the coordinate determination step, the distance-driven forward projection is performed to the image information in the coordinate system at each projection angle to acquire projection information at the projection angle. Then, by collecting the projection information at each projection angle, the projection information may be acquired. 
         [0031]    According to the above CT image generation device and method, the model error in the distance-driven projection of the conventional technology can be reduced by performing the distance-driven projection by use of multiple image coordinate systems. 
         [0032]    In the CT image generation device of the present invention, the CT image generation device performs at least one iteration of the forward projection and back projection. In the iteration of the forward projection and back projection, the distance-driven forward projection is first performed to the image information acquired using the distance-driven back projection to acquire projection information. After that, the distance-driven back projection may be performed to the projection information acquired using the distance-driven forward projection to acquire image information. 
         [0033]    In the CT image generation method of the present invention, at least one iteration of the forward- and back-projection is performed in the CT image generation method. In the iteration of the forward- and back-projection, projection information may be first acquired by performing the distance-driven projection to the image information acquired using the distance-driven back projection. After that, image information may be acquired by performing the distance-driven back projection to the projection information acquired using the distance-driven forward projection. 
         [0034]    According to the above CT image generation device and method, the iterative reconstruction including the distance-driven forward projection and back projection is performed using multiple image coordinate systems. Accordingly, a model error in the iterative reconstruction including the distance-driven forward projection and back projection of the conventional technology can be reduced. Accordingly, reconstruction accuracy of the iterative reconstruction technology that has attracted attention in the CT image reconstruction is increased, artifacts of CT images are reduced, and an actual CT device and a simulation system of the CT device can be further improved. 
         [0035]    The present invention further provides the CT image generation system. The CT image generation system includes: an X-ray device to scan a scan target by using an X-ray; a detection receiving device to detect and receive projection of the X-ray; a data storage device to store projection information on the received X-ray; and the CT image generation device of the present invention. 
         [0036]    According to the CT image generation system of the present invention, the distance-driven forward projection and/or back projection is performed using multiple image coordinate systems. Accordingly, a model error in the distance-driven forward projection and back projection of the conventional technology can be reduced. As a result, the reconstruction accuracy of the iterative reconstruction technology and filtered back projection technology in the CT image reconstruction can be increased, and artifacts of CT images can be reduced. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0037]      FIG. 1A  shows a principle of a distance-driven forward projection and back projection method; 
           [0038]      FIG. 1B  shows a principle of the distance-driven forward projection and back projection method; 
           [0039]      FIG. 1C  shows a schematic model error view of the distance-driven forward projection and back projection method; 
           [0040]      FIG. 2  shows a module showing a configuration of a CT image generation system including a CT image generation device of a first embodiment of the present invention; 
           [0041]      FIG. 3A  is a schematic view of each coordinate system when two coordinate systems are used; 
           [0042]      FIG. 3B  is a schematic view of each coordinate system when two coordinate systems are used; 
           [0043]      FIG. 4  is a schematic view of selecting a coordinate system on the basis of a projection angle when two coordinate systems are used; 
           [0044]      FIG. 5A  shows an interpolation principle when two coordinate systems are used; 
           [0045]      FIG. 5B  shows an interpolation principle when two coordinate systems are used; 
           [0046]      FIG. 6  shows an image accumulation principle when two coordinate systems are used; 
           [0047]      FIG. 7  shows a flowchart showing a CT image generation method of the first embodiment; 
           [0048]      FIG. 8A  shows a model error reduction principle when two coordinate systems are used; 
           [0049]      FIG. 8B  shows a model error reduction principle when two coordinate systems are used; 
           [0050]      FIG. 9A  shows a flowchart showing establishment of multiple coordinate systems in the second embodiment of the present invention; 
           [0051]      FIG. 9B  shows a schematic view showing a rotational angle of each coordinate system when multiple coordinate systems are used; 
           [0052]      FIG. 10A  shows a schematic view of each coordinate system when three coordinate systems are used; 
           [0053]      FIG. 10B  shows a schematic view of each coordinate system when three coordinate systems are used; 
           [0054]      FIG. 10C  shows a schematic view of each coordinate system when three coordinate systems are used; 
           [0055]      FIG. 11  shows a schematic view of selecting a coordinate system on the basis of a projection angle when three coordinate systems are used; 
           [0056]      FIG. 12A  shows an interpolation principle when three coordinate systems are used; 
           [0057]      FIG. 12B  shows an interpolation principle when three coordinate systems are used; 
           [0058]      FIG. 13A  shows a model error reduction principle when three coordinate systems are used; 
           [0059]      FIG. 13B  shows a model error reduction principle when three coordinate systems are used; 
           [0060]      FIG. 14  shows a flowchart showing a filtered back projection of a third embodiment of the present invention; and 
           [0061]      FIG. 15  shows a flowchart showing a projection of the third embodiment. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0062]    Hereafter, based on the figures, specific embodiments of the present invention are described in detail. The specific embodiments are described in detail below for understanding of the contents of the present invention, but do not limit the present invention. 
