JPH0427858B2 - - Google Patents

Description

Detailed Description of the Invention (Industrial Application Field) The present invention relates to a backprojection calculation method and a backprojection calculation device for a tomography apparatus that performs high-speed backprojection calculations using data collected around a subject. , More specifically, the number M of back projection data including the number N of real sample data is M=k・N (k is an integer) and M=M ₁ ,
The present invention relates to a backprojection calculation method and a backprojection calculation device for a tomography apparatus that can flexibly respond to changes such as M ₁ /2, M ₁ /4, . . .

(Prior art) Conventionally, a subject is irradiated with fan-beam X-rays from multiple angular directions (hereinafter referred to as viewing directions), projection data is collected, and a computer performs calculation processing on these projection data. The back projection calculation device of an X-ray tomography device (hereinafter referred to as a CT device), which calculates the X-ray absorption of each part of the object and backprojects (reconstructs) the tomographic image of the object, is well known. ing.

In such a back projection calculation device, the number M of back projection data is calculated based on the original number N of real channel data, so that M=k·N (k is an integer), that is, each channel is divided into k equal parts. In some cases, k times the back projection data is calculated (hereinafter, this is referred to as (k-1) point interpolation). More specifically, in actual CT equipment, 7-point interpolation (8x) and 3-point interpolation (4x) are necessary for calculation, and 5-point interpolation (6x) and 2-point interpolation (3x) are required. may become necessary.

In such a case, a conventional back projection calculation device of a CT apparatus has the following configuration (explained using an example of performing 7-point interpolation and 3-point interpolation).

(1) Back projection data selection circuits for 7 points and 3 points are prepared and used by dynamically switching.

(2) Control table for 7-point interpolation and 3-point interpolation
It consists of RAM (Random Access Memory) and dynamically rewrites the contents.

(3) A backprojection calculation device is constituted by a backprojection data selection circuit with the maximum number of interpolation points, that is, 7-point interpolation, and even in the case of 3-point interpolation, data for 7-point interpolation is generated by interpolation calculation.

(Problems to be Solved by the Invention) However, the above methods (1) and (2) are accurate and have good image quality and resolution, but have the problem of being expensive. Furthermore, the method (2) has the problem that it takes a long time to rewrite the contents of the RAM. Furthermore, although the method (3) is highly economical, it takes a long time to calculate the interpolation, and furthermore, there are problems in that the image resolution deteriorates due to unnecessary interpolation.

The present invention has been made in view of these points, and its purpose is to provide a CT apparatus that is excellent in high-speed processing performance and high resolution, can flexibly respond to changes in the number of interpolation points, and is economical. The present invention provides a backprojection calculation method and a backprojection calculation device.

(Means for solving the problem) The back projection operation of the present invention that achieves the above object is as follows:
(k/2 ⁿ -1) point interpolation (k/2 ⁿ =k, k/
2, k/4, ... and a positive integer, i.e. n=0,
1, 2, ...), the tomography apparatus generates back projection data of k・N, k/2・N, k/4・N, ... for the original number of sample data N and performs back projection. In the back projection calculation method, (k/2-1) points,
When performing interpolation at either (k/4-1) points, (k/8-1) points, ^etc. , the same In addition to allocating backprojection data, the backprojection center position is shifted by a predetermined amount from the case of (k-1) point interpolation, and the same calculation process as for (k-1) point interpolation is performed to perform backprojection. I'm starting to do that.

(Example) The present invention will be described in detail below. First of all,
Let us now explain the principle of the present invention.

(1) Relationship between interpolation and back projection data In general, one view of real sample data (actual channel data; number of data N) of 7-point interpolation and one view of interpolated data (total number of back projection data M = 8N) The relationship is depicted in Figure 1a. In addition, in the case of three-point interpolation, the result is as shown in FIG. 1b. The selection range of each data when performing back projection in interpolation of each point by nearest neighbor interpolation is as shown in Figure 1 a and b. It should be noted that the 3-point interpolation data is generated at each point, and that the 3-point interpolation data is generated at each quadrant of the actual sample data, and the center position. Further, in the case of seven-point interpolation, the relationship between the deviation in the backprojection direction from the center (deviation in backprojection data) and the selected data is as shown in FIG.

