Information processing apparatus, image reconstruction method, and computer-readable medium

Back projection voxels smaller in size than forward projection voxels are created. Back projection is performed by the use of computed pixel values and measured pixel values at intersection points between straight lines connecting an X-ray source with the centroids of the back projection voxels and an X-ray detection panel.

BACKGROUND

Field of Art

The present disclosure relates to an information processing apparatus, an image reconstruction method, and a computer-readable medium, in particular ones suited for use in creation of a reconstructed image by a sequential image reconstruction method.

Description of the Related Art

For example, an X-ray computed tomography (CT) apparatus irradiates a target with X rays from a plurality of directions to create a plurality of X-ray projection images, and computes an X-ray-absorption coefficient inside the target from the plurality of X-ray projection images, and makes an image of their distribution. As an image reconstruction method, there is a method called sequential image reconstruction (or sequential approximate image reconstruction or the like), for example.

By the sequential image reconstruction method, first, an area where an image is to be reconstructed is divided into a plurality of voxels, and an initial image (initial values of the voxels (absorption coefficients)) is given and forward projection is performed. The ratio of a projection image obtained by the forward projection and a projection image detected by an X-ray detection panel through actual projection of X rays is subjected to back projection, and the values of voxels are repeatedly updated until a predetermined condition for completion of computation is satisfied. Japanese Patent No. 5133690 discloses a technique for back projection by such the sequential image reconstruction by which the projection image is interpolated based on the positions of the voxels and back projection is performed by the use of the interpolated projection image.

To obtain an image with few artifacts by the sequential image reconstruction method, it is important that a matrix indicative of forward projection and a matrix indicative of back projection are in a relationship of transposed matrix. It would be easy to satisfy this property when respective matrix elements can be stored in a storage device inside the apparatus. However, when the required size of a reconstructed image is large, the number of the matrix elements grows immensely, and storing those matrix elements in the storage device is not realistic in many cases.

In the computation on forward projection and the computation on back projection, it is not easy to create matrix elements as necessary and, at the same time, execute efficient parallel computation when the matrixes of forward projection and back projection are in the relationship of transposed matrix. This is because, when a computation method is set up such that either forward projection or back projection is suited to parallel computation, the efficiency of parallel computation is generally sacrificed in the other computation in which the other projection acts as a symmetric matrix. For example, when the computation for back projection corresponding to the transposed matrix in the ray-driven computation for forward projection is parallelized, atomic operation sacrificing parallelism is included.

Accordingly, in the reconstruction of a large-sized image, the computation on forward projection and the computation on back projection are executed in parallel by algorithms convenient to their parallel computation, and the relationship of transposed matrix between forward projection and back projection is abandoned in many cases.

SUMMARY

As described above, according to the conventional technique, there is a problem in that it is not easy to shorten the processing time and improve the accuracy of a reconstructed image in the case of performing the computation by the sequential image reconstruction method. An embodiment of the present invention is devised in light of the foregoing circumstances. An embodiment of the present invention may, in the reconstruction of an image by the sequential image reconstruction method, shorten the processing time, and improve the accuracy of the reconstructed image.

An information processing apparatus of an embodiment of the present invention is an information processing apparatus that performs a process for reconstructing an image in a reconstruction area by the use of pixel values based on radiation generated by a radiation source and detected by a detection unit, the apparatus including a forward projection unit that performs forward projection of a plurality of forward projection voxels set in the reconstruction area to create forward projection data and a back projection unit that performs back projection onto back projection voxels smaller in size than the forward projection voxels based on the forward projection data.

DESCRIPTION OF THE EMBODIMENTS

FIG. 1is a diagram illustrating an example of configuration of a radiography system. An X-ray source1as an example of radiation source emits an X ray to an X-ray detection panel2. The X ray emitted from the X-ray source1reaches the X-ray detection panel2(its detection surface) through a photographic subject on a stand. The X-ray detection panel2acquires X-ray projection image data of the photographic subject. The X-ray detection panel2has a plurality of pixels arranged in a two-dimensional matrix pattern, for example. The values of the pixels (pixel values) take values according to the intensity of the X ray. The X-ray imaging apparatus including the X-ray source1and the X-ray detection panel2may be a cone-beam CT apparatus, for example. However, the X-ray imaging apparatus may be any apparatus as far as it is configured to take an X-ray image and is capable of sequential image reconstruction. In addition, the reconstructed image may be a 2D image or a 3D image. The X-ray imaging apparatus as described above can be implemented by a publicly-known technique and detailed explanations thereof will be omitted here.

