JP2009074997A - Computerized tomographic apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To find a true rotation center in a short calculation time using transmitted data from an analyte obtained by half scan or helical scan. <P>SOLUTION: This computerized tomographic apparatus comprises a radiation source 1, a radiation detector 3 for detecting a radiation beam through the analyte 4, rotating means 5 and 13 for relatively rotating the analyte to this radiation beam, a rotation center determining section 20B that determines the correlation between an additional value of the transmitted data in a many points interconnected in the rotation direction on a sinogram of the assembly of many transmitted data of the analyte obtained during the relative rotation of the analyte smaller than one rotation and an additional value of the transmitted data at many points defining radiation routes opposite to the former many points, respectively, which are determined by setting of a virtual rotation center while varying the virtual rotation center, and sets the virtual rotation center at which the correlation is best as the rotation center, and a reconstitution section 20C for obtaining a tomogram of the analyte from many transmitted data detected by the radiation detector 3. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to an industrial or medical computer tomography apparatus with improved rotation center calibration.

  In recent years, high-resolution industrial computer tomography apparatuses (hereinafter referred to as CT scanners) for inspecting small electronic components and the like with high resolution have been developed.

  Conventionally, this type of CT scanner is configured to detect an X-ray beam transmitted through an object from an X-ray tube with a two-dimensional X-ray detector and obtain a transmission image of the object (patent) Reference 1). In this CT scanner, when a cross-sectional image is taken, a large number of transmission images are obtained from the subject while rotating the subject once (also referred to as scanning).

  Reconstruction processing is executed using a large number of transmission images obtained by this scan, and one to many cross-sectional images of the subject are created. The reconstruction of the cross-sectional image is usually performed by a filter-corrected back projection method (FBP (Filtered Back Projection) method).

  Further, in the high-resolution CT scanner, a rotary table for placing a subject is disposed between the X-ray tube and the X-ray detector, and the rotary table and the X-ray are compared with the X-ray tube (X-ray focal point F). The position can be freely set to move the line detector closer or further away (x direction). As a result, the geometrical arrangement relationship of the X-rays such as an imaging distance FCD (Focus to Rotation Center Distance) and a detection distance FDD (Focus to Detector Distance) can be freely changed, whereby an imaging magnification (magnification rate) = FDD / FCD not only can be easily changed, but also has features that can handle objects of various sizes. Further, the rotary table can be moved up and down (z direction), thereby changing the imaging region of the subject.

  Furthermore, the high-resolution CT scanner shown in Patent Document 1 has a configuration capable of so-called half-scanning, which can acquire a cross-sectional image from transmission data less than 360 °. It is also possible to scan while lowering or raising the rotary table at a constant speed. This is a configuration capable of a helical scan generally performed in medical CT. With a CT scanner equipped with such a scanning method, even a long and narrow subject can be imaged at once.

  By the way, in order to process a large number of transmission data and obtain a cross-sectional image with good resolution, it is necessary to accurately grasp the rotation center position on the transmission data in units smaller than one pixel.

  The center of rotation can be obtained from the scan data itself of the subject. Incidentally, Patent Document 2 describes that the center of rotation is obtained from scan data itself obtained by normal scanning (one rotation scanning), and Patent Document 1 discloses a half scan and a helical scan that could not be performed conventionally. The method of obtaining the center of rotation from the scan data itself of the subject is described.

The centers of rotation described in these patent documents are obtained from the principle that “transmission data of X-ray paths in opposite directions are substantially the same”. Patent Document 1 uses this principle to make “radiation paths in opposite directions to transmission data at multiple points on the sinogram where transmission data are arranged and the multiple points determined by setting a virtual rotation center. The correlation with the transmission data at multiple points is obtained while changing the virtual rotation center, and the virtual rotation center is obtained as the rotation center in the actual CT scanner rotation means with the best value of the correlation.
JP 2005-195494 A JP 2000-298105 A

  In the high-resolution CT scanner disclosed in Patent Document 1, the correlation between the multiple points on the sinogram and the multiple points in the opposite direction is calculated while changing the virtual rotation center, and the rotation center calibration is performed from the scan data of the subject itself. Is going. This makes it possible to find the center of rotation from the scan data itself of half scan and helical scan (applicable to normal scan).

  However, this rotation center finding method searches for a rotation center with the best correlation by changing the virtual rotation center. However, the number of search points for the virtual rotation center is large, and there are a large number of points on the sinogram. Since the correlation is calculated with respect to, there is a problem that it takes a long calculation time to find the true center of rotation. In particular, in the case of helical scan, since the calculation of correlation is performed on a three-dimensional sinogram with a huge amount of data, a much longer calculation time is required compared to half scan, so it has not been put into practical use. .

  The present invention has been made in view of the above circumstances, and is a computer tomography that can be used in practice to determine the true center of rotation in a shorter calculation time than before by using transmission data from a subject obtained by half scan or helical scan. An object is to provide a photographing apparatus.

In order to solve the above problems, the present invention provides a radiation source that emits radiation, a radiation detector that detects a radiation beam that passes through the subject from the radiation source, and the subject with respect to the radiation beam. A computer for obtaining a tomographic image of the subject from a large number of transmission data of the subject detected by the radiation detector at a number of rotational positions due to the relative rotation of the subject, respectively. In tomography equipment,
On the sinogram created from a large number of transmission data of the subject, the added value of transmission data at a plurality of points connected in the direction of the relative rotation and the multiple points determined by setting a virtual rotation center are respectively opposite in direction. Rotation to obtain the correlation with the added value of transmission data at multiple points forming a radiation path while changing the virtual rotation center, and to determine the virtual rotation center at which the correlation appears best as the true rotation center in the rotating means It is the structure provided with the center search means.

  The sinogram is composed of a collection of a large number of transmission data of the subject obtained during the relative rotation of the subject that is less than one rotation.

The present invention also provides a radiation source that emits radiation, a radiation detector that detects a radiation beam that passes through the subject from the radiation source, and a rotating unit that rotates the subject relative to the radiation beam. And a rotation axis direction moving means for moving the subject relative to the radiation beam in the rotation axis direction, and performing the relative rotation and the relative movement in the rotation axis direction in parallel. In a computed tomography apparatus for obtaining a tomographic image of the subject from a large number of transmission data of the subject detected by the radiation detector,
On the sinogram created from a large number of transmission data of the subject, the added value of transmission data at a plurality of points connected in the direction of the relative rotation and the multiple points determined by setting a virtual rotation center are respectively opposite in direction. Rotation to obtain the correlation with the added value of transmission data at multiple points forming a radiation path while changing the virtual rotation center, and to determine the virtual rotation center at which the correlation appears best as the true rotation center in the rotating means It is the structure provided with the center search means.