       1. Model Error 
       [0063]    First, the principle of a distance-driven forward projection and back projection method and its model error are explained.  FIG. 1A  and  FIG. 1B  show the principle of the distance-driven forward projection and back projection method.  FIG. 1C  is a schematic view of a model error of the distance-driven forward projection and back projection method. 
         [0064]    As shown in  FIG. 1A  and  FIG. 1B , in the distance-driven forward projection/back projection method, data  108  between two intersections acquired by projecting, to a detector  103 , two rays  105  formed by passing two midline intersections  107  of a certain pixel  104  (a pixel shown with a shadowed square in the figure) of an image  102  on a scan plane to scan a scan target from a source point  101  of the forward projection/back projection is data (shown by light shadow in the figure) relating to the pixel  104  in the corresponding detector  103 . 
         [0065]    However, actually, the data relating to the pixel  104  in the detector  103  further includes  109  (shown by deep shadow in the figure), namely, a detector section between an intersection acquired by projecting, to the detector, a ray  106  passing the outermost of the pixel  104  from the source point  101  of the forward projection/back projection and the side end point of the data  108 . Here,  109  is a model error in the distance-driven forward projection/back projection algorithm. 
         [0066]    Hereafter, the above model error is analyzed in detail. First, a plane rectangular coordinate system having a coordinate in parallel to a pixel boundary is established. An angle θ formed by the forward projection/back projection direction and the coordinate axis is an angle of the forward projection/back projection (hereinafter may also be generally named a projection angle). Here, a direction of the forward projection/back projection (hereinafter may also be generally named a projection direction) is a direction formed by a ray passing the pixel  104  from the source point  101  as a base point. Since the pixel  104  is actually very small, a specific position where the ray passes the pixel  104  is not limited. For example, the position can be set as a central point passing the pixel  104 . When the angle θ of the forward projection/back projection is near 0 degree/90 degrees/180 degrees/270 degrees, the model error is small. On the other hand, the angle θ of the forward projection/back projection is near 45 degrees/135 degrees/225 degrees/315 degrees, the model error is large.  FIG. 1C  is a schematic model error of the forward projection/back projection to show a relationship between the model error and angle θ of the forward projection/back projection. 
         [0067]    The above model error distribution is explained in detail in reference to examples. A plane rectangular coordinate system A is established to have an X axis in the horizontal direction and a Y axis in the vertical direction in  FIG. 1A  and  FIG. 2B . The angle θ formed by a direction of the forward projection/back projection and a positive X-axis direction (set in the right direction in  FIG. 1A , and  FIG. 1B ) is an angle of the forward projection/back projection. For example, the counterclockwise direction from the positive X-axis direction can be positive. When the projection angle is near 270 degrees in the above plane rectangular coordinate system A,  FIG. 1A  shows that the section  109  is small (in other words, the model error is small). When the projection angle is near 315 degrees in the above rectangular coordinate system A, the section  109  is large (in other words, the model error is large). The model error distribution as shown in  FIG. 1C  is acquirable in any established plane rectangular coordinate system that has a coordinate axis in parallel to the pixel boundary and that thus is not limited to the above established specific coordinate system. 
       2. First Embodiment 
       [0068]    Hereafter, on the basis of the figures, a CT image generation device and method of the first embodiment of the present invention and a CT image generation system having the CT image generation device are explained in detail. 
       [2-1. Configuration of CT Image Generation System Having CT Image Generation Device] 
       [0069]      FIG. 2  shows a module showing a configuration of the CT generation system having the CT image generation device of the first embodiment. As shown in  FIG. 2 , a CT image generation system  1  includes an X-ray device  10 , a detection receiving device  20 , a data storage device  30 , and a CT image generation device  40  of this embodiment. 
         [0070]    The X-ray device  10  scans a scan target by using X-rays. The X-ray device  10  is, e.g., an X-ray scanner, and the scan target is, e.g., a human body. 
         [0071]    The detection receiving device  20  detects and receives projection of the X-ray. The detection receiving device  20  is, e.g., an X-ray detector (probe), and receives X-ray that is transmitted from the X-ray device  10  and that has scanned a scan target. 