Therefore, by performing the following processing and setting the relationship between the actual sample data and the interpolated data as shown in FIG. Incidentally, in the case of this three-point interpolation, the relationship between the deviation in the backprojection direction from the center (deviation in the backprojection data) and the selected data is shown in FIG.

(a) Double the generated 3-point interpolation backprojection data by assigning the same data of two consecutive channels of 7-point interpolation.

(b) The center position is + from the normal 7 points.
Shift by 0.5.

(c) Calculation of back projection data selection address is performed by rounding.

From the above, the following can be said.

(k/2 ⁿ −1) point interpolation ((k/2 ⁿ =k,
k/2, k/4, ... and a positive integer, that is, n=
0, 1, 2, ...), k・N, k/2・N, k/4・N, ... for the original number of sample data N.
In a backprojection calculation method that generates backprojection data and performs backprojection, (k/2-1) points, (k/4-
1) When performing interpolation at either point, (k/8-1) point,..., assign the same backprojection data to 2 ⁿ consecutive channels corresponding to (k-1) point interpolation, The center position of the back projection is shifted by C+2 ^n-1 -0.5 from the case of (k-1) point interpolation by the data number of the center position of C...(k-1) point interpolation, counting from 0. Therefore, even in interpolations other than (k-1) point interpolation, back projection can be performed using the same calculation process as in (k-1) point interpolation.

(2) Backprojection calculation in the Juan beam direct reconstruction method The geometric configuration in the Juan beam backprojection is based on the fourth
Notated in the figure. In Fig. 4, X _k is the position of the X-ray generation point (X-ray tube focal point), PA is the reconstruction area,
O is the reconstruction center (Iso-Center; this point is taken as the origin of the x,y plane). The reconstruction area PA is
Straight lines parallel to the X-axis and Y-axis, respectively, x = x ₁ , x ₂ , x ₃ ,
..., x _2n and y=y ₁ , y ₂ , y _{3 ,} . The spacing between the straight lines in the x and y directions is Δx and Δy, respectively. A straight line X _k O from any point Q (x, y) in the reconstruction area PA,
Or, if the foot of the perpendicular drawn on the extension is Q', then the distances QQ' and X _k Q' are respectively p(=p(i,
j, k)) and h (=h(i, j, k)). Now, if point Q(x, y) is a reconstruction point,
The point can be expressed as Q(x _i , y _j ) or Q(i, j), and the radiation absorption coefficient μ at the reconstruction point Q
The back projection calculation to obtain (i, j) is expressed as equation (1).

μ(i,j)=b・_Vn 〓 ^k=1 w(i,j,k)・D{CHA
(i, j, k)} (1) Also, the following equations hold true.

w (i, j, k) = [{p (i, j, k)} ² + {h (
i,
j, k)} ² ] ^-1 (2) CHA (i, j, k) = CCH (k) - a・tan ^-1
p(i, j, k)/h(i, j, k) (3) p(i, j, k)=x _i・sinθ _k −y _j・cosθ _k −y _j・
cosθ _k (4) h(i, j, k) = L−x _i・cosθ _k −y _j・sinθ _k (5) However, i=1, 2,...2・m _j j=1, 2,... , 2・n k=1, 2,..., Vm a and b...Proportionality constant (a>0) L...Distance between radiation generation point X _k and reconstruction center O θ _k ...Straight line OX _k is positive on the Angle formed with the direction CHA (i, j, k)...θ=θ _k direction, that is, point Q (x _i , y _j ) in the k-th view
Data No. of back projection that passes through D {CHA (i, j, k)}...The data No.
Intensity of backprojection data w(i, j, k)...Weighting coefficient of backprojection data passing through point Q(x _i , y _j ) in the k-th view Also, the following equation holds on y=y _j .