  The calculation of the added value of the transmission data by the rotation center finding means is performed by setting the rotation angle of the relative rotation to φ, the radiation path angle along the surface of the relative rotation from the radiation source to θ, and the virtual rotation set. A forward path correlation area and a reverse path correlation area, which are sets of points that form radiation paths that are opposite to each other and change in accordance with θc on the θφ plane of the sinogram, are set. And the inverse path correlation region, the addition value of the transmission data from one end to the other end in the direction of the relative rotation is obtained.

  With this configuration, when the virtual rotation center is set, a forward path correlation area and a reverse path correlation area are set, and the transmission data from one end to the other end in the relative rotation direction of these areas is added. Thus, the transmission data addition value in the forward radiation path and the transmission data addition value in the reverse radiation path can be easily obtained.

  Further, among the boundary lines of the forward path correlation area and the reverse path correlation area, the boundary lines that change due to the θc are all set to straight lines parallel to the θ direction, so that the comparison is made when the virtual rotation center is changed. Thus, it is possible to calculate the transmission data addition value easily.

  According to the present invention, it is possible to provide a computer tomography apparatus that can be used for practical purposes in which a true rotation center is obtained in a shorter calculation time than before by using transmission data from a subject obtained by half scanning or helical scanning. it can.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(Embodiment 1)
FIG. 1 is a block diagram showing Embodiment 1 of a computed tomography apparatus according to the present invention. FIG. 1 (a) is a plan view of the apparatus, and FIG. 1 (b) is a front view of the apparatus.

  In this CT scanner, an X-ray tube 1 and an X-ray detector 3 for detecting an X-ray beam 2 irradiated from the X-ray tube 1 are arranged to face each other. Between them, a rotary table 5 on which the subject 4 is placed is installed. 6 is a rotation axis, 7 is an X-ray optical axis, C is a rotation center, and D is a detection center.

  The X-ray tube 1 is a microfocus X-ray tube having a generated X-ray focal point F of about 1 μm and is supported on a base 8 via a support frame 9.

  The X-ray detector 3 uses, for example, an X-ray flat panel detector (FPD) that detects a X-ray beam 2 transmitted through the subject 4 from the X-ray tube 1 in which a plurality of detection elements are two-dimensionally arranged. It is done. The X-ray detector 3 is supported by the x shift mechanism 10 on the base 8 through a support frame 11 so as to be movable in the x direction.

  The rotary table 5 is supported by a rotation / lifting mechanism 13 installed in the y shift mechanism 12 on the base 8. Accordingly, the subject 4 is rotated along the imaging surface 14 in the X-ray beam 2 by the rotation / elevation operation by the rotation / elevating mechanism 13 and is moved up and down in the z direction orthogonal to the imaging surface 14. The subject 4 is moved together with the rotary table 5 in the y direction across the X-ray beam 2 by the y shift mechanism 12 and moved between the X-ray tube 1 and the X-ray detector 3 by the x shift mechanism 10. Thus, the shooting distance FCD can be changed.

  On the other hand, in the X-ray detector 3, the support frame 11 is moved in the x direction by the x shift mechanism 10, whereby the detection distance FDD can be changed.

  In this CT scanner, in addition to the above-described components, a data processing unit 20 that processes transmission data acquired by the X-ray detector 3, a display unit 21 that displays processing results and the like, and a data processing unit 20 A mechanism control unit 22 for controlling the x shift mechanism 10, the y shift mechanism 12 and the rotation / lifting mechanism 13 based on the control command; an X-ray control unit 23 for controlling the tube voltage and tube current of the X-ray tube 1; A high voltage generator 24 for applying a predetermined high voltage / current to the X-ray tube 1 in accordance with a control instruction from the X-ray control unit 23 is provided. In addition, the CT scanner is provided with an X-ray shielding box (not shown) for housing a portion including the X-ray tube 1, the subject 4 and the X-ray detector 3.

  The x shift mechanism 10 and the y shift mechanism 12 have encoders (not shown) attached thereto. The mechanism control unit 22 reads the FCD value, the FDD value, and the y value from the output of the encoder, and then sends them to the data processing unit 20. The mechanism control unit 22 controls the mechanism so that the imaging magnification and the position of the subject 4 become the instruction values of the data processing unit 20 using the FCD value, the FDD value, the y value, and the like that are feedback values.

  For example, a normal computer is used as the data processing unit 20. Specifically, the data processing unit 20 includes a CPU, a main memory, a disk, an input unit such as a keyboard and a mouse, an interface, and the like. A scan control unit 20A that obtains transmission data while performing scanning, and a rotation center obtaining unit 20B that obtains a rotation center position (or rotation axis position) on the data from the transmission data obtained by the scan control unit 20A; A reconstruction unit 20C is provided that creates a tomographic image of the subject 4 by data processing from a large number of transmission data transmitted through the subject 4.

Next, the operation of the half scan in the CT scanner having the above configuration will be described.
In this embodiment, a case where the rotation center is obtained will be described by taking as an example a so-called half scan in which transmission data is obtained from a rotation of 180 ° + fan angle or more (less than 360 °). Here, it is assumed that the subject 4 does not move up and down during the half scan.

  First, prior to obtaining the center of rotation, the principle of finding the center will be described with reference to FIG. The basic principle of finding the center of rotation is that “transmission data of X-ray paths in opposite directions are substantially the same”.

  FIG. 2 is a diagram showing an X-ray path on the imaging surface. If the subject 4 is considered to be fixed, the X-ray focal point F rotates with respect to the subject 4. One X-ray path can be represented by a rotation angle φ and an arrangement angle θ of the X-ray path along the imaging surface 14 (corresponding to the radiation path angle in the claims).

If (θ, φ) and (θr, φr) are opposite in the same route,
θr = − (θ−θc) + θc = 2 · θc−θ (1)
φr = φ−π−2 · (θ−θc) (2)
The relationship is established. Here, θc is an arrangement angle of the rotation center C.

  FIG. 3 is a sinogram showing a transmission data set P (θ, φ) on the imaging surface 14 obtained by half scanning. The vertical axis represents the rotation angle φ, and the horizontal axis represents the arrangement angle θ (θ1 to θ2).