A control apparatus3controls the positions of the X-ray source1and the X-ray detection panel2, provides an instruction for X-ray irradiation from the X-ray source1, acquires X-ray projection image data obtained by the X-ray detection panel2, and others. A data input/output apparatus4outputs the X-ray projection image data acquired by the control apparatus3, and inputs an instruction from the user into the control apparatus3, and others. A data processing apparatus5reconstructs the image of the photographic subject (for example, tomographic image) by the sequential image reconstruction method on the basis of the X-ray projection image data output from the data input/output apparatus4.

FIG. 2is a diagram illustrating a configuration of hardware in the data processing apparatus5.

Referring toFIG. 2, the data processing apparatus5has a CPU201, a GPU202, a ROM203, a RAM204, an HDD205, an input I/F206, a communication I/F207, an output I/F208, and a bus209.

The CPU201serves as an arithmetic operation unit and a control unit, and controls all or some of the operations in the data processing apparatus5according to various programs recorded in the ROM203, the RAM204, and the HDD205.

The GPU202serves as an arithmetic operation unit and a control unit together with the CPU201. The GPU202controls all or some of operations in the data processing apparatus5according to the various programs recorded in the ROM203, the RAM204, and the HDD205. The GPU202has a plurality of processors and can perform parallel processing by the plurality of processors. In the embodiment, a case of performing parallel processing by the GPU202will be explained as an example.

The ROM203stores programs, arithmetic parameters, and others used by the CPU201or the GPU202. The RAM204stores primarily the programs used by the CPU201or the GPU202, the parameters varying as appropriate at execution of the programs, and others. The HDD205stores the programs and arithmetic parameters used by the CPU201or the GPU202, and others. The program for executing the process described in the flowchart ofFIG. 10described later is stored in the ROM203or the HDD205. In addition, the parameters necessary for executing the programs and the data on reconstructed images obtained by executing the programs are stored in the HDD205.

The input I/F206is an interface for the user to input operations such as a mouse, a keyboard, a touch panel, buttons, switches, levers, and the like, for example. The information necessary for processing by the data processing apparatus5described later (the information to be preset) is input via the input I/F206. The communication I/F207is an interface for transmitting and receiving data between the data processing apparatus5and an external apparatus connected to the data processing apparatus5. The external apparatus is the data input/output apparatus4, for example. Besides, data transmission and reception between the data processing apparatus5and an external apparatus connected to the data processing apparatus5via a network are carried out by the use of the communication I/F207. The output I/F208is an interface for transmitting and receiving data between the data processing apparatus5and a peripheral device connected to the data processing apparatus5. The peripheral device is a computer display, for example.

The foregoing apparatuses are connected to the bus209and can exchange data with one another via the bus209.

The hardware in the data processing apparatus5can be implemented by hardware of a publicly-known information processing apparatus (a personal computer or the like) and is not limited to the configuration illustrated inFIG. 2. In addition, the processor performing parallel computation is not limited to the one with a GPU. For example, a processor performing parallel computation by operating a plurality of CPUs in parallel may be implemented.

In the embodiment, the data processing apparatus5derives an absorption coefficient xJof a voxel J basically according to the following equation (1). The reconstructed image (the image of the photographic subject) is created from the absorption coefficient xJof the voxel J.

In the equation (1), k denotes the number of iterations, ciJand ciJ′denote elements of a projection matrix indicative of weights to an X ray i on voxels J and J′, and yidenotes the pixel value actually detected by the X-ray detection panel2upon receipt of the X ray i.

The data processing apparatus5performs a process of reconstructing an image in a reconstruction area by the use of the pixel values based on the X ray created by the X-ray source1as an example of radiation source and detected by the X-ray detection panel2as an example of detection unit. At this time, the data processing apparatus5performs forward projection processing and back projection processing. The forward projection processing is a process for forward-projecting a plurality of set forward projection voxels onto the reconstruction area to create forward projection data. The back projection processing is a process for back-projecting the forward projection data onto back projection voxels smaller in size than the forward projection voxels. An example of functions of the data processing apparatus5will be explained below.

