JPH04343836A - Device for x-ray computerized tomograph - Google Patents

Abstract

PURPOSE:To provide an X-ray CT device of simple constitution which is capable of taking images of a number of slices in a short time. CONSTITUTION:Helical scan is performed using a coned beam and X-ray projection data are detected by a two-dimensional X-ray detector. The coned beam is regarded as a beam parallel to the direction of slice thickness, and of the projection data those which correspond to a certain slice position and positions adjacent thereto through 360 degrees are selected and reconfiguration of normal convolution/backprojection method is performed according to the selected data and thereby slices are reconfigured.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an X-ray computed tomography apparatus (hereinafter referred to as an X-ray CT apparatus) that performs helical scanning using a conical or pyramidal X-ray beam.

0002

2. Description of the Related Art X-ray CT apparatuses are widely used not only for medical purposes but also for industrial purposes as devices for taking tomographic images of subjects. In particular, in medical applications, it occupies an important position as an image diagnostic device. Although the subject is three-dimensional, since the X-ray CT apparatus images (scans) tomographic images (slices), it is necessary to scan a large number of slices in order to image the entire subject. The scanning speed of recent X-ray CT devices is much faster than that of earlier ones.
Although the overall shooting time has become shorter, there is a demand for shooting even faster. This is because (1) the number of slices scanned is increasing as CT devices become more important, and (2) in the case of a method called dynamic scanning, the movement of contrast medium injected into the body is photographed. This is because short-time photography is required. In order to shorten the imaging time, two types of methods have been proposed and put into practical use. One is a helical scan method, and the other is a method using a cone beam.

The method using a cone beam is, as shown in FIG. The projection data obtained by projecting the
This is a method of collecting data using a dimensional X-ray detector 14. For convenience of the following explanation, coordinates are determined as shown in FIG. Here, the slice plane is defined by an X-Y coordinate plane, and the slice thickness direction is defined as the Z axis.

As shown in FIG. 15, at a certain slice position (a certain position z in the Z direction) in a normal scanning method, at a certain projection angle (rotation angle θ with respect to the Y axis in the XY plane). The collected projection data is P(z, θ)
shall be. The normal scanning method is a method in which a scanning position is fixed and 360-degree projection data is collected, and the scanning position is sequentially moved in the Z direction to collect the next 360-degree projection data. Therefore, the projection data P(z, θ) is collected in order from 0 degrees to 360 degrees for each projection position, as shown in (1), (2), . . . in FIG. In this case, the scan position and the slice position are the same, and the image at that position is reconstructed using 360-degree projection data in one vertical column at the same projection position.

Next, the helical scan method will be explained. The projection data collected using this method is expressed as PH(z, θ)
shall be. In helical scanning, the scanning position z is changed in synchronization with the change in the projection angle θ, so the projection data P
H(z, θ) is collected in the order shown in FIG. In order to reconstruct an image at a certain slice position, one vertical column of 360-degree projection data is required, but in the helical scan method, one vertical column of 360-degree projection data does not exist. Therefore, it is necessary to virtually synthesize the projection data PH(z, θ) in one vertical column. This means that the same projection angle θ
A common method is to interpolate two or more pieces of data having different scan positions z. For example, projection data I shown by a broken line circle is obtained by interpolating the left and right projection data L and R according to the position in the Z direction.

As is clear from FIGS. 16 and 17, the helical scan method requires a shorter overall scan time than the normal scan method. However, since projection data is interpolated in the slice direction, there are drawbacks such as large blurring in the slice thickness direction and poor resolution in the slice direction.

Next, a conventional scanning method using a cone beam will be explained. In the normal scan method and the helical scan method, all projection data is perpendicular to the Z-axis, but in the case of a cone beam, it is spread in the Z-axis direction as shown in FIG. Therefore, the scan position z of the projection data differs depending on the position in the X and Y directions. Therefore, the scan position of the projection data is defined as a position on the Z axis (x=y=0), and this is defined as PC(z, θ). As shown in FIG. 18, when a cone beam is used, a large number of projection data can be collected simultaneously. Also, like the normal scanning method, the scanning position is fixed while 360-degree projection data is being collected. Therefore, the projection data PC(z, θ
) are collected in the order shown in FIG.