As is apparent from this sinogram, each of the points J _{1 to} J _N connected within the width φw in the direction of the rotation angle φ at the one angle θ within the arrangement angle θ1 to θ2 range, respectively. If the points forming the reverse radiation path are points J ₁ ′ to J _N ′, these points J ₁ ′ to J _N ′ are also connected with a width φw in the direction of the rotation angle φ at the other angle θr.

Therefore, the multipoint determined by setting the addition value of the transmission data at the multipoints J ₁ to J _N (forward path) connected in the direction of the rotation angle φ and the virtual rotation center (rotation center at an undefined stage of rotation) θc. When the set virtual rotation center θc is correct, the added value of the transmission data at the multiple points J ₁ ′ to J _N ′ (reverse path) each forming a reverse radiation path is substantially the same value from the basic principle described above. Thus, the set virtual rotation center θc can be determined as the true rotation center. That is, the transmission data addition value at the multipoints J ₁ to J _N and the transmission data addition at the multiplicity points J ₁ ′ to J _N ′ that form radiation paths that are opposite to the multiplicity points J ₁ to J _N , respectively. The true center of rotation is obtained using the fact that the values are substantially the same based on the variable setting of the virtual center of rotation θc.

Furthermore, it demonstrates in detail using FIG.
A forward path correlation region R and a reverse path region Rr, which are sets of points that form radiation paths in opposite directions that change according to the virtual rotation center θc, are set on the θ, φ plane of the sinogram. As the forward path region R, a region sandwiched between the line L1 (boundary line) and the line L2 is set, and further, when the virtual rotation center θc is set, the line L1r formed by the reverse path point of the point on the line L1, The reverse path region Rr sandwiched between the line L2r created by the reverse path point of the point on L2 is automatically determined. Then, if the virtual rotation center θc is correct, (to J ₁ without J _N) phi width of the forward path correlation region R of the sum and the inverse path region Rr of the phi direction the width of the corresponding reverse path (J ₁ ' It can also be seen that the added value of J _N ′) is substantially the same. That is, the φ direction addition value of the transmission data from the line L1 as one end in the region R to the line L2 as the other end and the transmission data φ from the line L1r as one end in the region Rr to the line L2r as the other end. When the direction addition value is compared, the reverse paths (θ and θr) are substantially the same. In other words, it is symmetric about θc.

  Therefore, in the present invention, if the virtual rotation center is correct, the φ direction addition value in the forward path correlation region R and the corresponding reverse path region Rr is substantially the same between the backward paths. The rotation center θc is obtained as the true rotation center θc.

  In principle, each line defining the correlation region does not need to be horizontal or straight.

  Next, an example of processing for obtaining the rotation center will be described with reference to FIG. FIG. 4 is a sinogram showing a transmission data set P (θ, φ) on the imaging surface 14.

  In the figure, θc is a virtual rotation center, and θcs and θce represent a lower limit and an upper limit for searching for the true rotation center θc, respectively. Data is obtained within the arrangement angles θ1 to θ2 and in the range of φ = 0 to φlast (less than 2π). α1 is a constant, and the data range to be used is 0 to π + 2 · (θce−θ1) + α1.

The constant α1 is set so that the use data range does not exceed φlast.
φlast ≧ π + 2 · (θce−θ1) + α1 (3)
Decide to be.

  Now, when the virtual center of rotation θc is set on the θφ plane of the sinogram and the forward path correlation region R is determined as shown in FIG. 4, the corresponding reverse path correlation region Rr using the equations (1) and (2). Is determined as shown in FIG. Here, the points A, B, G, and H of the region R and the points A ′, B ′, G ′, and H ′ of the region Rr have mutually opposite paths.

The lines L1r, L2r, L1, and L2 that define the correlation region are expressed by the following relational expressions based on φ and θ, respectively.
Line L1r: φ = 2 · (θc−θcs) (4)
Line L2r: φ = 2 · (θ−θ1) + α1 (5)
Line L1: φ = π + 2 · (θ−θcs) (6)
Line L2: φ = π + 2 · (θc−θ1) + α1 (7)
By determining the line as described above, the reverse path of the line L1 always forms the line L1r and the reverse path of the line L2 forms the line L2r even when θc changes.

  Here, the inclined lines L1 and L2r shown in FIG. 4 are fixed lines that do not depend on θc, whereas the horizontal lines L2 and L1r depend on θc and remain horizontal with respect to changes in Δθc. It changes by twice (2 · Δθc).

  In this embodiment, if the set virtual rotation center is correct, the φ direction addition value in the forward path correlation region R and the corresponding reverse path region Rr is substantially the same between the reverse paths. The center of rotation θc is obtained.

  Next, a processing flow for executing rotation center finding from a large number of transmission data of the subject 4 collected on the sinogram obtained by the half scan will be described with reference to FIG. This processing flow describes only basic calculations.

  Step S1: First, θ and θc (which also depends on θc because the areas are different) are used as arguments, and the transmission direction addition of the respective transmission data of the correlation areas Rr and R for each θc set for each Δθc. Values PRr (θ, θc) and PR (θ, θc) are calculated in sequence and stored. That is, the calculation here is a double loop calculation of θc and θ, and θc is performed for each search step Δθc in the range of θcs to θce. Further, for θ, all data points of θ1 to θ2 are set for each θc. Calculate

In the correlation region Rr, the line L1r to the line L2r are added by the following equation (8).
2 · (θ-θ1) + α1 (superscript Σ, the same applies hereinafter)
PRr (θ, θc) = Σ P (θ, φ) (8)
φ = 2 · (θc−θcs) (subscript of Σ, the same applies hereinafter)
On the other hand, in the correlation region R, the line L1 to the line L2 are added by the following equation (9).
π + 2 · (θc−θ1) + α1
PR (θ, θc) = Σ P (θ, φ) (9)
φ = π + 2 · (θ−θcs)
However, if the calculation is performed as is using Equation (8) and Equation (9), the overlapping calculation portion increases and is wasted. Therefore, in actuality, an additional point (see FIG. 4 so as to add the increment of the added value by 2 · Δθc).

