Chirality-based method for determining the absolute configuration of a chiral compound

Abstract

This invention relates to a tomographic gamma-ray scanning method for transmission imaging and a method for solving the track matrix, including: establishing a voxel model of a rectangular container of nuclear waste; performing layer-by-layer scanning measurements on the voxel model to acquire scanning data; solving the track matrix of TGS transmission imaging using the above method: dividing the two-dimensional plane into 9 regions using the four sides of a rectangular clipping window; denoting the codes at both ends of the line segment to be clipped as code1 and code2 respectively, and determining the relationship between code1 and code2 and the clipping window: if code1=code2=0, the line segment is completely visible and is selected; if code1&code2≠0, & is a bitwise AND operation, the line segment is completely invisible and is discarded; if neither code1=code2=0 nor code1&code2≠0 is satisfied, a perpendicular line is drawn from the vertex of the clipping window to the line segment; if the foot of the perpendicular is within the clipping window, an intersection operation is performed on the line segment; if the foot of the perpendicular is outside the clipping window, it is discarded; and reconstructing the linear attenuation coefficient. This invention effectively avoids the shortcomings of the traditional Cohen-Sutherland algorithm and improves the efficiency of track matrix solving.

Description

Technical Field

[0001] This invention belongs to the field of tomographic gamma scanning technology, and in particular to a tomographic gamma scanning method in transmission imaging and a method for solving the track matrix. Background Technology

[0002] Tomographic gamma scan (TGS) is a passive gamma analysis method, belonging to the category of non-destructive analysis (NDA). TGS technology was developed based on segmented gamma scan (SGS), specifically designed to address the limitations of SGS in accurately measuring high- and medium-density, non-uniformly distributed nuclear waste. [1] Linear attenuation coefficient reconstruction is a crucial part of TGS transmission measurement reconstruction. Currently, reconstruction algorithms are mainly divided into two categories: one is analytical reconstruction algorithms that directly perform mathematical inverse calculations on the image to be reconstructed based on Radon transform theory, mainly including the Filter Back Projection (FBP) algorithm and the Radon inverse transform algorithm. The other is iterative reconstruction algorithms that transform the voxel values ​​and projection values ​​of the reconstructed image into a series of linear equations, and obtain the image to be reconstructed by solving these linear equations, mainly including algebraic iterative reconstruction algorithms and statistical iterative reconstruction algorithms. Algebraic iterative reconstruction algorithms mainly include algebraic reconstruction techniques (ART algorithms) and synchronous iterative reconstruction algorithms. Synchronous iterative reconstruction algorithms mainly include SART algorithms, DROP algorithms, etc. Statistical iterative reconstruction algorithms mainly include MLEM algorithms, OSEM algorithms, etc. Currently, commonly used algorithms in TGS image reconstruction include the Expectation-Maximization Algorithm (EM) algorithm and the ART algorithm. [3][4] The EM algorithm is an iterative algorithm based on mathematical statistics. It has good operability and convergence, and exhibits excellent noise resistance and reconstructed image quality within a certain number of iterations, but its convergence speed is too slow. The ART algorithm, due to its large computational load and long reconstruction time, with most of the time spent calculating projection and backprojection, has been continuously improved in terms of reconstruction efficiency through algorithm improvements and hardware acceleration over the years, but it still has excellent noise resistance.

[0003] Two key factors in TGS transmission imaging are solving the track matrix and the projection matrix. Common methods for calculating the track matrix include the averaging method, Monte Carlo simulation, and computer graphics clipping methods. Clipping methods process a defined graphic along the window boundaries according to pre-set window parameters and display the graphic within the window. The purpose of clipping is to remove parts of the graphic outside the user-defined window, providing clear and distinct objects for image recognition and processing. Clipping line segments is one of the most fundamental problems that computer graphics needs to solve. Currently, four widely used classic clipping algorithms are: the Liang Youdong-Barsky algorithm using parametric form... [6] Nicholl-Lee-Nicholl algorithm based on region segmentation [7] Cyrus-Beck algorithm suitable for polygonal windows [8] Cohen-Sutherland Algorithm Based on Region Coding [9] The Liang-Barsky algorithm uses the parametric representation of line segments to simplify the calculation of the intersection coordinates of the line containing the clipped line segment and the border of the rectangular clipping window into the calculation of the parameter values ​​corresponding to the intersection points. Then, based on the comparison between the intersection point parameters and the parameter definition range of the clipped line segment, it determines the valid intersection points, thus obtaining the portion of the line segment to be retained after clipping. The Nicholl-Lee-Nicholl algorithm reduces the number of intersection point calculations by adding more region tests based on the encoding algorithm. The Cyrus-Beck algorithm is an early clipping algorithm proposed for handling convex polygon clipping windows. For concave polygons, there is currently no universal algorithm; the common approach is to segment concave polygons into convex polygons, such as the extension line segmentation method and the rotation segmentation method.