FIG. 3is a diagram illustrating a functional configuration of the data processing apparatus5. An example of functions of the data processing apparatus5for creating a reconstructed image will be explained below.

A forward projection area creation unit301performs a first voxel creating process. Specifically, the forward projection area creation unit301divides an area of the image to be reconstructed into a plurality of voxels J′. In the following explanation, the area of the image to be reconstructed will be called reconstruction area as necessary. In the embodiment, for ease of explanation, the reconstruction area is a parallelepiped (more specifically, a rectangular parallelepiped or a cube). The voxels J′ are parallelepipeds (more specifically, rectangular parallelepipeds or cubes) of the same size. In the following explanation, the voxels created by the forward projection area creation unit301will be called forward projection voxels as necessary.

Next, the forward projection area creation unit301gives initial values of absorption coefficients xJ′of the forward projection voxels J′ to the forward projection voxels J′. The initial values of absorption coefficients xJ′of the forward projection voxels J′ may be arbitrary values.

A forward projection computation unit302refers to the absorption coefficient xJ′of the forward projection voxels J′ to derive a projection image in the X-ray detection panel2(that is, performing forward projection).FIG. 4is a diagram explaining a method of forward projection.FIG. 4illustrates four forward projection voxels401to404.FIG. 4also describes the absorption coefficients of the four forward projection voxels401to404as x1, x2, x3, and x4, respectively.

A straight line connecting the X-ray source1(X-ray irradiation position) and a pixel (its center) in the X-ray detection panel2constitutes one direction of the X ray i. The forward projection computation unit302determines the projection voxels through which the X ray i on the straight line passes. In the example ofFIG. 4, the forward projection voxels through which the X ray i on a straight line400passes are the forward projection voxels402to404. Then, the forward projection computation unit302derives the lengths by which the X ray i on the straight line400passes through (crosses over) the forward projection voxels402to404as projection matrix elements ci2, ci3, and ci4in the forward projection voxels402to404. Then, the forward projection computation unit302derives the total sum of values obtained by multiplying the absorption coefficients x2, x3, and x4of the forward projection voxels402to404by the elements ci2, ci3, and ci4of the projection matrix in the forward projection voxels402to404. The total sum constitutes a pixel value pi(computed value) detected by the X-ray detection panel2from the X ray i on the straight line400. That is, the forward projection computation unit302carries out a computation in the following equation (2) to derive the pixel value piobtained by the X-ray detection panel2from the X ray i:

In the equation (2), S denotes an aggregation of identification numbers for the forward projection voxels through which the X ray i passes while the X-ray source1and the X-ray detection panel2rotate around the reconstruction area during image taking. The forward projection computation unit302carries out the computation in the equation (2) for at least two X rays i (straight lines connecting the X-ray source1and pixels of the X-ray detection panel2) in parallel. The number of computations to be performed in parallel depends on the performance of the GPU202(the number of processors and the like).

FIG. 5is a diagram illustrating positions where pixel values piare computed by forward projection. As illustrated inFIG. 5, pixels values p1to p4are obtained at intersection points501to504between straight lines connecting the X-ray source1(the center of the X-ray irradiation start position) with four pixels (their centers) in the X-ray detection panel2and the X-ray detection panel2(its detection surface). Similarly, pixel values are obtained for the other pixels in the X-ray detection panel2. These pixel values are computed in parallel.

A back projection area creation unit303performs a second voxel creating process. Specifically, the back projection area creation unit303creates a plurality of voxels J smaller in size than the forward projection voxels J′ in the reconstruction area. In the following explanation, the voxels J created by the back projection area creation unit303will be called back projection voxels J. In the embodiment, the back projection area creation unit303creates the back projection voxels J by dividing each of the forward projection voxels J′ into a plurality of portions by the same method.

FIG. 6is a diagram explaining a method of creating back projection voxels J.FIG. 6illustrates conceptually the state in which the back projection voxels J are created from one forward projection voxel J′.FIG. 6represents the case in which the forward projection voxel J′ and the back projection voxels J are both rectangular parallelepipeds as an example.