In the actual calculation, θc = θcs is set, and the addition value is calculated by the equations (8) and (9), and the addition value is calculated by the following equation while increasing θc by Δθc from the next step.
2. (θc′−θcs)
PRr (θ, θc ′) = PRr (θ, θc) −ΣP (θ, φ) (8 ′)
φ = 2 · (θc−θcs)
π + 2 · (θc′−θ1) + α1
PR (θ, θc ′) = PR (θ, θc) + ΣP (θ, φ) (9 ′)
φ = π + 2 · (θc−θ1) + α1
In the above equation, θc ′ = θc + Δθc. In addition, since the lines L1r and L2 serving as the boundary lines are parallel to the θ direction, the addition of the expressions (8 ′) and (9 ′) is easy calculation without depending on θ. .

  Step S2: After completing the addition process described above, θc is set. The setting of θc is performed by setting θc = θcs as a starting point, setting θc every Δθc from θcs, and setting until θc = θce. That is, the correlation process of the two added values described above is executed for θc = θcs after step S3, and thereafter, the next θc is set every Δθc, and the correlation process after step S3 is repeated.

Step S3: After that, since the correlation value is added in the subsequent step S6, the correlation value is reset.
Step S4: The data point is changed from θ1 to θ2.
Step S5: Calculate a reverse path θr with respect to θ.

  Step S6: The absolute value (| PR (θ, θc) −PRr (θr, θc) |) of the difference between the transmission data addition values of the forward path and the reverse path is added to the correlation value. However, when θr is not in the range of θ1 to θ2, no addition is performed. Further, in this addition, since θr is generally different from the data point, interpolation calculation is performed.

Step S7: Returning to step S4, the same processing is repeated by changing the data point of θ.
Step S8: Then, the correlation value obtained in step S6 is divided by the number of repetitions of addition (number of addition points) in step S4 to obtain a normalized correlation value.
Step S9: Returning to step S2, the correlation value is calculated while changing θc, and θc that minimizes the correlation value, that is, θc that provides the best correlation between the forward path and the reverse path is set as the true rotation center. Here, good correlation means that the correlation is deep, that is, the degree of coincidence is good. The smaller the correlation value, the better the correlation.

  Therefore, according to the embodiment as described above, in half scan, the transmission data addition value of a plurality of points in the φ direction of the forward pass and the transmission data addition value of the plurality of points in the φ direction of the corresponding reverse pass are repeated in the half scan. Is added to the correlation value to obtain a normalized correlation value, and θc is changed and θc having a small correlation value is used as the rotation center, so that the true rotation can be easily performed from the transmission data of the subject 4 itself. You can find the center. This is because the correlation value is calculated for the transmission data addition value, so the correlation value can be calculated while changing only θ, and the calculation time for obtaining the rotation center from the scan data itself of the subject 4 is greatly increased. Can be shortened.

  Further, among the boundary lines of the forward path correlation region and the reverse path correlation region, all boundary lines that change due to the rotation center θc are set to straight lines parallel to the θ direction, and thus transmission when θc is changed. The calculation of the data addition value is facilitated (formulas (8 ′) and (9 ′)), and the time for obtaining the rotation center can be shortened.

(Modification of Embodiment 1)
(Modification 1)
In the first embodiment, in step S1, the φ direction addition values PRr (θ, θc) and PR (θ, θc) of the transmission data are calculated and stored, and then the correlation value is calculated in the θc loop of step S2. However, for example, the φ direction addition value may be calculated in the θc loop in step S2 or in the θ loop in step S4.

(Modification 2)
The rotation center finding in the first embodiment can be applied not only to the half scan but also to the case where the rotation range φlast shown in FIG. 4 is 2π (normal scan) or beyond, for example. When φlast exceeds 2π, the regions R and Rr may overlap depending on the setting of the constant α1, but the center of rotation can be obtained without any problem.

(Modification 3)
In addition, the rotation center finding in the first embodiment can be applied not only to a normal reconstruction in which one cross-sectional image on the imaging surface 14 is generated using only transmission data on the imaging surface 14, but other than that, for example, The present invention can be similarly applied to cone beam reconstruction in which a large number of cross-sectional images are created using transmission data detected at each position in the vertical direction of the imaging surface 14.

(Modification 4)
Furthermore, in the above embodiment, the X-ray detector 3 uses a two-dimensional detector, but the center of rotation can also be obtained using a one-dimensional detector that detects along the imaging surface 14.

(Embodiment 2)
The second embodiment is an example of obtaining a rotation center in a so-called helical scan operation in which the subject 4 is moved up and down in parallel with the rotation instead of the half scan (first embodiment). . Since the hardware configuration of the CT scanner is the same as that of the first embodiment (see FIG. 1), the description thereof is omitted here.

  In the second embodiment, particularly different points are the scanning operation by the scan control unit 20A in the data processing unit 20 and the processing example of the rotation center finding of the rotation center finding unit 20B.

Hereinafter, the operation of the helical scan in the CT scanner will be described.
First, prior to obtaining the rotation center, the principle of obtaining the rotation center will be described with reference to FIG. The basic principle of finding the center of rotation is that “transmission data of X-ray paths in opposite directions are substantially the same”.

  FIG. 6 is an X-ray path diagram (bird's eye view) of a helical scan. Now, when the subject 4 is considered fixed, the X-ray focal point F moves on the spiral focal locus 30 with respect to the subject 4. To do. Here, when two X-ray focal positions FA and FA ′ shown in FIG. 6 are taken and X-ray paths A and A ′ connecting these two focal positions FA and FA ′ are formed, these are clearly the same path. There is a reverse path relationship.

  Therefore, when such a helical scan X-ray path diagram is viewed from the axial direction AA, the helical scan X-ray path diagram as shown in FIG. 7 is obtained. The X-ray path can be expressed by the rotation angle φ and the arrangement angle θ of the X-ray path along the imaging surface 14.

Assuming that the forward path A is (θ, φ) and the reverse path and A ′ is (θr, φr), between (θ, φ) and (θr, φr), as described above,
θr = − (θ−θc) + θc = 2 · θc−θ (1)
φr = φ−π−2 · (θ−θc) (2)
The relationship is established. Here, θc is an arrangement angle of the rotating shaft 6.