Δp(k)=p(i+1,j,k)−p(i,j,k)=Δx・sinθ _k (6) Δh(k)=h(i+1,j,k)−h(i,j, k) = -Δx・cosθ _k (7) (3) Back projection data can be obtained from equation (1), but rounding is necessary in calculating the back projection data selection address (formula (3)). be. However, rounding in pipeline operations generally complicates the circuit and increases the number of steps in the operation. This results in higher costs and longer calculation cycles (making it difficult to build pipelines). On the other hand, the second term of equation (3) is (4)
It becomes negative/positive corresponding to the positive/negative of p in the expression. or,
In order to make the device at low cost, tan ^-1 (p/h)≧
It is better to configure it with only 0 values. In order to satisfy these conditions, the following configuration is possible.

(a) For 7-point interpolation When p<0 CHA (i, j, k) = trunc {CCH (k) + 0.5 +
ATAN(i, j, k)} …(3-1a) ・If p≧0 CHA(i, j, k)=trunc[CCH(k)+0.5+
1's Complement {ATAN (i, j, k)}] ... (3-1b) ・ATAN (i, j, k) = | a・tan ^-1
p (i, j, k) / h (i, j, k) | ... (3-1c) However, ATAN ... trunc data in units of 0.5 (decimal part truncated data) 1's Complement ... 0.5 is LSB ( Least
Significant Bit) 1's complement (b) For 3-point interpolation - When p < 0 CHA (i, j, k) = trunc {CCH (k) + 1.0 +
ATAN(i, j, k)} …(3-2a) ・When p≧0 CHA(i, j, k)=trunc[CCH(k)+1.0+1′s
Complement {ATAN (i, j, k)}] ... (3-2b) Note that the intermediate calculation and intermediate result of the back projection calculation are as follows.

μ(i, j, k)=b・_l 〓 ^k=1 w(i, j, k)・D
{CHA (i, j, k)} ... (1-1) However, l = 1, 2, ..., Vm μ (i, j, k) = μ (i, j, k-1) + b・w ( i, j, k)・D{CHA(i, j,
k)} (1-2) However, k=1, 2,..., Vm μ(i, j, k)=0 FIG. 5 is a block diagram of a high-speed backprojection calculation device according to an embodiment of the present invention. This shows the configuration of a device that directly constructs a fan beam in units of one view. In FIG. 5, PL and HL are register memory groups including adders, register files, registers, etc. The register memory group PL is the initial value p(l, j, k) of p(i, j, k) (formula (4)) for each view.
(j = 1, 2, ..., 2n, 2n = 320 pieces) and Δp(k) ((6)
expression) and use it. Also, register memory group
In PL, during the back projection calculation, the next p data is updated and generated according to equation (6-1).

p(i+1,j,k)=p(i,j,k)+Δp(k)
(6-1) However, i = 1, 2, ..., 2 m _j -1 The register memory group HL is h for each view.
Initial value h(l, j, k) of (i, j, k) (formula (5))
(j = 1, 2, ..., 2n, 2n = 320 pieces) and Δh(k) ((7)
expression) and use it. Also, register memory group
In HL, during the back projection calculation, the next h data is updated and generated according to equation (7-1).

h(i+1,j,k)=h(i,j,k)+Δh(k)
(7-1) However, i=1, 2, . . . , 2·m _j −1 WGT is a table equipped with an arithmetic unit, table data ROM, registers, etc. Table WGT
are the outputs p and h of the register memory groups PL and HL
is input, the weighting coefficient of w(i, j, k) in equation (2) is calculated, and the result w is given to the multiplier MUL.
CHA is a back projection data selection circuit equipped with an arithmetic unit, table data ROM, registers, gates, etc. The selection circuit CHA selects the register memory group PL and
Using the outputs p and h of HL and CHA(k) given via the data line DT as input, (3-1a),
Calculate CHA (i, j, k) in each equation (3-1b), (3-2a), and (3-2b), and use the resulting
Give HMA to fast access memory HM. still,
The back projection data selection circuit CHA will be explained in more detail later with reference to FIG. HM is a small-capacity high-speed access memory (RAM) that stores back projection data (interpolated) D {CHA (i, j, k)}
(Formula (1)) is stored and used. In the high speed access memory HM, output data corresponding to the output HMA of the back projection data selection circuit CHA is read out and output to the multiplier MUL.