The back projection area creation unit303sets division points at which four parallel sides of the forward projection voxel J′ are each divided into n portions, and divides the forward projection voxel J′ such that the division points are passed in the directions vertical to the sides. There are three sets of four parallel sides of the forward projection voxel J′. The back projection area creation unit303divides the forward projection voxel J′ in such a manner as described above for each of the three sets. Accordingly, as illustrated inFIG. 6, the plurality of back projection voxels J is created by dividing the one forward projection voxel J′. In the example ofFIG. 6, the four sides parallel in the height direction are divided into eight portions, the four sides parallel in the lateral direction are divided into five portions, and the four sides parallel in the depth direction are divided into four portions. Therefore, 160 (=8×5×4) back projection voxels J are created from the one forward projection voxel J′.

A back projection computation unit304refers to the pixel values picomputed by the forward projection computation unit302and the pixel values yiactually detected by the X-ray detection panel2to derive the absorption coefficients of the back projection voxels J (that is, performing back projection).

FIG. 7is a diagram illustrating an example of pixel values for use in back projection.FIG. 7illustrates four back projection voxels701to704out of the back projection voxels J in the reconstruction area, created by dividing one forward projection voxel700.

Straight lines711to714connecting the X-ray source1(the center of the X-ray irradiation start position) with centroids701ato704a(centers) of the back projection voxels701to704constitute respective directions of the X ray i. The back projection computation unit304performs back projection by the use of the pixel values at intersection points721to724between the straight lines711to714and the X-ray detection panel2(its detection surface). That is, only one pixel value at one position is referred to in order to derive the absorption coefficient of one back projection voxel J.

As illustrated inFIG. 7, the intersection points721to724between the straight lines711to714and the X-ray detection panel2(detection surface) do not necessarily fall at centers731to736of pixels of the X-ray detection panel2. Accordingly, in the embodiment, the back projection computation unit304derives the pixel values at the intersection points721to724by interpolating the pixel values at the centers731to736of the pixels around the intersection points. In the following description, the case of deriving the pixel values at the intersection points721to724by performing bilinear interpolation depending on the distances between the intersection points721to724and the centers731to736of the pixels around the intersection points will be explained as an example.

Referring toFIG. 8, the distances between the intersection point723and the centers731and732of the pixels around the intersection point723are set as D1and D2, respectively. In addition, the pixel values at the centers731and732of the pixels around the intersection point are set as v1and v2, respectively. Accordingly, pixel value V at the intersection point723is expressed by the following equation (3):
V=(D2×v1+D1×v2)/D3  (3)

The back projection computation unit304computes the foregoing pixel value V from each of the pixel value picomputed by the forward projection computation unit302and the pixel value yiactually detected by the X-ray detection panel2. In the following explanation, the pixel value determined by the equation (3) from the pixel value picomputed by the forward projection computation unit302will be called computed pixel value as necessary. In addition, the pixel value determined by the equation (3) from the pixel value yiactually detected by the X-ray detection panel2will be called measured pixel value as necessary.

As illustrated inFIG. 8, the distances D1, D2, and D3described above are determined at the intersection point723. Therefore, the computed pixel value P1at the intersection point723is determined by the following equation (3a) from the pixel values p1and P2computed by the forward projection computation unit302:
P1=(D2×p1+D1×p2)/D3  (3a)

In addition, the measured pixel value Y1at the intersection point723is determined by the following equation (3b) from the pixel values y1and y2actually detected by the X-ray detection panel2:
Y1=(D2×y1+D1×y2)/D3  (3b)

Referring toFIG. 7, the computed pixel values and the measured pixel values at the other intersection points721and722to724can also be determined in the same manner as the computed pixel value P1and the measured pixel value Y1.FIG. 9is a diagram explaining an example of a method of back projection.FIG. 9illustrates16back projection voxels901to916.