         [0072]    The data storage device  30  stores projection information on the received X-ray. The data storage device  30  is realized by a ROM, RAM, HDD, memory card, etc. 
         [0073]    The CT image generation device  40  of this embodiment analyzes projection information acquired by scanning a scan target on a scan plane by using the X-ray to generate an image of the scan target. The CT image generation device  40  is realized by a computer, single chip microcomputer, CPU, MPU, integrated circuit, etc. 
       [2-2. Characteristics Module of CT Image Generation Device] 
       [0074]    Hereafter, subsequently, based on  FIG. 2 , a characteristics module of the CT image generation device  40  of this embodiment is explained. 
         [0075]    The CT image generation device  40  of this embodiment operates as a specific function unit such as the general-purpose processing unit  41 , coordinate determination unit  42 , distance-driven processing unit  43 , and image information processing unit  44  by making a processor execute a predetermined program. Naturally, the CT image generation device  40  of this embodiment is realizable not only by this but also by an integrated circuit by use of, e.g., FPGA. 
       [2-2-1. General-Purpose Processing Unit] 
       [0076]    The general-purpose processing unit  41  establishes multiple coordinate systems on a scan plane. In this embodiment, establishing of two coordinate systems is explained. Establishing of three or more coordinates is explained later. 
         [0077]      FIG. 3A  and  FIG. 3B  are schematic views of respective coordinate systems when two coordinate systems are used.  FIG. 3A  shows a coordinate system  201  that is the same as the plane rectangular coordinate system A established in the above sentence. Hereafter, such a coordinate system is called a reference coordinate system.  FIG. 3B  shows a coordinate system  202  acquired by rotating the reference coordinate system shown in  FIG. 3A  to a predetermined angle. Hereafter, such a coordinate system is called a rotation coordinate system. Here, the reference coordinate system and the rotation coordinate system are arbitrarily determined for easy explanation, and are equivalent. In the figures, a section  203  shown by shadow shows a section of an active reconstruction image. 
         [0078]    As shown in  FIG. 3A  and  FIG. 3B , each included angle between coordinate axes of respective two coordinate systems established by the general-purpose processing unit  41  on the scan plane is the same as each other, 45 degrees. Namely, a rotation angle of the rotation coordinate system relative to the reference coordinate system is 45 degrees (the counterclockwise direction is positive). Based on the principle of even distribution, two coordinate systems are established within the scan plane (360 degrees). As a result, high accuracy is achieved by as few coordinate systems as possible, the processing load brought by combining coordinate systems with each other is reduced, and high CT image reconstruction accuracy is securable. Naturally, the rotation angle of the rotation coordinate system relative to the reference coordinate system may be other than 45 degrees, and may be any angle selected from angles over 0 degree and under 90 degrees. 
       [2-2-2. Coordinate Determination Unit] 
       [0079]    The coordinate determination unit  42  selects a coordinate system for the distance-driven back projection or distance-driven forward projection from multiple coordinate systems established by the general-purpose processing unit  41  on the basis of a projection angle. In this embodiment, the situation of selecting from two coordinate systems is explained, and the situation of selecting from three or more coordinate systems is explained later. 
         [0080]      FIG. 4  is a schematic view of selecting a coordinate system on the basis of a projection angle in case in which two coordinate systems are used. As shown in  FIG. 4 , the reference coordinate system  201  is used for the forward projection/back projection within the angular range shown by  301 , and the rotation coordinate system  202  is used for the forward projection/back projection within the angular range shown by  302 . 
         [0081]    The coordinate determination unit  42  selects a coordinate system whose certain coordinate axis and a projection angle form the smallest included angle from the coordinate systems  201  and  202 , and by use of the selected coordinate system, the distance-driven back projection or distance-driven forward projection is performed at the projection angle. As a result, the model error in the distance-driven forward projection and back projection can be minimized. 
       [2-2-3. Distance-Driven Processing Unit] 
       [0082]    The distance-driven processing unit  43  performs the distance-driven back projection or distance-driven forward projection on the basis of the coordinate system selected by the coordinate determination unit  42  in accordance with a projection angle. 
         [0083]    In the distance-driven back projection, based on the coordinate system selected by the coordinate determination unit  42 , the distance-driven processing unit  43  performs the distance-driven forward projection to projection information at each projection angle to acquire image information in each coordinate system. In the distance-driven forward projection, based on the coordinate system selected by the coordinate determination unit  42 , the distance-driven processing unit  43  performs the distance-driven forward projection to the image information in each coordinate system corresponding to each projection angle to acquire the projection information at the projection angle. 