Next, when the X-ray path diagram of the helical scan is viewed from the directions of the BB arrow and the CC arrow shown in FIG. 7, the helical scan X-ray path diagram as shown in FIGS. 8A and 8B is obtained. Since the imaging surface 14 is set to be orthogonal to the rotation axis 6, the slopes of the path A and the path A ′ with respect to the imaging surface 14 are the same. As a result, the z-direction detection channel positions zd and zdr (based on the imaging surface 14) by the X-ray detectors 3 of the path A and the path A ′ are as follows:
zd = a · (−π / 2− (θ−θc)) · 2 / {1 + cos (2 · (θ−θc))} (10)
zdr = −zd = a · (π / 2 + θ−θc) · 2 / {1 + cos (2 · (θ−θc))}
= A · (π / 2− (θr−θc)) · 2 / {1 + cos (2 · (θr−θc))} (11)
It is calculated by the following formula. Where a is a constant and has the following formula:
a = helical pitch × magnification ratio (= FDD / FCD) / 2π (12)
Obtained from.

  The lines zd (θ) and zdr (θr) represented by the expressions (10) and (11) are lines obtained by projecting the focal locus 30 from the focal position onto the X-ray detector 3. Given θ and φ of the forward path, θr, φr, zd, and zdr can be calculated from the equations (1), (2), (10), and (11). And the reverse path is obtained. The center of rotation is obtained by utilizing the fact that transmission data P (θ, zd, φ) and P (θr, zdr, φr) are substantially the same.

  Next, the operation of finding the rotation center will be described using a three-dimensional sinogram shown in FIG. This sinogram represents a transmission data set P (θ, zd, φ) obtained by scanning. In the figure, θc is a virtual rotation center, and θcs and θce respectively represent a lower limit and an upper limit of the θc search. It is assumed that the data is within the arrangement angles θ1 to θ2 and φ = 0 to π + 2 · (θce−θ1) + α2. Here, α2 is a constant, and the use data range can be changed by changing the constant α2.

  Here, when the virtual rotation center θc is set and the forward path correlation region R is determined as shown in FIG. 9A, the corresponding reverse path correlation region Rr is obtained from the above equations (1) and (2). Determined.

  The regions R and Rr in the θφ plane of the sinogram are three-dimensional regions including all zd as shown in FIG. Within the region R, there is a forward path surface zd (θ) defined by equation (10), while there is a reverse path surface zdr (θr) defined by equation (11) within region Rr. Here, the points A, B, G, H on the forward path surface of the region R and the points A ′, B ′, G ′, H ′ on the reverse path surface of the region Rr are mutually reverse paths.

The correlation region R on the θφ plane of the sinogram is sandwiched between the lines L1 and L2, and the correlation region Rr is a region sandwiched between the lines L1r and L2r, and each of the lines L1r, L2r, L1 defining the correlation region. , L2 are expressed by the following relational expressions using φ and θ, respectively.
Line L1r: φ = 2 · (θ−θ1) (13)
Line L2r: φ = 2 · (θ−θ1) + α2 (14)
Line L1: φ = π + 2 · (θc−θ1) (15)
Line L2: φ = π + 2 · (θc−θ1) + α2 (16)
By determining the line as described above, the reverse path of the line L1 always forms the line L1r and the reverse path of the line L2 forms the line L2r even when θc changes.

  Here, the inclined lines L1r and L2r shown in FIG. 9 are fixed lines that do not depend on θc, whereas the horizontal lines L1 and L2 depend on θc and remain horizontal with respect to changes in Δθc. It changes by twice (2 · Δθc).

  In the present embodiment, if the set virtual rotation center is correct, the φ direction addition value in the forward path correlation region R and the corresponding reverse path region Rr is substantially the same between the backward paths. The center of rotation θc is obtained.

  Next, a processing flow for executing rotation center finding from a large number of transmission data of the subject 4 collected on the sinogram obtained by the helical scan will be described with reference to FIG. This processing flow describes only basic calculations.

  Step T1: First, θ, zd, and θc (depending on θc because the regions are different) are used as arguments, and transmission of each of the correlation regions Rr and R for each θc set for each search step Δθc. The φ direction addition value PRr (θ, zd, θc) and PR (θ, zd, θc) of the data are sequentially calculated and stored. That is, the calculation here is a triple loop calculation of θc, θ, and zd, and is performed for each search step Δθc in the range of θcs to θce for θc, and for θ and zd, θ and zd for each θc. Calculate all data points. The added value is handled as an image of θ and zd at each θc. However, since the φ direction addition value PRr does not depend on θc, only one value needs to be calculated.

In the correlation region Rr, the line L1r to the line L2r are added by the following equation (17). However, it does not depend on θc.
2 ・ (θ−θ1) + α2
PRr (θ, zd, θc) = ΣP (θ, zd, φ) (17)
φ = 2 ・ (θ−θ1)
On the other hand, in the correlation region R, the line L1 to the line L2 are added by the following equation (18).
π + 2 · (θc−θ1) + α2
PR (θ, zd, θc) = ΣP (θ, zd, φ) (18)
φ = π + 2 · (θc−θ1)
Here, if the calculation is performed as is using the equation (18), the overlapping calculation part is increased and is wasted, so in fact, the addition point of the addition point (2. Calculation is made so as to add the increment of addition value by Δθc).

In the actual calculation in the correlation region R, θc = θcs is set, the addition value is calculated by the equation (18), and the addition value is calculated by the following calculation formula while increasing θc by Δθc from the next step.
π + 2 · (θc′−θ1) + α2
PR (θ, zd, θc ′) = PR (θ, zd, θc) + ΣP (θ, zd, φ)
φ = π + 2 · (θc−θ1) + α2
π + 2 · (θc′−θ1)
−Σ P (θ, zd, φ) (18 ′)
φ = π + 2 · (θc−θ1)
In the above equation, θc ′ = θc + Δθc. In addition, since the lines L1 and L2 serving as the boundary lines are parallel to the θ direction, the addition of Expression (18 ′) is easy calculation without depending on θ.

  Step T2: After completing the above-described calculation process, θc is set. θc is set from θcs to θce every Δθc. That is, the correlation process of the two addition values described above is executed for θc = θcs after step T3, and thereafter, the next θc every Δθc is set. Similarly, the correlation process after step T3 is repeatedly executed.

Step T3: Since the correlation value is added in the subsequent step T6, the correlation value is reset.
Step T4: The data point is changed from θ1 to θ2.
Step T5: From θ and θc, the forward path zd and the reverse paths θr, zdr are calculated by the above formulas (1), (10), and (11).

  Step T6: The absolute value (| PR (θ, zd, θc) −PRr (θr, zdr, θc) |) of the difference between the transmission data addition values of the forward path and the reverse path is added to the correlation value. However, when θr is not in the range of θ1 to θ2, no addition is performed. Further, in this addition, since θr, zd, and zdr are generally different from data points, interpolation calculation is performed.