[0004] The Cohen-Sutherland clipping algorithm is one of the earliest and most widely used clipping algorithms. The basic idea is as follows: First, a region code is used to identify the region where the endpoints of a line segment are located. Based on the code, the specific location of the line segment can be identified. For line segments that are not entirely within or entirely outside the window, their intersection points with the window need to be calculated. The portion outside the window is discarded, and the remaining portion is treated as a new line segment for further evaluation. After two clipping evaluations, it can be determined whether the line segment is partially cut off or completely discarded. However, because the Cohen-Sutherland algorithm cannot effectively determine whether a line segment is outside the window, it also calculates intersections for line segments that are partially outside the clipping window, significantly reducing computational efficiency.

[0005] References:

[0006] Li Lei. Research on Chromatographic Gamma Scan Transmission and Emission Reconstruction Technology for Barrelled Nuclear Waste [D]. Chengdu University of Technology, 2015.

[0007] Estep R J, Prettyman T H, Sheppard G A. Tomographic gamma scanning toassay heterogeneous radioactive waste[J]. Nuclear science and engineering,1994, 118(3): 145-152.

[0008] Kim J, Jung S, Moon J, et al. A feasibility study on gamma-raytomography by Monte Carlo simulation for development of portable tomographicsystem[J]. Applied Radiation and Isotopes, 2012, 70(2): 404-414.

[0009] Aijing H, Xianguo T, Rui S, et al. An improved OSEM iterativereconstruction algorithm for transmission tomographic gamma scanning[J].Applied Radiation and Isotopes, 2018, 142: 51-55.

[0010] Tuaç Y, Güney Y, Arslan O. Parameter estimation of regression modelwith AR (p) error terms based on skew distributions with EM algorithm[J].Soft Computing, 2020, 24(5): 3309-3330.

[0011] NIOGOLL T M, LEE D T, NIOHOLL R A. A effcient new algorithm for 2-Dline clipping:its devclopment and analysis[J].CG,,1987,21(4):253-262.

[0012] LIANG YD, BARSKY BA. A new concept and method for line clipping[J]. ACM, 1984, 3(1): 1-22.

[0013] Zhang Quanhu, Sui Hongzhi, Lü Feng, Li Ze, Gu Zhongmao. Reconstruction method of tomographic gamma-ray transmission image [J]. Atomic Energy Science and Technology, 2004(02): 162-165.

[0014] HEARND, BAKERMP. Computer Graphics: C Language Edition [M], 2nd Edition (Reprint). Beijing: Tsinghua University Press, 1998. Summary of the Invention

[0015] The technical problem to be solved by the present invention is to provide a tomographic gamma scanning method and a method for solving the transmission imaging track matrix, which effectively avoids the defects of the traditional Cohen-Sutherland algorithm and improves the efficiency of track matrix solving.

[0016] To solve the above problems, the technical solution adopted in this invention is: a method for solving the trajectory matrix of transmission imaging, including...

[0017] S31. Divide the two-dimensional plane into 9 regions using the four sides of the rectangular clipping window, and label each region with a 4-bit binary code: the three regions above the clipping window are 1001, 1000, and 1010 from left to right, the region on the left side of the clipping window is 0001, the region on the right side is 0010, the region inside the clipping window is 0000, and the three regions below the clipping window are 0101, 0100, and 0110 from left to right.