       [2-2-4. Image Information Processing Unit] 
       [0084]    The image information processing unit  44  generates an image of the scan target based on the image information acquired by performing the distance-driven back projection to the projection information. 
         [0085]    In the distance-driven back projection, the image information processing unit  44  acquires image information by performing interpolation and addition to the image information in each coordinate system acquired by the distance-driven back projection performed by the distance-driven processing unit  43 . Additionally, in the distance-driven forward projection, the image information processing unit  44  performs interpolation to the image information to acquire image information in each coordinate system established by the general-purpose processing unit  41 . 
         [0086]    Hereafter, the interpolation performed by the image information processing unit  44  is explained specifically.  FIG. 5A  and  FIG. 5B  shows the interpolation principle when two coordinate systems are used. The image interpolation between multiple coordinate systems (two herein) is calculated by areas occupied by pixels between the coordinate systems.  FIG. 5A  shows a specific method of performing interpolation calculation of pixels of the rotation coordinate system  202 , and acquiring a pixel in the reference coordinate system  201 . By calculating a ratio relationship (area ratio) of areas of overlapping sections between a certain pixel of the determined reference coordinate system and pixels of the rotation coordinate system, each covered pixel in the rotation coordinate system is weighted and accumulated by using this area ratio. For example, a pixel value C(x, y) of a pixel x, y) (shown by shadow in the figure) of the reference coordinate system  201 , the pixel being acquired by the interpolation to the rotation coordinate system  202 , is calculable by Formula 1. 
         [0000]        C ( x,y )= ca×A+cb×B+cc×C+cd×D   (1)
 
         [0087]    In Formula 1, ca, cb, cc, and cd, as shown in the figure, show occupation ratios of the areas (pixel overlapping section areas) of the overlapping sections between the pixel(x, y) in the reference coordinate system and the pixel A, pixel B, pixel C, and pixel D in the rotation coordinate system relative to the pixel area, namely pixel overlapping section area ratios. In Formula, A, B, C, and D show pixel values of the pixel A, pixel B, pixel C, and pixel D in the rotation coordinate system, respectively. 
         [0088]    The same method is used also when the interpolation calculation of the reference coordinate system is performed to the rotation coordinate system. In the back projection, it is necessary to perform the interpolation calculation of an image of each rotation coordinate system to the reference coordinate system. In the projection, it is necessary to perform the interpolation calculation of an image of the reference coordinate system to each rotation coordinate system. 
         [0089]      FIG. 5B  shows a specific example of calculating the overlapping section area ratio. By defining the pixel block in the reference coordinate system into smaller blocks, the number of blocks in the pixels in the rotation coordinate system are summed to show area ratios of the overlapping sections. In the embodiment, the interpolation relationships and interpolation coefficients of the pixels, i.e., the area ratios are calculated in advance by a processor and stored in the storage device. 
         [0090]    Hereafter, subsequently, processing of the image information processing unit  44  is explained.  FIG. 6  shows an image accumulation principle when two coordinate systems are used. In this embodiment, the situation of accumulating two coordinate systems is explained, and is similar to the situation of accumulating three or more coordinate systems. As mentioned above, in the back projection, respective angles are distributed over the different coordinate systems to perform the back projection and to generate back projection images in multiple coordinate systems (two systems herein). After the interpolation of an image  601  in the rotation coordinate system  202  on the reference coordinate system through the above interpolation method, an interpolation image  602  is acquired. Further, the interpolation image  602  is accumulated with an image  603  in the reference coordinate system  201  to acquire a final result image, i.e., an image  604  of a scan target. 
       [2-3. Process of CT Image Generation Method] 
       [0091]    Hereafter, based on the figures, the CT image generation method of this embodiment is explained. The CT image generation method of this embodiment analyzes the projection information acquired by scanning a scan target on the scan plane by using X-rays, and generates an image of the scan target. 
         [0092]      FIG. 7  is a flowchart of the CT image generation method of the first embodiment. As shown in  FIG. 7 , the CT image generation method of this embodiment includes: a general-purpose processing step S 1  for establishing multiple coordinate systems on the scan plane; a coordinate determination step S 2  for selecting a coordinate system used for the distance-driven back projection or distance-driven forward projection from multiple coordinate systems established at the general-purpose processing step S 1  on the basis of a projection angle; a distance-driven processing step S 3  of performing the distance-driven back projection or distance-driven projection on the basis of the coordinate system selected at the coordinate determination step S 2  in accordance with a projection angle; and an image information processing step S 4  for generating an image of a scan target on the basis of the image information acquired by performing the distance-driven back projection to the projection information at the distance-driven processing step S 3 . 