Step T7: Returning to Step T4, the same processing is repeated by changing the data point of θ.
Step T8: Then, the correlation value obtained in step T6 is divided by the number of additions repeated in step T4 (the number of addition points) to obtain a normalized correlation value.
Step T9: Returning to step T2, the correlation value is calculated while changing θc, and θc that minimizes the correlation value, that is, θc that provides the best correlation between the forward path and the reverse path is set as the rotation center. Here, good correlation means that the correlation is deep, that is, the degree of coincidence is good. The smaller the correlation value, the better the correlation.

  Therefore, according to the embodiment as described above, in the helical scan, the transmission data addition value at the plurality of points in the φ direction of the forward path and the transmission data addition value at the plurality of points in the φ direction of the corresponding reverse path while repeating θ. Is added to the correlation value to obtain a standardized correlation value, and the rotation center is easily determined from the transmission data itself of the subject 4 by changing θc and setting θc having a small correlation value as the rotation center. Can be sought. This is because the correlation value is calculated for the transmission data addition value, so the correlation value can be calculated while changing only θ, and the calculation time for obtaining the rotation center from the scan data itself of the subject 4 is greatly increased. Can be shortened.

(Modification of Embodiment 2)
(Modification 5)
In Embodiment 2, the φ direction addition values PRr (θ, zd, θc) and PR (θ, zd, θc) of the transmission data are calculated for the entire range of θ, zd in Step T1, for example. You may make it calculate only in the reverse path surface and forward path surface prescribed | regulated by Formula (11) and Formula (10), respectively. Also, zd may be calculated only in the narrow range used.

(Modification 6)
In the second embodiment, when the absolute value of (θ−θc) is small, equations (10) and (11) that define the forward path surface and the reverse path surface can be substituted by the following equations.
zd = a · (−π / 2− (θ−θc)) (10 ′)
zdr = −zd = a · (π / 2 + θ−θc)
= A · (π / 2− (θr−θc)) (11 ′)
At this time, the forward path surface and the reverse path surface are planes.

(Modification 7)
In the second embodiment, the φ direction addition values PRr (θ, zd, θc) and PR (θ, zd, θc) of the transmission data are calculated and stored in step T1, and then the correlation value is calculated in the θc loop of step T2. However, for example, the φ direction addition value may be calculated in the θc loop or in the θ loop of step T4.

(Modification 8)
In the second embodiment, the data range {φ = 0 to π + 2 · (θce−θ1) + α2} and the correlation region can be freely set by changing the constant α2, and the relative position is arbitrarily maintained in the rotation angle φ direction. It can be set by shifting. When the constant α2 is increased, the regions R and Rr overlap, but the center of rotation can be obtained without any problem.

(Modification 9)
In addition, the rotation center finding means according to the second embodiment may be applied to the rotation center finding even when the rotation center position fluctuates as the helical scan progresses. be able to. That is, in the second embodiment, the φ-direction center of gravity φg of the correlation region used for obtaining the rotation center θc is approximately:
φg = π / 2 + θ2-θ1 + α2 / 2 (19)
It is calculated by the following formula. The obtained rotation center θc can be said to be the rotation center position at the φ-direction center of gravity φg.

  This is because the data center and the correlation region are shifted in the φ direction while maintaining the relative positions, φg is changed stepwise, and the rotation center θc is obtained after interpolation to obtain the rotation center θc as the rotation angle φ. Can be determined for each. If the image is reconstructed using the obtained rotation center θc for each rotation angle φ, the image quality can be improved.

(Modification 10)
In the second embodiment, the correlation regions R and Rr on the sinogram θφ plane are determined as shown in FIG. 9, but the present invention is not limited to this. For example, the correlation regions R and Rr shown in FIG. 4 may be determined. In this case, only the calculation of the φ direction addition value in step T1 is different, but this is a calculation according to the calculation in step S1.

(Modification 11)
Further, the correlation regions R and Rr in the sinogram θφ plane can be determined as shown in FIG. In this case, only the calculation of the φ direction addition value in step T1 is different.
In FIG. 11, the lines L1r, L2r, L1, and L2 at the boundary between the correlation regions R and Rr are expressed by the following relational expressions using φ and θ, respectively.
Line L1r: φ = 2 · (θc−θcs) (20)
Line L2r: φ = 2 · (θc−θcs) + α3 (21)
Line L1: φ = π + 2 · (θ−θcs) (22)
Line L2: φ = π + 2 · (θ−θcs) + α3 (23)
By determining the line as described above, the reverse path of the line L1 always forms the line L1r and the reverse path of the line L2 forms the line L2r even when θc changes.

  Here, the inclined lines L1 and L2 are fixed lines that do not depend on θc, whereas the horizontal lines L1r and L2r depend on θc and are twice as large as the change in Δθc while maintaining the horizontal ( 2 · Δθc).

  Therefore, in the processing flow for executing the rotation center finding from a large number of transmission data on the sinogram of the line determined as described above, in step T1, as in the second embodiment, each of the correlation regions Rr, R is determined. The φ direction addition values PRr (θ, zd, θc) and PR (θ, zd, θc) of the transmission data are calculated and stored.

In the correlation region Rr, the line L1r to the line L2r are added by the following equation (24).
2 · (θc−θcs) + α3
PRr (θ, zd, θc) = ΣP (θ, zd, φ) (24)
φ = 2 · (θc−θcs)
On the other hand, in the correlation region R, the line L1 to the line L2 are added by the following equation (25). Here, it does not depend on θc.
π + 2 · (θ−θcs) + α3
PR (θ, zd, θc) = ΣP (θ, zd, φ) (25)
φ = π + 2 · (θ−θcs)
Here, if the calculation is performed as it is using the equation (24), the overlapping calculation part is increased and is wasted as in the second embodiment, so that the calculation avoiding the overlapping calculation is performed.

(Modification 12)
Further, the correlation regions R and Rr in the sinogram θφ plane can be determined as shown in FIG. In this case, only the calculation of the φ direction addition value in step T1 is different.
In FIG. 12, the lines L1r, L2r, L1, and L2 at the boundary between the correlation regions R and Rr are expressed by the following relational expressions using φ and θ, respectively.
Line L1r: φ = 2 · (θ−θ1) (26)
Line L2r: φ = 2 · (θc−θ1) + α4 (27)
Line L1: φ = π + 2 · (θc−θ1) (28)
Line L2: φ = π + 2 · (θ−θ1) + α4 (29)
By determining the line as described above, the reverse path of the line L1 always forms the line L1r and the reverse path of the line L2 forms the line L2r even when θc changes.