Of the back projection voxels, the back projection computation unit304determines the back projection pixels whose centroids are passed through by the X rays i (the straight lines711to714connecting the X-ray source1with the centroids701ato704aof the back projection voxels701to704). In the example illustrated inFIG. 9, the X ray i passes through the centroid of the back projection voxel909. The back projection computation unit304derives the length by which the X ray i passes through (crosses over) the determined back projection voxel909as an element Ci9of the projection matrix in the back projection voxel909. Then, the back projection computation unit304acquires the measured pixel value Yiand the computed pixel value Piat the intersection point between the X ray i and the X-ray detection panel2(its detection surface). Then, the back projection computation unit304derives the value obtained by multiplying the ratio of the computed pixel value Pito the measured pixel value Yi(=Pi/Yi) by the projection matrix element Ci9as absorption coefficient xJof the back projection voxel909. That is, the back projection computation unit304derives the absorption coefficient xJof the back projection voxel J by carrying out a computation in the following equation (4):

In the equation (4), T denotes an aggregation of X rays i passing through the centroid of the back projection voxel J while the X-ray source1and the X-ray detection panel2rotate around the reconstruction area at the time of image taking. The back projection computation unit304derives the absorption coefficients xJof all the back projection voxels J in such a manner as described above. The back projection computation unit304carries out the computation in the equation (4) for at least two back projection voxels J in parallel. The number of computations performed in parallel (the number of the absorption coefficients xJof the back projection voxels J determined in parallel) depends on the performance of the GPU202(the number of processors and the like). To compute the absorption coefficients xJof the back projection voxels J, the back projection computation unit304secures memory areas necessary for the computation for the individual back projection voxels J.

An image updating unit305divides the absorption coefficient xJof the back projection voxel J by a coefficient CJ, and then multiplies the obtained value by final absorption coefficient xJ(k)of the back projection voxel J at the number of iterations k. The resulting value constitutes a final absorption coefficient xJ(k+1)of the back projection voxel J at the number of iterations k+1. The absorption coefficient xJof the back projection voxel J is computed by the back projection computation unit304. The coefficient CJis intended to standardize the coefficient of the back projection voxel J. (Final) absorption coefficient xJ(0)of the back projection voxel J at the number of iterations k (=0) is given as an initial value. For example, the initial value of (final) absorption coefficient of the back projection voxel J can be obtained by multiplying the initial value of the absorption coefficient xJ′of the forward projection voxel J′ to which the back projection voxel J belongs by a weight coefficient of the back projection voxel J. The weight coefficient of the back projection voxel J can be the ratio of the cubic content of the back projection voxel J to the cubic content of the forward projection voxel J′ to which the back projection voxel J belongs, for example.

The image updating unit305derives the final absorption coefficient xJ(k+1)of the back projection voxel J by performing the computations based on the foregoing equation (1) as described above. In the embodiment, the part in the parentheses on the right side of the equation (1) except for 1/CJis replaced by the contents of the equation (4).

A conversion unit306converts the final absorption coefficient xJ(k+1)of the back projection voxel J updated by the image updating unit305into the absorption coefficient of the forward projection voxel J′ to which the back projection voxel J belongs. For example, the conversion unit306can derive the total sum of values obtained by multiplying the final absorption coefficients xJ(k+1)of the back projection voxels J belonging to the forward projection voxel J′ by the weight coefficients of the back projection voxels J as the absorption coefficient of the forward projection voxel J′. The weight coefficients of the back projection voxels J can be the ratios of the cubic contents of the back projection voxels J to the cubic content of the forward projection voxel J′ to which the back projection voxels J belong. The conversion unit306refers to the final absorption coefficients xJ(k+1)of the back projection voxels J belonging to the forward projection voxel J′ to derive the absorption coefficient of the forward projection voxel J′, and releases the memory areas secured for deriving the absorption coefficients of the back projection voxels J.

A determination unit307determines whether to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J. For example, when the total sum of absolute values of differences between the absorption coefficients xJ(k)and xJ(k+1)of the back projection voxel J at the numbers of iterations k and k+1 is equal to or smaller than a threshold, the determination unit307determines to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J. Alternatively, the determination unit307may determine to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J when a predetermined number of iterations is passed.

When the determination unit307determines not to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J as described above, the forward projection computation unit302performs the following process. That is, the forward projection computation unit302updates the current value of the forward projection voxel J′ to the latest absorption coefficient of the forward projection voxel J′ derived by the conversion unit306. Then, the forward projection area creation unit301to the determination unit307perform their processes with the use of the updated absorption coefficient of the forward projection voxel J′. This processing is performed until the determination unit307determines to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J.