The above-mentioned back projection data is generated by a high-speed arithmetic processing device, stored in a main memory (none of which is shown), and is transferred to a high-speed access memory HM via a data line DT at a predetermined timing. Back projection data generated by a high-speed arithmetic processing device is processed by, for example, (k/2 ⁿ −1) point interpolation (k/2 n −1) point interpolation (k/2 n −1)
2 ⁿ = k, k/2, k/4, ... and a positive integer, i.e., n = 0, 1, 2, ...), k・N, k/2 for the original number of sample data N・N,k/
A case where back projection data of 4.N, . . . is generated and back projected is explained as follows.

(k/2-1) point, (k/4-1) point, (k/8
-1) When interpolating any of the points, etc., k/2 ⁿ・N interpolated data are
Generate a ₀ , a ₁ , ..., a _n-1 (where m = k/2 ⁿ・N), and generate a ₀ , ..., a ₀ (2 ⁿ in total) a ₁ , ..., a ₁ (2 ⁿ in total) 慊 慊 慊 慊 a _n-1 ..., a _n-1 (2 ⁿ in total) Consecutive 2 channels corresponding to (k-1) point interpolation It is designed to allocate 2 ⁿ items in a row to 2 ⁿ items.

MUL is a pipeline (3 stages) multiplier. The multiplier MUL receives the output w(i, j, k) from the table WGT and the high-speed access memory HM.
and D{CHA(i,j,k)} are given as inputs 2 and 1, and the multiplication result is output to the adder ADD. ADD is a pipeline (three-stage) adder, which receives the outputs from the multiplier MUL and the memory MM as inputs 1 and 2, and performs addition thereof. The addition result is stored in memory MM.
The MM is a high-speed, large-capacity RAM memory that stores backprojection result data (intermediate result and final result data corresponding to each pixel (formula 1-2)). Memory MM
The read and write operations (access addresses are different) are possible in the same cycle. CTL is the control unit. The control unit CTL generates a clock, controls the timing of each part, controls the number of calculations for each line, controls read and write addresses of the memory MM (initial value setting, update, etc.), and communicates with an external device (not shown). Control exchange (via C bus), register memory group PL and
Transfer of initial data to HL, high-speed access memory HM, back projection data selection circuit CHA, etc., memory
Controls MM initialization, data transfer from memory MM to external devices, etc. Further, the number of data for each line, the start address of the memory MM for each line, etc. are held in the ROM memory of the control unit CTL.
DT is a data line (bus) that connects this device to an external device such as a high-speed arithmetic processing device, and C is a control line that connects this device and the external device. Also, C ₁ to C ₈
are a control line and a data line connecting the control unit CTL and each part of this device. It should be noted that each section in FIG. 5 operates in parallel to perform backprojection calculations at the highest speed allowed by this apparatus.

FIG. 6 is a block diagram of the back projection data selection circuit CHA. ATAN is arithmetic unit and table data
It is an arithmetic unit consisting of ROM, etc., and ADDR is a 12-bit adder. Arithmetic unit ATAN is (3-1c)
Calculate ATAN (i, j, k) in the equation. The calculation result AT (12 bits) is given to input 2 of the adder ADDR. CCH is a register, and CCH(k)+0.5 in formula (3-1a) or (3-1b), or
CCH(k)+ of formula (3-2a) or (3-2b)
1.0, and this output CCH (12 bits) is used as an adder.
Given to input 1 of ADDR. The adder ADDR is
If p<0, add input 1 and input 2 ((3-
1a) or (3-2a)),
If p≧0, 1 of input 1 data and input 2 data
Addition (calculation based on formula (3-1b) or formula (3-2b)) is performed between multiple pieces of data (this addition calculation assumes that the virtual decimal point is between bit 0 and bit 1). are doing). The upper 11 bits of this output are given to the lower 11 bits of register HMAR. That is, the LSB (0th bit) of adder ADDR
will be truncated. A.G.
is an AND gate and HMAR is a register. AND gate AG generates a carry in the operation in adder ADDR, and at this time,
When p<0, a true value of 1 is generated and this is stored in a register.
otherwise, a false value of 0 is given to the MSB of register HMAR. Also, register HMAR sends its output to fast access memory.
Output to HM as address data HMA.