[0008] In each of FIGS. 16, 17, and 19, one circle represents one projection data, but the projection angles with respect to the Z-axis direction are not the same. In the case of FIGS. 16 and 17, all projection data is perpendicular to the Z axis, so projection data at projection angles 180 degrees apart become projection data facing each other, as shown in FIG. 20(a). . On the other hand, in the case of a cone beam, the center of the slice position is the same as that shown in FIG. 20(a), but the projection data begin to intersect as shown in FIG. 20(b) as it moves away from the center. This angle increases in proportion to the deviation from the center.

Therefore, X-ray C using a cone beam
Reconfiguration in the T device becomes a mathematically very difficult problem. Therefore, although some approximations are made to reconstruct the
Slices far from the center have poor accuracy.

The simplest method for reconstructing an X-ray CT device using a cone beam is to assume that the X-ray tube is located very far away and that all projection data of the cone beam are perpendicular to the Z axis. It is an approximation that there is. As a result, images can be reconstructed using the convolution backprojection method, similar to normal scanning. However, this approximation does not have sufficient accuracy in slices away from the center.

Another approximate reconstruction method is described in Reference 1 (L.
A. Feldkamp, et. al: Prac
tical conebeam algorithm,
J. Opr. Soc. Am. A, 6, p
p. 612-619, 1980) is well known. Although this method has better accuracy than the above-mentioned methods, there are problems such as the reconstruction is complicated, the accuracy varies depending on the slice, and even this method is not sufficient.

[0012] In this way, in order to shorten the photographing time,
Both of the two conventionally proposed methods have advantages and disadvantages, and no method has been realized that has a simple configuration, is highly accurate, and is capable of scanning a large number of slices in a short period of time. Note that a system that combines these two methods has been researched, but has not been put into practical use. For example, see Reference 2 (Hiroyuki Kudo, Tsuneo Saito, "Three-dimensional CT image reconstruction from conical beam projection using helical scanning", M.
The reconstruction method described in BE88-63, 9-16) assumes that the subject is small, and the reconstruction is complicated and impractical.

[0013]

[Problems to be Solved by the Invention] The present invention has been made to address the above-mentioned circumstances, and its purpose is to provide an X-ray CT device with a simple configuration that can image a large number of slices in a short time. It is to be.

Another object of the present invention is to provide a helical scan type X-ray CT apparatus using a cone beam, which has good accuracy and whose accuracy does not depend on the slice position.

[0015]

[Means for Solving the Problems] The X-ray CT apparatus according to the present invention includes a means for irradiating a subject with cone-shaped X-rays, and a means for changing the projection angle of the X-rays. A helical scan means for changing the projection position; a two-dimensional detection means for detecting X-rays transmitted through the subject and collecting projection data of the subject; and a slice position, out of the projection data collected by the two-dimensional detection means. and means for reconstructing a tomographic image at the slice position using projection data at a projection position adjacent to the slice position.

[0016]

[Operation] According to the X-ray CT apparatus of the present invention, a helical scan is performed using cone-shaped X-rays, and normal reconstruction is performed by regarding the cone beam as a beam parallel to the slice thickness direction. With this configuration, multiple slices can be scanned in a short time, and while interpolation of projection data is not required, errors do not vary depending on the slice position, and images with less blur in the slice thickness direction can be obtained.

[0017]

[Example] Hereinafter, with reference to the drawings, X-ray CT according to the present invention
An example of the device will be described. First, a helical scan method using a cone beam according to the present invention will be explained with reference to FIG. A pyramid-shaped X-ray (
A two-dimensional X-ray detector 14 such as an image intensifier collects projection data based on the X-rays transmitted through the subject 18. The X-ray tube 10 and the two-dimensional detector 14 rotate around the subject 18 around the Z-axis along the body axis of the subject 18, and at each projection angle at a predetermined angle between 0 degrees and 360 degrees. Collect projection data. At that time,
In synchronization with the rotation of the X-ray tube 10 and the two-dimensional detector 14, the bed 16 on which the subject 18 is placed is moved in the Z-axis direction. In this scan, assuming that the subject 18 is stationary, the X-ray tube 10 moves along a helical trajectory as shown in FIG. Therefore, projection data is also collected in a helical manner. In the case of this helical scan method, the feed amount of the bed for a projection angle of 360 degrees is determined by the spread width of the beam in the Z-axis direction (here, the Z-axis of the two-dimensional detector
axial length).