       [2-4. Advantageous Effect of First Embodiment] 
       [0093]    Hereafter, based on the figures, an advantageous effect of this embodiment is explained in detail. 
         [0094]      FIG. 8A  and  FIG. 8B  show the model error reduction principle when two coordinate systems are used. In  FIG. 8A  and  FIG. 8B , the horizontal axis shows an angle of the forward projection/back projection, and the vertical axis shows a model error. 
         [0095]    When a different coordinate system is selected in response to a different angle of the forward projection/back projection as shown in  FIG. 8A , the largest model error portions (near 45 degrees/135 degrees/225 degrees/315 degrees) in the single coordinate system shown in  FIG. 1C  are deleted. The model error in the coordinate system corresponding to each projection angle is reduced. Accordingly, as shown in  FIG. 8B , the overall combined model error after the results of the forward projection/back projection at respective angles are combined is obviously reduced in comparison with the distance-driven model error in the single coordinate system in  FIG. 1C , and a low model error is maintained even at each forward projection/back projection angle. 
         [0096]    As mentioned above, according to the CT image generation device and method of the present invention, the model error in the distance-driven forward projection and back projection of the conventional technology can be reduced by performing the distance-driven forward projection and/or back projection by use of multiple image-coordinates systems. As a result, the iterative reconstruction technology in the CT image reconstruction and the reconstruction accuracy of the filtered back projection technology can be enhanced, artifacts of CT images can be reduced, and an actual CT device and the simulation system of the CT device can be improved. 
       3. Second Embodiment 
       [0097]    The second embodiment of the present invention reduces a model error further and increases the reconstruction accuracy by using three or more coordinate systems on the basis of the first embodiment. Hereinafter, differences of the second embodiment from the first embodiment are explained, but the same or similar points as or to the first embodiment are not explained. 
       [3-1. Features of Second Embodiment] 
     [3-1-1. Establishment of Coordinate Systems] 
       [0098]    According to a technical proposal of the present invention, with the increase in coordinate systems, the portions with large errors are reduced, and the combined model error becomes smaller as the number of coordinate systems is larger. However, in the actual execution, since combination calculations increase as the number of coordinate systems is larger, the number of coordinate systems is selectable based on this embodiment. 
         [0099]    In this embodiment, the general-purpose processing unit  41  establishes N number of coordinate systems (N is an integer equal to two or more) on the scan plane on the basis of an accuracy requirement of the CT image generation device  40  or CT image generation system  1 . At the general-purpose processing step S 1 , N number of coordinate systems (N is an integer equal to two or more) are established on the scan plane on the basis of an accuracy requirement of the CT image generation method. As a result, the number of coordinate systems is determined based on the accuracy requirement, and as few coordinate systems as possible are selected on the assumption that the accuracy requirement is met, so that the processing load due to the combination of the coordinate systems can be reduced, and the required CT image reconstruction accuracy is securable. 
         [0100]      FIG. 9A  is a flowchart showing establishment of multiple coordinate systems in the second embodiment.  FIG. 9B  is a schematic view showing a rotation angle of each coordinate system when multiple coordinate systems are established. The process of establishing multiple coordinate systems in  FIG. 9A  is based on the following ideas. In other words, in embodiment, the selection of the number of coordinate systems may use two coordinate systems first, and the number of coordinate systems may be increased until an accuracy requirement is met when it is difficult for two coordinate systems to meet the accuracy requirement. In execution, it is recommended that the number of the coordinate systems be set to the power of two. Part of the calculation time for the result data of the projection and back projection performed in the reference image coordinate system  201  after the increase in the number of the coordinate systems can be saved by repeatedly using the former calculation results. 
         [0101]    In the method for selecting a rotation angle of the coordinate system, when the number K of selected coordinate systems is larger than two, X-axis rotational angles of K−1 number of coordinate systems (the second and following coordinate systems in the figure) are optimally distributed within 0 to 90 degrees as shown in  FIG. 9B . Naturally, other angles may be selected separately, but the rotation angles of K−1 number of coordinate systems must not be the same. 
         [0102]    That is, included angles between respective coordinate axes of multiple coordinate systems established on the scan plane may be equal to each other. In accordance with the principle of even distribution, multiple coordinate systems are established within the scan plane (360 degrees). As a result, as high accuracy as possible is achieved using the small number of coordinate systems, the processing load due to the combination of the coordinate systems is reduced, and as high CT image reconstruction accuracy as possible is securable. Naturally, the included angles between respective coordinate axes of multiple coordinate systems established on the scan plane may be any angle except 0 degree, and different from each other. 