FIGS. 7a and 7b are flowcharts of scanning, image reconstruction, and backprojection calculations performed under the conditions (1) to (3) below. During this scan and image reconstruction, each part of the CT device and each part of the back projection calculation device operate in parallel, but looking at the back projection processing and other relationships, the back projection of the n-th view and the back projection of the n+1 view Other processing is proceeding in parallel.

(1) Perform direct reconstruction of the fan beam in units of one view.

(2) This is an example where processing other than backprojection processing (preprocessing, filtering, interpolation processing, backprojection preparation, etc.) and backprojection processing are performed in parallel.

(3) It shows the order of processing sequentially, and does not necessarily completely show the parallel operation of the device or the parallelism of processing. For example, it is not easy to express that in one view backprojection, backprojection of one point, updating of p and h values, counting of processing times, conditional branching, etc. are performed in parallel.

In addition to the above-mentioned embodiments, the present invention can be implemented in various ways. For example, the back projection calculation device shown in FIG. 5 can be constructed by appropriately selecting one of the following (1) to (8).

(1) The structure around the adder ADD is shown in Figure 8 a or b. In a, input 2 of adder ADD
The output of memory MM and the output of adder ADD are given to , and one of them is selected within adder ADD. In b, the output of memory MM and adder ADD
The outputs of are input to the selector S, and one of them is selected and connected to the input 2 of the adder ADD. Although not shown, a configuration is also conceivable in which the output of the memory MM, the output of the adder ADD, and data with a value of 0 are given to the input 2 of the adder ADD, and any one of them is selected. These are used for backprojection of n views (multiple views) at once. In this case, the memory MM can be configured with a low-speed, large-capacity dynamic RAM or the like, which is advantageous in terms of cost.

(2) A buffer register is provided after the multiplier MUL (before the adder ADD) and after the adder ADD.

(3) Register memory groups PL and HL consisting of adders, register files, registers, etc.

(4) Back projection data selection circuit CHA and table
A WGT configured with table data ROM (or table data RAM), arithmetic units, registers, etc.

(5) High-speed access memory HM and memory MM divided into multiple parts.

(6) The control unit CTL is connected to the microprogram memory,
A device consisting of a decoder, control device, etc.

(7) Unified or separated data lines (data bus) and control lines.

(8) A combination of multiple devices.

Further, the configuration of the back projection data selection circuit shown in FIG. 6 may be configured as shown in (1) or (2) below.

(1) The adder ADDR is configured with one or more bits, and the output (upper bit group) of the adder ADDR is directly connected to the register HMAR, excluding the AND gate AG.

(2) Apply the output of the arithmetic unit ATAN to the input of the 1′s Complement arithmetic unit, and if p<0, the arithmetic unit
The output of ATAN is directly applied to input 2 of adder ADDR. On the other hand, if P≧0, 1′s
The output of the complement operator is selected to be given to input 2 of the adder ADDR, and the adder ADDR is configured with a simple adder.

Although the above embodiments have been described with respect to an X-ray CT device, the present invention is not limited to this, and can be applied to tomography devices such as an MR tomography device (imaging device using nuclear magnetic resonance absorption phenomenon), a γ camera, etc. It can also be applied to those that perform back projection.

(Effects of the Invention) As described above, according to the back projection calculation method and back projection calculation apparatus for a tomography apparatus of the present invention, the following effects can be expected.

(1) Table data ROM switch (switching)
It is possible to flexibly respond to changes in the number of backprojection interpolation points without or without changing the contents of the table data RAM.

(2) Since only one type of ROM is required (or an inexpensive ROM can be used instead of an expensive RAM), the configuration of the device can be simplified and costs can be reduced.

(3) High-speed processing is possible because there is no need for extra interpolation processing (or no need to dynamically change the contents of RAM).

(4) Since no extra interpolation processing is required, high resolution, high spatial resolution, etc. can be maintained.

Furthermore, by adopting the configuration of the back projection data selection circuit as shown in FIG. 6, the configuration of the adder ADDR can be configured with the minimum number of bits, which is economical. In addition, since the back projection data selection circuit does not require rounding, the number of stages of pipeline arithmetic units is small, and it is easy to use.
This contributes to the realization of high-speed and inexpensive equipment.