FIG. 3 is a diagram of the two-dimensional detector 14 viewed from directly above. When an image intensifier is used as the two-dimensional detector 14, data is sampled and collected for each rectangular area surrounded by the grid shown in FIG. Figure 3
The vertical direction in FIG. 15 is the spreading direction of the fan beam shown in FIG. 15, and this is generally called the channel direction. The lateral direction is generally called the slice direction. Therefore, a collection of data in the vertical direction in FIG. 3 constitutes one projection data. The sampling pitch in the channel direction is equal angle, and one projection data has 512 channels here. Since the X-rays are irradiated from almost directly above, the projection data near the center is almost the same as the projection data of the normal scanning method. The length d of each rectangle in the Z direction is set to be equal so that sampling is performed at equal intervals in the Z axis direction, that is, the slice direction.

The projection data collected by the scan of the present invention will be explained. As in the case of using a normal cone beam, the projection data in this case also has a spread in the Z-axis direction as shown in FIG. Therefore, the scan position z of the projection data differs depending on the position in the X and Y directions. Therefore, here we set the scan position of the projection data on the Z axis (x=y
= 0), and let this be PCH (z, θ). When one PCH (z, θ) is indicated by one circle as in the case of FIG. 18, the projection data PCH (z, θ) are collected in the order shown in FIG.

A certain slice, for example zt in FIG.
Consider the case of reconstructing slices in . In order to reconstruct this slice, projection data of 360 degrees (or 180 degrees + fan angle in the case of half scan) at this position is required, so from among all projection data, projection data at position zt is required. , that is, the projection data in one vertical column in FIG. 4 is collected. However, in reality it is 36 in a vertical row.
Since there is no projection data at 0 degrees, projection data at a position adjacent to zt is collected. These projection data are indicated by black circles in the figure.

Since the projection angles in the Z-axis direction of the projection data collected in this manner are not the same, the projection data of projection angles 180 degrees apart are as shown in FIG. Therefore,
Reconstruction of this projection data is also a very difficult problem mathematically, but when comparing FIG. 5 with FIG. 20(b) in the case of the conventional method using a cone beam, there are the following characteristics. 1) In the case of the present invention shown in FIG. 5, the intersecting angle is smaller than in the conventional example shown in FIG. 20(b). 2) The intersection angle in FIG. 20(b) varies depending on the slice position, but in the case of FIG. 5, the distribution of the intersection angle does not depend on the slice position.

Therefore, considering that the X-ray tube 10 is quite far from the Z-axis, it is assumed that all projection data is perpendicular to the Z-axis, that is, the cone beam is parallel to the slice thickness direction. There is also little error. In this way, the image can be reconstructed using the convolution backprojection method, similar to normal scanning.

Therefore, if the following method is used, the helical scanning method using a cone beam will have good accuracy, and the accuracy will not depend on the slice position.
Reconfiguration can be performed. That is, 1) Helical scanning is performed using a cone beam to collect projection data.

2) The position of the projection data in the Z direction is defined as the position where the projection data crosses the Z axis, and the projection data at the same position and adjacent position as the slice position are selected from among all the projection data at a projection angle of 0. Collect about ~360 degrees. 3) Perform convolution backprojection on each collected projection data, assuming that the projection data is perpendicular to the Z-axis.

A first embodiment of the present invention based on this principle will be described. FIG. 6 is a system block diagram in an embodiment of the present invention. Here, an example will be described in which the present invention is applied to a so-called third generation X-ray CT apparatus, and an image is reconstructed using 360-degree projection data. The output of the two-dimensional detector 14 is supplied to a storage device 20. The storage device 20 includes a raw data storage section 20a, an edited raw data storage section 20b, and a reconstructed image storage section 20c.
has. Data in storage device 20 is supplied to reconfiguration device 24 via bus line 22 . The output of the reconstruction device 24 is stored in the reconstructed image storage section 20c and displayed on the image display device 26. A central processing unit (CPU) 28 that performs overall control is connected to the bus line 22. C
An operation console 30 is connected to the PU 28 for allowing the operator to set scan conditions as appropriate. Here, operation console 3
0 specifies the beam width in the Z-axis direction and the total number of scans in addition to the scan conditions set in a normal X-ray CT apparatus in order to command a cone beam helical scan. However, unlike normal helical scanning, the table feed speed is linked to the beam width in the Z-axis direction, so there is no need to specify it.