         [0103]    In the explanation of the above specific example, examination is performed since the time of establishing two coordinate systems until the number of coordinate systems is acquired to meet the accuracy requirement. When the number of the coordinate systems has been known to meet the accuracy requirement, the number of the coordinate systems may be determined directly, naturally. 
       [3-1-2. Selection of Coordinate System] 
       [0104]    Similarly to the case where two coordinate systems are used, the coordinate determination unit  42  selects a coordinate system whose coordinate axis and a projection angle form the smallest included angle from multiple coordinate systems, and the selected coordinate system is used for the distance-driven forward projection or distance-driven back projection. As a result, the model error in the distance-driven forward projection and back projection can be minimized. 
         [0000]    [3-2. Case where Three Coordinate Systems are Present] 
         [0105]    As a representative case where three or more coordinate systems are used, the case where three coordinate systems are used is explained in detail based on the figures hereafter. The cases where the other numbers of coordinate systems are used are similar to each other, and not explained here. 
         [0106]      FIGS. 10A ,  10 B, and  10 C are schematic views of respective coordinate systems in the case where three coordinate systems are present.  FIG. 10A  shows a reference coordinate system  204 .  FIG. 10B  shows a rotation coordinate system  205  acquired by rotating the reference coordinate system by 30 degrees (counterclockwise rotation is positive).  FIG. 10C  shows a rotation coordinate system  206  acquired by rotating the reference coordinate system by 60 degrees (counterclockwise rotation is positive). 
         [0107]      FIG. 11  is a schematic view to select a coordinate system based on a projection angle in the case where the number of coordinate systems is three. This case is similar to the case where two coordinate systems are used. A coordinate system whose coordinate axis and the projection angle form the smallest included angle is selected from three coordinate systems for use in the distance-driven back projection or distance-driven forward projection. As shown in  FIG. 11 , angle ranges corresponding to  304 ,  305 , and  306  use the coordinate systems  204 ,  205 , and  206 , respectively. 
         [0108]      FIG. 12A  and  FIG. 12B  are interpolation principle views in the case where three coordinate systems are used. 
         [0109]    Similarly to the case where two coordinate systems are used, a pixel value C 21  (x, y) of a pixel (x, y) of the reference coordinate system  204  (shown by shadow in the figure) acquired by the interpolation to the rotation coordinate system  205  can be calculated by Formula 2, as shown in  FIG. 12A . 
         [0000]        C   21 ( x,y )= ca×A+cb×B+cc×C+cd×D   (2)
 
         [0110]    As shown in  FIG. 12B , a pixel value C 22  (x, y) of a pixel(x, y) of the reference coordinate system  204  (shown by shadow in the figure) acquired by the interpolation to the rotation coordinate system  206  can be calculated by Formula 3. 
         [0000]        C   22 ( x,y )= ca×A+cb×B+cc×C+cd×D   (3)
 
         [0111]    As shown in the figure, ca, cb, cc, and cd in Formula show ratios of image overlapping section areas of the pixel (x, y) in the reference coordinate system and the pixel A, pixel B, pixel C, and pixel Din the rotation coordinate system relative to the pixel area, namely pixel overlapping section area ratios. In Formula, A, B, C, and D show pixel values of the pixel A, pixel B, pixel C, and pixel D in the rotation coordinate system, respectively. 
         [0112]    Similarly to the case where two coordinate systems are used, when three coordinate systems are used, the result after the interpolation of the coordinate system  205  and coordinate system  206  and the image of the coordinate system  204  are accumulated in the distance-driven back projection to acquire a final reconstruction image. For example, an accumulation value I m  (x, y) can be calculated by Formula 4. 
         [0000]        I   m ( x,y )= C   1 ( x,y )+ C   21 ( x,y )+ C   22 ( x,y )  (4)
 
         [0113]    C 1 (x, y) is reconstruction image data of the coordinate system  204 , and C 21 (x, y) and C 22  (x, y) are image data in which the coordinate system  2  and coordinate system  3  are respectively interpolated to the coordinate system  1 . 
         [0114]      FIG. 13A  and  FIG. 13B  show a model error reduction principle when three coordinate systems are used. In  FIG. 13A  and  FIG. 13B , the horizontal axis shows an angle of the forward projection/back projection, and the vertical axis shows a model error. As shown in  FIG. 13A  and  FIG. 13B , when three coordinate systems are selected for different angles of the forward projection/back projection, the overall combined model error after the results of respective forward projections/back projections are combined is obviously reduced relative to the distance-driven model error in the single coordinate system in  FIG. 1C , and simultaneously further reduced relative to the distance-driven model error in the two coordinate systems shown in  FIG. 8B . The distance-driven model error is maintained low in each angle of the forward projection/back projection. 