When the determination unit307determines to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J, an output unit308stores the latest absorption coefficient of the forward projection voxel J′ derived by the conversion unit306as data of the reconstructed image. Then, the output unit308creates display data of the reconstructed image on the basis of the data of the reconstructed image and displays the reconstructed image on a computer display. Besides, the output unit308may transmit the data of the reconstructed image to an external device.

The output unit308may display the reconstructed image on the computer display each time the absorption coefficient of the forward projection voxel J′ is obtained from the conversion unit306, regardless of the result of determination by the determination unit307. In this case, the determination unit307may determine whether to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J on the basis of the result of the user operation on the reconstructed image displayed on the computer display.

Next, an example of processing by the data processing apparatus5will be explained with reference to the flowchart ofFIG. 10.

At step S1001, the forward projection area creation unit301divides the reconstruction area into a plurality of portions to create a plurality of forward projection voxels J′. Then, the forward projection area creation unit301sets initial values to the plurality of forward projection voxels J′.

Next, at step S1002, the back projection area creation unit303creates back projection voxels J smaller in size than the forward projection voxels J′ in the reconstruction area (seeFIG. 6and the like).

Next, at step S1003, the forward projection computation unit302sets the number of iterations k to zero.

Next, at step S1004, the forward projection computation unit302performs forward projection. Specifically, the forward projection computation unit302performs the computation in the equation (2) to derive the pixel value pi(computed value) obtained by the X-ray detection panel2from the X ray i. As described above, the forward projection computation unit302derives the pixel values piin parallel for a plurality of X rays i.

Next, at step S1005, the back projection computation unit304performs back projection. Specifically, the back projection computation unit304derives the computed pixel values Pi, from the pixel values piobtained at step S1004, at intersection points on the X-ray detection panel2between the straight lines connecting the X-ray source1with the centroids of the back projection voxels J (see the equation (3a),FIGS. 7 and 8, and the like). In addition, the back projection computation unit304derives the measured pixel values Yiat the intersection points on the X-ray detection panel2between the straight lines connecting the X-ray source1with the centroid of the back projection voxel J (see the equation (3b),FIGS. 7 and 8, and the like). Then, the back projection computation unit304carries out the computation in the equation (4) to derive the absorption coefficients xJof the back projection voxels J. As described above, the back projection computation unit304derives the absorption coefficients xJin parallel for the plurality of back projection voxels J.

Next, at step S1006, the image updating unit305derives the final absorption coefficient xJ(k+1)of the back projection voxels J by the use of the absorption coefficients xJof the back projection voxels J derived at step S1005(see the equations (1) and (4), and the like).

Next, at step S1007, the conversion unit306converts the final absorption coefficient xJ(k+1)of the back projection voxel J derived at step S1006into the absorption coefficient of the forward projection voxel J′ to which the back projection voxel J belongs.

Next, at step S1008, it is determined whether to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J. As a result of the determination, when it is not to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J, the process moves to step S1009.

At step S1009, the forward projection computation unit302updates the current value of the forward projection voxel J′ to the latest absorption coefficient of the forward projection voxel J′ derived at step S1007. Then, the process moves to step S1010, and the forward projection computation unit302adds 1 to the number of iterations k. Afterwards, step S1004and the subsequent steps are performed with the use of the absorption coefficient of the forward projection voxel J′ updated at step S1009. In this manner, at step S1008, steps S1004to S1010are repeatedly performed until it is determined to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J.

When it is determined at step S1008to terminate the computation of the absorption coefficient xJ(k+1)of the back projection voxel J, the process moves to step S1011. At step S1011, the output unit308stores the latest value of the forward projection voxel J′ derived at step S1007as data of the reconstructed image. Then, the output unit308processes the data of the reconstructed image to data suited to the apparatus as the destination of the data and outputs the same. Then, the process according to the flowchart ofFIG. 10is terminated.