The CPU 28 controls the X-ray generator 32 including the X-ray tube 10, the bed 16, and the two-dimensional X-ray detector 14 to perform cone beam helical scanning. X-ray generation section 3
2 is paired with a two-dimensional X-ray detector 14 while irradiating the subject with cone beam X-rays, in the body axis direction (Z-axis) of the subject.
Rotate around the center of rotation. The two-dimensional X-ray detector 14 converts the projection data of the X-rays transmitted through the subject into digital values and stores them in the first raw data storage section 20a of the storage device 20. The projection data is sampled as described above in FIG.

The bed 16 moves in the Z-axis direction in synchronization with the rotation of the X-ray generator 32 and the two-dimensional X-ray detector 14. The moving speed is set so that the bed 16 is moved by the beam width in the Z-axis direction for one rotation of the X-ray generator 32 and the two-dimensional X-ray detector 14.

Once projection data of 360 degrees or more has been collected in the raw data storage unit 20a, edit the raw data (select projection data to be used for reconstructing a certain slice) and reconstruct the image using the following procedure. conduct.

As shown in FIG. 3, the width of the projection beam in the Z direction on the Z axis (the length of the two-dimensional detector in the Z direction in the example) is L, the sampling interval of the projection data in the Z direction is d, Let N=L/d. Further, as shown in FIG. 4, when the interval between projection angles of projection data is h and the number of projections per rotation is M, M=360/h. The total number of scans is S
N (this is specified by the operator) and the total number of projections is MM, then MM=M×SN.

Let M/N be the parameter RMN. RMN
is generally a fairly large number, so here 3≦R
Let it be MN. Furthermore, here, RMN is an integer. However, even when RMN is not an integer, implementation can be performed in substantially the same manner as in the embodiment.

In FIG. 4, since the first vertical column is the slice position, the projection data of the single vertical column is necessary, but since it may not exist, the projection data of adjacent positions are also selected as shown by black circles.

Here, images that can be reconstructed (number of slices)
As shown in Fig. 4, GN=N×(
SN-1). Also, set the position of the first slice to Z=
Set to 0.

Let the number of projections projected (and collected) so far be a parameter MC. MC is two-dimensional X-ray detector 1
4 is updated every time N pieces of projection data of one projection are stored in the storage unit 1. This update is performed independently from the flowchart below.

In FIG. 4, the numbers of N projection data collected in one projection are 1, 2, . . . N from the left. When the projection number is m and the projection data number is n, each projection data in FIG. 4 can be expressed as PCH (m, n).

The raw data edited for image reconstruction is stored in the edited data storage section 22b of the storage device 20. This edited raw data is represented by GCH (Gi, Gm). Here, Gi is the slice (image) number, Gi = 1 to G
It is N. Also, Gm is the projection data number, and Gm=
1 to M.

FIG. 7 is a flowchart showing the main operating procedures of this embodiment. First, in step #1000,
Initialize the necessary data. The data to be initialized will be described later. In step #2000, M pieces of projection data necessary for reconstructing the Gi-th slice are selectively read from the raw data PCH (m, n) in the raw data storage unit 20a, and these are Raw data GCH (Gi, Gm)
It is written into the edited data storage section 22b as follows. The details will be described later.

At step #3000, the reconstruction device 24 reconstructs the Gi-th slice. Reconstruction is performed using the convolution backprojection method. The projection data used for reconstruction is GCH (Gi, G
m) (here, Gm=1 to M).

At step #4000, the Gi-th slice is stored in the reconstructed image storage section 20c of the storage device 20. At this time, the slice position z is also stored. Step #5
At 000, the Gi-th slice is displayed on the image display device 26. In step #6000, z←z+d is set in order to update the slice position. In step #7000, Gi←Gi+1 is set to update the slice number.

At step #8000, in order to determine whether processing of all slices has been completed, it is determined whether Gi≦GN. If YES, the process returns to step #2000 and processes the next slice. If no, that is, if Gi>GN, processing of all slices has been completed, and the operation is completed.