       4. Third Embodiment 
       [0115]    In the third embodiment of the present invention, the first and second embodiments are applied to the filtered back projection and iterative reconstruction in the CT image reconstruction. Hereafter, differences of the third embodiment from the first and second embodiments are mainly explained. The same or similar points as or to the first and second embodiments are not explained. 
       [4-1. Filtered Back Projection] 
       [0116]    In the back projection, the back projections in different angles are calculated in different coordinate systems, and finally, image results in different coordinate systems are interpolated, and accumulated to final image information. 
         [0117]    When the present invention is applied to the filtered back projection of the CT image reconstruction, the coordinate determination unit  42  selects a coordinate system from multiple coordinate systems established by the general-purpose processing unit  41  to perform the distance-driven back projection to projection information of each projection angle on the projection plane in accordance with the projection angle, the distance-driven processing unit  43  acquires image information in each coordinate system by performing the distance-driven back projection to projection information of each projection angle in accordance with the coordinate system selected by the coordinate determination unit  42 , and the image information processing unit  44  performs interpolation and addition to image information in each coordinate system to acquire image information, and generates an image of a scan target on the basis of acquired image information. 
         [0000]    When the present invention is applied to the filtered back projection of the CT image reconstruction, the following steps are performed. In the coordinate determination step S 2 , in accordance with each projection angle on the projection plane, a coordinate system is selected from multiple coordinate systems established at the general-purpose processing step S 1  to perform the distance-driven back projection to projection information at the projection angle. In the distance-driven processing step S 3 , on the basis of the coordinate system selected in the coordinate determination step  2 , the distance-driven back projection is performed to projection information at each projection angle to acquire image information in each coordinate system. In the image information processing step  4 , interpolation and addition is performed to the image information in each coordinate system to acquire image information, and on the basis of the acquired image information, an image of the scan target is generated. 
         [0118]    Hereafter, a specific example of the present invention applied to filtered back projection is explained based on the figures.  FIG. 14  is a flowchart of the filtered back projection processing of the third embodiment. As shown in  FIG. 14 , first, data filtering is performed to CT projection data (projection information), and after that, the back projection is performed. Then, based on a result of the back projection, a CT image is generated. In the back projection, parameters such as the number of coordinate systems and rotation angles are initialized at Step  701 . At Step  702 , coordinate systems are established based on the parameters, and an initially reset image corresponding to each coordinate system is set. At Step  703 , an interpolation coefficient between an image pixel in each rotation coordinate system and an image pixel in the reference coordinate system is calculated. At Step  705 , a coordinate system whose coordinate axis and a projection angle form the smallest included angle is selected to be a coordinate system for the back projection of the data at the projection angle. At Step  706 , the back projection is performed in the selected coordinate system, and its result is accumulated in the image corresponding to the selected coordinate system. At Step  707 , interpolation calculations of corresponding back projection images in all the coordinate systems are performed for accumulation in the image in the reference coordinate system. 
         [0119]    In the specific example of the above filtered back projection, Step  702  corresponds to the general-purpose processing step S 1  of the present invention, Step  705  corresponds to the coordinate determination step S 2  of the present invention, Step  706  corresponds to the distance-driven processing step S 3  of the present invention, and Step  707  corresponds to the image information processing step S 4  of the present invention. The respective steps in the specific example are applied to a specific modification of the filtered back projection, and be adjustable and changeable in their order in accordance with an actual situation. 
         [0120]    As mentioned above, the present invention is applied to the filtered back projection in the CT image reconstruction. Accordingly, the model error in the distance-driven back projection of the conventional technology is reduced, and reconstruction accuracy of the filtered back projection technology in the CT image reconstruction is increased. Consequently, artifacts of CT images are reduced, and actual CT devices and simulation systems of CT devices can be improved. 
       [4-2. Iterative Reconstruction] 
       [0121]    When the present invention is applied to the iterative reconstruction of the CT image reconstruction, after the distance-driven back projection is performed as mentioned above, accuracy of the reconstruction is increased by performing further at least one iteration of the forward- and back-projections. In the iteration of the forward- and back-projections, projection information is acquired by first performing the distance-driven forward projection to the image information acquired by the distance-driven back projection. After that, image information is acquired by performing distance-driven back projection to the image information acquired by the distance-driven forward projection. 
         [0122]    The back projection has been already explained. In the forward projection, an image for projection is first calculated by interpolation, and mapped to different coordinate systems. Further, based on a projection angle, the images in the different coordinate systems are selected and projected to collect projection data at all the angles and to then generate final projection data. 