In the embodiment as described above, the back projection voxels J smaller in size than the forward projection voxels J′ are created. Back projection is performed by the use of the computed pixel values Piand the measured pixel values Yiat the intersection points721to724between the straight lines connecting the X-ray source1with the centroids of the back projection voxels J and the X-ray detection panel2. Therefore, it is possible to suppress missing of information on projection image at the time of back projection and perform appropriate parallel computation. Accordingly, in reconstructing the image by the sequential image reconstruction method, it is possible to achieve both shortened processing time and improved image accuracy. In addition, it is possible to suppress artifacts in the reconstructed image caused by mismatching of forward projection and back projection, and suppress increase in the capacity of the used internal storage device, thereby reducing the memory capacity for use in reconstruction processing.

In the embodiment, the forward projection voxels are divided into back projection voxels as an example. However, when the size of the back projection voxels is made smaller than the forward projection voxels, it is not necessarily required to create the back projection voxels by dividing the forward projection voxels. For example, the reconstruction area may be divided regardless of the forward projection voxels to create the back projection voxels smaller in size than the forward projection voxels.

In addition, in the embodiment explained above, the shape of the forward projection voxels and the back projection voxels is parallelepiped as an example. However, the shape of the forward projection voxels and the back projection voxels is not limited to being parallelepiped. To reconstruct a 3D image, an arbitrary solid shape can be employed for the shape of the forward projection voxels and the back projection voxels. To reconstruct a 2D image, an arbitrary plane shape can be employed for the shape of the forward projection voxels and the back projection voxels. In addition, the forward projection voxels and the back projection voxels may be different in shape.

In addition, in the embodiment explained above, the back projection voxels are the same in size as an example. However, the back projection voxels are preferably different in size according to the distance from the X-ray source1.FIGS. 11A and 11Bare diagrams illustrating variation examples of a method of setting the back projection voxels. Specifically,FIG. 11Ais a diagram illustrating pixel values taken into the back projection voxels of the same size.FIG. 11Bis a diagram illustrating an example of pixel values taken into the back projection voxels different in size according to the distance from the X-ray source1.

As illustrated inFIGS. 11A and 11B, the irradiation range of the X ray becomes wider in areas at larger distances from the X-ray source1. In addition, in the embodiment, back projection is performed by the use of the pixel values at the intersection points between the straight lines connecting the X-ray source1with the centroids of the back projection voxels and the X-ray detection panel2. Therefore, as illustrated inFIGS. 11A and 11B, it is possible to suppress missing of the pixel values of the X-ray detection panel2in the area distant from the X-ray source1even with the use of a relatively large back projection voxels1101.

In contrast, as illustrated inFIG. 11A, when a back projection voxel1102of the same size as that of the back projection voxel in an area distant from the X-ray source1is used in the area close to the X-ray source1, the following result is obtained. That is, in the area of the back projection voxel1102, the pixel value at an intersection point1103is reflected on the absorption coefficient of the back projection voxel1102but the pixel values at intersection points1104to1106are not reflected on the absorption coefficient of the back projection voxel1102.

Meanwhile, as illustrated inFIG. 11B, creating small back projection voxels1107to1110in an area close to the X-ray source1allows the pixel values at the intersection points1103to1106to be reflected on the absorption coefficients of the back projection voxels1107to1110.

As described above, it is preferred that the back projection voxels are made smaller in areas at shorter distances from the X-ray source1. However, it is not necessarily required to do this in the entire reconstruction area. For example, this may be done only in part of the reconstruction area depending on the arrangement of the X-ray source1and the X-ray detection panel2, the required accuracy of the reconstructed image, and the like. That is, (at least one) back projection voxel smaller in size than the back projection voxels in the areas at relatively long distances from the X-ray source1needs to be in the area relatively at a short distance from the X-ray source1.

In addition, in the embodiment, back projection is performed by the use of the computed pixel values Piand the measured pixel values Yiat the intersection points721to724between the straight lines connecting the X-ray source1with the centroids of the back projection voxels J and the X-ray detection panel2as an example. However, it is not necessarily required to use the centroids of the back projection voxels J as far as arbitrary points in the back projection voxels J are used as representative points.

The foregoing embodiment is a mere exemplification for carrying out the present invention. The technical scope of the present invention should not be interpreted in a limited way. That is, the present invention can be carried out in various manners without deviating from its technical ideas or major features.

Other Embodiments

This application claims the benefit of Japanese Patent Application No. 2015-236712, filed Dec. 3, 2015, which is hereby incorporated by reference herein in its entirety.