Here, the inclined lines L1r and L2 are fixed lines that do not depend on θc, whereas the horizontal lines L1 and L2r depend on θc, and the change in Δθc is twice that while maintaining the horizontal ( 2 · Δθc).
Note that the calculation of the φ direction addition value in step T1 is the same as that in the tenth modification, and a description thereof will be omitted here.

(Modification 13)
The rotation center finding in the second embodiment correlates reverse paths separated by about 0.5 rotations. Here, this correlation is referred to as π correlation. In the helical scan, when the helical pitch is small, correlations such as about 1.5 rotations, about 2.5 rotations, etc. are possible. This is called 3π correlation, 5π correlation,... (Nπ correlation).

Here, for example, in the case of 3π correlation, the correlation region can be similarly set by using the following expression instead of Expression (1), Expression (2), Expression (10), and Expression (11).
θr = − (θ−θc) + θc = 2 · θc−θ (1 ′)
φr = φ-3π−2 · (θ−θc) (2 ′)
zd = a · (−3π / 2− (θ−θc)) · 2 / {1 + cos (2 · (θ−θc))}
...... (10 '')
zdr = −zd = a · (3π / 2 + θ−θc) · 2 / {1 + cos (2 · (θ−θc))}
= A · (3π / 2− (θr−θc)) · 2 / {1 + cos (2 · (θr−θc))}
...... (11 ")
An analogy can also be easily made in the case of nπ correlation (n is an odd number).

(Modification 14)
In the second embodiment, when the helical scan completely captures the subject 4 in the direction of the rotation axis, the center of rotation can be simply obtained using FIG. FIG. 13 is a sinogram when the subject is completely imaged in the direction of the rotation axis.

  In this example, α2 is set to be large so that the correlation areas R and Rr cover the subject existence area 40. Here, if the X-ray absorption of the table 5 on which the subject 4 is placed is reduced, the values other than the subject existence area 40 are almost constant values (air values) on the sinogram. For this reason, it can be seen that the transmission data φ direction addition value in the correlation regions R and Rr matches the transmission data φ direction addition value in the correlation region R0 shown in FIG. The correlation region R0 is a fixed region that does not depend on θc, and is a rectangular region that covers the subject existence region 40. Therefore, instead of the addition values in the correlation regions R and Rr, the rotation center can be obtained using the addition values in the correlation region R0.

(Other variations on the first and second embodiments)
(Modification 15)
In the first embodiment, the center of rotation can be obtained in the same manner using the correlation regions R and Rr set in the second embodiment. That is, in the first embodiment (particularly, the normal scan in the second modification), the correlation regions R and Rr shown in FIGS. 9, 11, and 12 can be used.

(Modification 16)
In the first embodiment or the second embodiment, the basic principle of finding the rotation center is that the transmission data of the X-ray paths in opposite directions are substantially the same. The data may be data before or after logarithmic conversion, or may be data at any stage of processing.

(Modification 17)
The first embodiment or the second embodiment and the modification examples thereof can be applied not only to the half scan and the helical scan but also to the offset scan.

  This offset scan is set by shifting the center of rotation in the y direction, and scans with one side of the subject 4 protruding, so that even a large subject 4 can be imaged (Japanese Patent Laid-Open No. 2002-062268). reference). In other words, in any case of half offset, normal offset, and helical offset, the rotation center θc is simply shifted to the offset side, and the rotation center θc is obtained without any other special change. it can.

(Modification 18)
In the first embodiment or the second embodiment, the relationship between the forward path and the reverse path may be completely reversed. That is, a correlation loop may be performed with θr and φr, and the forward path (θ, φ) may be obtained from the reverse path to obtain the correlation. In addition, it is easily understood by those skilled in the art that the rotation during scanning, the direction of elevation, and the + direction of φ, θ, and zd may be reversed (the expression and the figure are slightly changed). I can do it.

(Modification 19)
The correlation region R in the first embodiment or the second embodiment is an example, and various other methods are possible. For example, in order to increase calculation accuracy, a plurality of sets of correlation regions R and Rr may be created. For example, in FIG. 9, α2 is divided into a plurality of parts (R1, R1r), (R2, R2r),..., And φ direction addition values (PR1r, PR1), (PR2r, PR2),. May be calculated so as to be correlated as a whole. At this time, if R1, R2,... May partially overlap each other, a gap may be provided.

(Modification 20)
In the first embodiment or the second embodiment, the processing flow describes only basic calculations as described above. For example, when the transmission data is added in the φ direction, since the start point and the end point of the addition are different from the data point, an interpolation calculation is necessary, but description regarding the interpolation calculation is omitted. In addition, the interpolation calculation is performed by adding the correlation values in step S6 or T6. For example, a cosine interpolation function (Patent Document 2 and FIG. 3 described above) is used for the interpolation calculation. The description about is omitted.

  Further, the processing flow first determines the search area of θc and the search step Δθc, and searches only once. However, if the search area and the search step Δθc are narrowed while reflecting the previous result, the search time is reduced. Can be shortened. There is also a method of searching while automatically determining the search step Δθc and the direction.

(Modification 21)
In the first or second embodiment, a low-cut filter can be applied in the θ direction or the zd direction to the φ direction addition values PRr (θ, zd, θc) and PR (θ, zd, θc) of the transmission data. For example, the influence of scattered radiation can be reduced, and the center of rotation can be obtained with high accuracy. Alternatively, the same effect can be obtained by applying a low-cut filter to the transmission data P (θ, zd, θc) in the θ direction or the zd direction before the addition.

(Modification 22)
In addition, in the addition of the correlation value in step S6 or T6, which is the processing flow described in the first embodiment or the second embodiment, the correlation value addition value (| PR (θ, zd, θc) −PRr (θr, zdr) , Θc |), the weight becomes smaller as the θ value is further away from θc, and the accuracy is improved. Various changes can be made. For example, the correlation value is not an absolute value addition but a square value. It is good also as addition.

  In addition, as the correlation value, a calculation formula is set such that the smaller the correlation (degree of coincidence) is, the more the calculation formula becomes larger as the correlation is improved. In this case, θc that maximizes the correlation value may be selected.