         [0123]    When the distance-driven projection is performed to the image information acquired by the distance-driven back projection, the image information processing unit  44  performs interpolation to the image information. Then, image information in each coordinate system is acquired. The coordinate determination unit  42  selects a coordinate system from multiple coordinate systems established by the general-purpose processing unit  41  to perform the distance-driven projection to the image information at each projection angle in accordance with the projection angle. The distance-driven processing unit  43 , on the basis of the coordinate system selected by the coordinate determination unit  42 , performs the distance-driven projection to the image information in the coordinate system at each projection angle to acquire image information at the projection angle, and collects projection information at each projection angle to acquire the projection information. 
         [0124]    When the distance-driven forward projection is performed to the image information acquired by the distance-driven back projection, the following steps are performed. Interpolation is performed to the image information at the image information processing step S 4  to acquire image information in each coordinate system. At the coordinate determination step S 2 , in accordance with each projection angle on the projection plane, a coordinate system is selected from the multiple coordinate systems established at the general-purpose processing step S 1  to perform the distance-driven forward projection to the image information at the projection angle. At the distance-driven processing step S 3 , on the basis of the coordinate system selected at the coordinate determination step S 2 , the distance-driven forward projection is performed to the image information in the coordinate system at each projection angle to acquire projection information at the projection angle, and the projection information at each projection angle is collected to acquire projection information. 
         [0125]    Hereinafter, on the basis of the figures, a specific example in which the present invention is applied to the iterative reconstruction, and a specific example of projection in the iterative reconstruction is mainly explained. 
         [0126]      FIG. 15  is a flowchart showing projection processing of the third embodiment. As shown in  FIG. 15 , in projection processing, CT projection data (projection information) is generated by performing the forward projection (projection) to CT image data (image information). Specifically, at Step  801 , parameters such as the number of coordinate systems and rotation angles are initialized. At Step  802 , coordinate systems are established based on the parameters and an image corresponding to each coordinate system is installed. At Step  803 , an interpolation coefficient between an image pixel in each coordinate system and an image pixel in the reference coordinate system is calculated. At Step  804 , by use of the interpolation method, an image of each coordinate system is acquired from an initial image, in other words, an image in each coordinate system is acquired by interpolating the input image in the reference coordinate system. At Step  806 , a coordinate system is selected based on a projection angle, and the coordinate system whose coordinate axis and the projection angle form the smallest included angle is a coordinate system for the forward projection at the angle. At Step  807 , in the selected coordinate system, the distance-driven forward projection is performed. At Step  808 , the processing ends. 
         [0127]    In the specific example of the above projection, Step  802  corresponds to the general-purpose processing step S 1  of the present invention, Step  806  corresponds to the coordinate determination step S 2  of the present invention, Step  807  corresponds to the distance-driven processing step S 3  of the present invention, and Step  804  corresponds to the image information processing step S 4  of the present invention. Each step in the specific example is applicable to a specific modification of projection, and the order thereof is adjustable and changeable in accordance with an actual situation. 
         [0128]    By performing the distance-driven projection by use of multiple image coordinate systems as mentioned above, the model error in the distance-driven projection of the conventional technology can be reduced. Further, by performing the iterative reconstruction including the distance-driven forward projection and back projection by use of multiple image coordinate systems, the model error in the iterative reconstruction including the distance-driven forward projection and back projection of the conventional technology can be reduced. Accordingly, the reconstruction accuracy of the iterative reconstruction technology that has attracted attention in the CT image reconstruction is increased. Further, artifacts are reduced to further improve actual CT devices and simulation systems of the CT devices. 
       5. Supplement 
       [0129]    As mentioned above, some embodiments and examples of the present invention have been described in detail. The present invention is not limited to these. Further various modifications, combinations, and deletions are possible within the spirit of the present invention. The embodiments acquired by modifications, combinations, and deletions are also contained within the present invention. 
         [0130]    For example, parameters and data of the present invention (for example, projection information, image information, etc.) can be stored in the form such as sinograms (Sinogram) that store and manage projection data, coordinate systems and interpolation coefficients that store and manage coordinate system parameters (numbers, rotation angles, etc.) and interpolation coefficients between coordinate system image pixels, an each-coordinate-system correspondence images that store and manage images corresponding to each coordinate system, and input/output result images that store and manage input (to projection)/output (to back projection) result images. 
         [0131]    For example, the CT image generation system.  1  of the present invention may further include a user interface module that provides a data interface for display, an image printer, etc. Accordingly, a user can easily acquire data such as an image of a scan target, the image being generated from the CT image generation device  40  or CT image generation system  1  of the present invention.