[Brief explanation of drawings]

Figures 1a, b, and c are diagrams explaining the principle of the present invention, and are diagrams showing the relationship between interpolation data and back projection. Figure 2 shows data selection near the center position during 7-point interpolation. The figure shown in FIG.
A diagram showing data selection near the center during point interpolation, FIG. 4 is a geometric configuration diagram in Fan beam backprojection, and FIG. 5 is a diagram showing a high-speed backprojection calculation device according to an embodiment of the present invention. The configuration diagram, FIG. 6, is the configuration diagram of the back projection data selection circuit in FIG. 5, and FIG. 7a.
and b are explanatory diagrams of the scan and image reconstruction flows and backprojection flows in the apparatus of FIG. FIG. HL and PL... register memory group, WGT... table, CHA... back projection data selection circuit, HM... high speed access memory, MUL... multiplier, MM... memory, ADD... adder, CTL... control unit, ATAN... calculation unit, CCH...Register, ADDR...Adder.

Claims (1)

[Claims] 1. A large amount of data for tomography is collected from the subject, and (k/2 ⁿ -1) point interpolation (where k/2 ⁿ = k,
k/2, k/4, ... and a positive integer, that is, n=
0, 1, 2, ...), k・N, k/2・N, k/4・N, ... for the original number of sample data N.
In a back projection calculation method for a tomography apparatus that generates back projection data and performs back projection, (k/2-1) point, (k/4-1) point, (k/8
−1) When performing interpolation at any of the points, (k
-1) Each successive channel corresponding to point interpolation
2 Assign the same backprojection data to ⁿ pieces, and
A tomography apparatus characterized in that the center position of back projection is shifted by a predetermined amount from that in the case of (k-1) point interpolation, and back projection is performed by the same calculation process as in (k-1) point interpolation. Back projection calculation method. 2 The back projection center position shift amount is (k-1)
2. A back projection calculation method for a tomography apparatus according to claim 1, wherein the calculation method is equivalent to point interpolation and is determined based on the following formula. C+2 ^n-1 -0.5 However, C... (k-1) Data number at the center position of point interpolation counted from 0 3 A large amount of data for tomography is collected from the subject, (k/2 ⁿ -1) 1) Point interpolation (k/2 ⁿ = k,
k/2, k/4, ... and a positive integer, that is, n=
0, 1, 2, ...), k・N, k/2・N, k/4・N, ... for the original number of sample data N.
In a back projection calculation device for a tomography apparatus that generates back projection data and performs back projection, a back projection calculation means by (k-1) point interpolation;
(k/2-1) point, (k/4-1) point, (k/8-
1) When performing interpolation at any of the points,..., k/2 ⁿ・N interpolated data a ₀ , a ₁ ,..., a _n-1 ( However, m=k/
2 ⁿ・N), a ₀ , ..., a ₀ (total of 2 ⁿ pieces) a ₁ , ..., a ₁ (total of 2 ⁿ pieces) 慊 慊 慊 慊 a _n-1 ..., a _{n -1} (total of ²ⁿ channels), and means to allocate ²ⁿ channels to consecutive ²ⁿ channels corresponding to (k-1) point interpolation, and to set the center position of the back projection to (k-1) point interpolation. -1) Backprojection calculation of a tomography apparatus characterized by comprising: backprojection data selection means for selecting backprojection data by shifting it by a predetermined amount from the case of point interpolation and providing the data to the backprojection calculation means. Device. 4. The tomography apparatus according to claim 3, wherein the back projection data selection means determines the shift amount of the back projection center position based on the following formula, corresponding to (k-1) point interpolation. Back projection calculation device. C+2 ^n-1 -0.5 However, C... (k-1) Data number of the center position of point interpolation, counted from 0 5 The back projection data selection means is CCH+AT or CCH-AT However, CCH (> 0)... Constant AT (≧0)... Back projection data to select
Equipped with a selection logic operation means based on any formula of a number corresponding to the deviation from CCH, and expressing CCH and AT as a number with a decimal point,
CCH + AT is calculated by adding CCH and AT, and CCH - AT is calculated by adding 1's complement of CCH and AT, and the decimal point of the calculation result is rounded down and only the integer part is used. A back projection calculation device for a tomography apparatus according to claim 3.