(Modification 23)
The mechanism relating to the scan control may be relatively the same. For example, the X-ray tube 1 and the X-ray detector 3 are integrally rotated around the subject 4 without rotating the subject 4. Alternatively, instead of moving the subject 4 up and down, the X-ray tube 1 and the X-ray detector 3 may be moved up and down integrally. Also, the orientation of the entire apparatus may be any way, for example, the entire orientation may be lateral so that the rotation axis is horizontal.

(Modification 24)
In the first and second embodiments, the FDD, FCD, and y position are made variable. However, it is not essential to find the rotation center, and the rotation center can be obtained effectively even if it is not variable. Can do.

(Modification 25)
In each of the above embodiments, the flat panel detector (FPD) is used as the X-ray detector 3 as described above. However, the detector is not limited to the flat panel detector, and various detectors having similar functions are used. Can also find the center of rotation.

(Modification 26)
In each of the embodiments described above, X-rays are emitted from the X-ray tube 1. However, instead of X-rays, other penetrating radiation such as γ-rays, neutron rays, microwaves, etc. is used. However, the center of rotation can be obtained.

(Modification 27)
In each of the above embodiments, the mechanisms 10 to 13 may be calibrated in advance, and θc may be predicted from the FDD, FCD, and y positions, and the center of rotation may be obtained based on this prediction. Thereby, since the center search area can be narrowed, the calculation time can be shortened.

(Modification 28)
The CT scanner according to the present invention can find the center of rotation regardless of its application (industrial use, medical use).

  Note that the present invention is not limited to the above-described embodiment and modifications thereof, and can be variously modified and implemented without departing from the scope of the invention in the implementation stage. Further, the embodiments may be combined as appropriate as possible, and in that case, combined effects can be obtained.

  Each of the above embodiments includes inventions at various stages, and various inventions can be extracted by appropriately combining a plurality of disclosed constituent elements. For example, when an invention is extracted by omitting some of the structural requirements shown in the embodiment, when the invention is extracted, the omitted portion is appropriately determined by a well-known conventional technique. It is to be supplemented.

The block diagram which shows Embodiment 1, 2 of the computer tomography apparatus which concerns on this invention. FIG. 4 is an X-ray path diagram on the imaging surface in the first and second embodiments. FIG. 6 is a diagram showing a sinogram of a photographing surface in the first and second embodiments. FIG. 3 shows a sinogram of the imaging surface in the first embodiment. The processing flow figure which calculates | requires a rotation center from the transmission data obtained by the half scan. FIG. 6 is a bird's-eye view showing an X-ray path by helical scanning in the second embodiment. AA arrow view shown in FIG. The BB arrow view and CCBB arrow view shown in FIG. FIG. 6 shows a three-dimensional sinogram in Embodiment 2. The processing flow figure which calculates | requires a rotation center from the transmission data obtained by the helical scan. FIG. 10 shows another example of a three-dimensional sinogram in the second embodiment. FIG. 10 shows another example of a different three-dimensional sinogram in the second embodiment. FIG. 10 is a diagram showing still another example of the three-dimensional sinogram in the second embodiment.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... X-ray tube, 2 ... X-ray beam, 3 ... X-ray detector, 4 ... Subject, 5 ... Rotary table, 6 ... Rotary axis, 7 ... X-ray optical axis, 9 ... Support frame, 10 ... X shift 11, support frame, 12, y shift mechanism, 13, rotation / lifting mechanism, 14, imaging surface, 20, data processing unit, 20 A, scan control unit, 20 B, rotation center finding unit, 20 C, reconstruction unit , 21 ... display section, 22 ... mechanism control section, 23 ... X-ray control section, 24 ... high voltage generator, 30 ... focal locus, 40 ... subject existence area, C ... rotation center, D ... detection center.

Claims (5)

A radiation source that emits radiation; a radiation detector that detects a radiation beam transmitted through the subject from the radiation source; and a rotating unit that relatively rotates the subject with respect to the radiation beam, In a computer tomography apparatus for obtaining a tomographic image of a subject from a plurality of transmission data of the subject detected by the radiation detector at a number of rotational positions due to relative rotation of the subject,
On the sinogram created from a large number of transmission data of the subject, the added value of transmission data at a plurality of points connected in the direction of the relative rotation and the multiple points determined by setting a virtual rotation center are respectively opposite in direction. Rotation to obtain the correlation with the added value of transmission data at multiple points forming a radiation path while changing the virtual rotation center, and to determine the virtual rotation center at which the correlation appears best as the true rotation center in the rotating means A computer tomography apparatus comprising a center finding means. The computed tomography apparatus according to claim 1,
The computed tomography apparatus according to claim 1, wherein the sinogram is a sinogram composed of a collection of a large number of transmission data of the subject obtained during relative rotation of the subject less than one rotation. A radiation source that emits radiation; a radiation detector that detects a radiation beam transmitted through the subject from the radiation source; a rotating unit that relatively rotates the subject with respect to the radiation beam; and the radiation beam On the other hand, there is a rotation axis direction moving means for moving the subject in the rotation axis direction relative to the rotation axis, and the radiation detector performs the relative rotation and the relative movement in the rotation axis direction in parallel. In a computed tomography apparatus for obtaining a tomographic image of a subject from a large number of transmission data of the subject to be detected,
On the sinogram created from a large number of transmission data of the subject, the added value of transmission data at a plurality of points connected in the direction of the relative rotation and the multiple points determined by setting a virtual rotation center are respectively opposite in direction. Rotation to obtain the correlation with the added value of transmission data at multiple points forming a radiation path while changing the virtual rotation center, and to determine the virtual rotation center at which the correlation appears best as the true rotation center in the rotating means A computer tomography apparatus comprising a center finding means. The computed tomography apparatus according to any one of claims 1 to 3,
The rotation center finding means is configured such that the rotation angle of the relative rotation is φ, the radiation path angle along the surface of the relative rotation from the radiation source is θ, the set virtual rotation center is θc, and the sinogram of the sinogram A forward path correlation region and a reverse path correlation region, which are sets of points that form radiation paths that are opposite to each other and change according to θc on the θφ plane, are set, and each of the forward path correlation region and the reverse path correlation region is set. A computed tomography apparatus characterized in that an addition value of the transmission data from one end to the other end in the direction of relative rotation is obtained. The computed tomography apparatus according to claim 4.
A computed tomography apparatus characterized in that, of the boundary lines between the forward path correlation area and the reverse path correlation area, all boundary lines that change due to θc are set to straight lines parallel to the θ direction.

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