FIG. 8 is a flowchart showing details of the initialization in step #1000 of FIG. Step #
At 1100, to initialize the slice position, z=
Set to 0. At step #1200, Gi=1 is set to initialize the slice number. At step #1300, raw data PCH (M+1, 1) is converted to edited data GCH (
1,1), mz=M+1. At step #1400, nz is set to 1, and the initialization ends.

FIG. 9 is a flowchart showing details of editing the raw data in step #2000 of FIG. In step #2100, initialization necessary for editing this slice is performed. The data to be initialized will be described later. Step #2
At 200, it is determined whether m≦MC in order to determine whether collection of necessary projection data has been completed. If yes, immediately execute the next step #2400. If no, i.e. m>MC, step #2
After waiting a certain period of time at step 300, the next step #2400 is executed. This is because this embodiment adopts a method in which projection data editing and image reconstruction are performed in parallel with scanning so that images can be viewed quickly, so editing and image reconstruction are faster than scanning speed. In this case, the projection data may not be collected in time, so the user waits for the projection data to be collected. Note that this embodiment may be modified so that projection data editing and image reconstruction are performed after scanning is completed, but in that case, these steps #2200 and
#2300 is unnecessary.

[0042] In step #2400, raw data storage section 2
The projection data PCH (m, n) of 0a is written into the edited data storage section 20b as projection data GCH (Gi, Gm) edited for reconstruction. As a result, the projection data indicated by the black circles shown in FIG. 4 is selected. At step #2500, m,
Update n. The details will be described later. At step #2600, Gm←Gm+1. Step #27
00, it is determined whether Gm≦M in order to determine whether it is necessary to continue editing. If yes, return to step #2200. If no, step #28
At 00, mz and nz are updated and editing of the raw data is completed. The details will also be described later.

FIG. 10 is a flowchart showing details of the initialization in step #2100 of FIG. In step #2110, Gm=1 is set to initialize the projection data number Gm of GCH (Gi, Gm). Step #
At 2120, m←mz. At step #2130,
Let n←nz. At step #2140, {(RMN+
1)/2} is set to r, and the initialization is completed.

FIG. 11 is a flowchart showing details of updating m and n in step #2500 of FIG. In step #2510, set m←m+1, and in step #25
20, r←r+1. At step #2530, r
Determine whether ≦RMN. If yes, complete the update. If no, in step #2540, r=1
Then, in step #2550, n←n-1, and in step #2560, it is determined whether n>0. If yes, complete the update. If no, step #25
70, set n=N, and in step #2580, m←m−
Set it to M and end the update. As a result, the projection data indicated by the black circles shown in FIG. 4 is selected.

FIG. 12 is a flowchart showing details of updating mz and nz in step #2800 of FIG. In step #2810, nz←nz+1, and in step #2820, it is determined whether nz≦N. If yes, complete the update. If no, step #2
At 830, nz=1, and at step #2840, mz
←Mz+M and end the update.

As explained above, according to this embodiment,
A helical scan is performed using a cone beam to collect projection data, and the position in the Z direction of the projection data is defined as the position where the projection data crosses the Z axis, and from among all projection data, the same position as the slice position, and Reconstruct the slice by collecting projection data for adjacent positions for projection angles from 0 to 360 degrees and convolving and backprojecting each collected projection data, assuming that the projection data is perpendicular to the Z axis. do. For this reason, the helical scanning method using a cone beam has good accuracy, and the accuracy does not depend on the slice position.
Reconfiguration can be performed. Therefore, X-ray C with a simple configuration that can take many slices in a short time
A T device is provided. Note that the present invention is not limited to the embodiments described above, and can be implemented with various modifications. A modified example will be explained below. Although the above embodiment assumes that convolution is performed in real space, convolution may also be performed in frequency space.

Regarding projection data that is not perpendicular to the Z axis,
Before convolution, correction may be performed in advance according to the angle of the projection data with respect to the Z axis. Although any correction method may be used, the method shown in Document 1 may be adopted.

A two-dimensional detector for detecting X-rays uses an image
It may be an intensifier, a plurality of multi-channel xenon detectors arranged side by side, or a two-dimensional arrangement of solid state detectors, semiconductor detectors, etc.

[0049] The intervals in the channel and slice directions of the projection data are such that the channel directions are at equal angles, as in this embodiment.
The slice directions may be at equal intervals, both at equal angles, or both at equal intervals.

In the embodiment, the spread width of the beam in the Z-axis direction was made to match the length of the two-dimensional detector in the Z-axis direction, but if the spread width of the beam in the Z-axis direction is narrowed, the accuracy can be improved. You can get the image. In that case, it is necessary to reduce the feed amount of the bed for the 360-degree projection angle in accordance with the spread width of the beam in the Z-axis direction. Furthermore, the width of the beam in the Z-axis direction may be set in stages so that it can be selected according to the scanning time and image quality requirements. That is, the beam width is set to be wide when short scan time is important, and the beam width is set to be narrow when image quality is important. Although the embodiment has been described with respect to a so-called third generation CT, the present invention can be similarly implemented in a so-called fourth generation CT. In the embodiment, the projection data for reconstructing one image was 360 degrees, but one image may be reconstructed using projection data of 180 degrees + fan angle. In the embodiment, all images are reconstructed, but only any desired image may be reconstructed.

In the embodiment, editing and reconstruction are performed in parallel with scanning, but editing and reconstruction may be performed after scanning, or only editing can be performed in parallel with scanning and reconstruction cannot be performed. This may be performed after the scan is completed.

In the embodiment, the collected projection data is stored once and then edited, but the collected projection data may be edited from the beginning and directly stored as reconstructed projection data.

[0053]

As explained above, according to the present invention, helical scanning is performed using cone-shaped X-rays, and normal reconstruction is performed by regarding the cone beam as a beam parallel to the slice thickness direction. With a simple configuration, a large number of slices can be photographed in a short time, and while interpolation of projection data is not required, errors do not vary depending on the slice position, and images with less blur in the slice thickness direction can be obtained. An X-ray CT apparatus with a simple configuration is provided.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing an overview of helical scanning using a cone beam in an embodiment of an X-ray CT apparatus according to the present invention.

FIG. 2 is a diagram explaining helical scanning.

FIG. 3 is a diagram showing a two-dimensional X-ray detector used in one embodiment.

FIG. 4 is a diagram showing the order of collection of projection data in one embodiment.

FIG. 5 is a diagram illustrating intersection angles of projection data of projection angles 180 degrees apart in one embodiment.

FIG. 6 is a system block diagram showing the configuration of one embodiment.

FIG. 7 is a flowchart showing the main operating procedures of one embodiment.

FIG. 8 is a flowchart showing details of the initialization process in FIG. 7;

FIG. 9 is a flowchart showing details of the raw data editing process in FIG. 7;

FIG. 10 is a flowchart showing details of the initialization process in FIG. 9;

FIG. 11 is a flowchart showing details of update processing of m and n in FIG. 9;

FIG. 12 is a flowchart showing details of mz and nz update processing in FIG. 9;

FIG. 13 is a diagram for explaining a cone beam.

FIG. 14 is a diagram showing a coordinate system in an X-ray CT apparatus.

FIG. 15 is a diagram for explaining projection angles.

FIG. 16 is a diagram showing the order of acquisition of projection data in a conventional X-ray CT apparatus of normal scan type.

FIG. 17 is a diagram showing the acquisition order of projection data in a conventional X-ray CT apparatus using a helical scan method.

FIG. 18 is a diagram showing the relationship between projection angle and projection position in a conventional X-ray CT apparatus using a cone beam.

FIG. 19 is a diagram showing the order of acquisition of projection data in a conventional X-ray CT apparatus using a cone beam.

FIG. 20 is a diagram showing intersection angles of projection data of projection angles 180 degrees apart in a conventional example.

[Explanation of symbols]

10...X-ray tube, 14...2-dimensional X-ray detector, 16...bed,
18... Subject, 20... Storage device, 24... Reconstruction device, 2
6...Display device, 28...CPU, 32...X-ray generation section.

Claims (1)

[Claims] 1. Means for irradiating a subject with cone-shaped X-rays, and helical scanning means for changing the projection angle of the X-rays and changing the projection position of the X-rays in conjunction with the change in the projection angle. and detects the X-rays that have passed through the subject,
a two-dimensional detection means for collecting projection data of the subject; and projection data of a tomographic image position and a projection position adjacent to the tomographic image position among the projection data collected by the two-dimensional detection means. An X-ray computed tomography apparatus comprising: means for reconstructing the tomographic image using an X-ray computed tomography apparatus.