[0018] S32. Denote the codes at both ends of the line segment to be clipped as code1 and code2 respectively, and determine the relationship between code1 and code2 and the clipping window:

[0019] If code1=code2=0, the line segment is fully visible, so we take it;

[0020] If code1&code2≠0, & is a bitwise AND operation, the line segment will be completely invisible and should be discarded;

[0021] If neither code1=code2=0 nor code1&code2≠0 is satisfied, then draw a perpendicular line from the vertex of the clipping window to the line segment, and then determine the position of the foot of the perpendicular. If the foot of the perpendicular is inside the clipping window, then perform an intersection operation on the line segment; if the foot of the perpendicular is outside the clipping window, then discard it.

[0022] Chromatographic gamma scanning methods, including

[0023] S1. Establish a voxel model of the square container for sample nuclear waste;

[0024] S2. Perform layer-by-layer scanning measurements on the voxel model to obtain scanning data;

[0025] S3. Solve the track matrix of TGS transmission imaging using the above method;

[0026] S4, Reconstruct the linear attenuation coefficient.

[0027] Furthermore, in step S1, each layer of the voxel model has Voxels, each voxel is [size missing] .

[0028] Furthermore, in step S2, the scanning method for each voxel layer is as follows:

[0029] S21. Select 5 equally spaced measurement points, measure three times at each measurement position, take the average value as the measurement value, and then calculate the projection data.

[0030] S22. Using the geometric center of the voxel model as the rotation center, rotate the voxel model clockwise by 0 degrees, 45 degrees, 90 degrees, and 135 degrees. After each rotation, select 5 equally spaced measurement points, measure three times at each measurement position, and take the average value as the measurement value. Then calculate the projection data.

[0031] Further, step S4 includes

[0032] S41, Given unknown quantities x j Assign initial values, ;

[0033] S42. For the nth subset, calculate the estimated values ​​of all projections within the subset:

[0034] ;

[0035] According to the formula

[0036]

[0037] Calculation error;

[0038] According to the formula

[0039]

[0040] Calculate the correction value for the j-th unknown;

[0041] right x j The value is corrected: ;

[0042] S43. Repeat step S42 until the operation of n subsets is completed, thus completing one round of iteration;

[0043] S44. Using the result of the previous iteration as the initial value, repeat steps S42 and S43 and perform a new round of iteration until a result that meets the convergence requirements is obtained.

[0044] The beneficial effects of this invention are as follows: The track matrix solution method of this invention uses the Cohen-Sutherland algorithm, which can accurately determine whether a line segment is inside the clipping window and whether it intersects with the clipping window. When a line segment is not inside the clipping window, it is directly discarded without needing to find its intersection. This solves the problem in the existing Cohen-Sutherland algorithm that it cannot accurately identify whether a line segment is outside the clipping window and therefore has to find the intersection of some line segments outside the clipping window, thus improving the solution efficiency. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the TGS transmission measurement system of the present invention;

[0046] Figures 2 to 5 This is a schematic diagram of layer-by-layer scanning measurement of a voxel model;

[0047] Figure 6 This is a schematic diagram of the region segmentation of the Cohen-Sutherland clipping algorithm of this invention;

[0048] Figure 7 This is a schematic diagram of the present invention where a perpendicular line is drawn from the vertex of the clipping window to the straight line segment;

[0049] Figure 8 This is a schematic diagram of an embodiment of the present invention in which a perpendicular line is drawn from the vertex of the clipping window to the straight line segment;

[0050] Figure 9 This is a flowchart of the Cohen-Sutherland pruning algorithm of this invention;

[0051] Figure 10(a) is a schematic diagram of the effect of the present invention in cutting off two straight line segments;

[0052] Figure 10(b) is a schematic diagram of the effect of cutting 10 straight line segments according to the present invention;

[0053] Figure 11(a) Schematic diagram of a pre-designed model of a single-medium material;

[0054] Figure 11(b) is a schematic diagram of the pre-designed model of the hybrid material;

[0055] Figure 12(a) shows the reconstruction results of the attenuation coefficient of concrete under an energy of 0.661 MeV according to the present invention;

[0056] Figure 12(b) shows the reconstruction results of the attenuation coefficient of polyethylene at an energy of 0.661 MeV according to the present invention;

[0057] Figure 12(c) shows the reconstruction results of the attenuation coefficient of the hybrid material at an energy of 0.661 MeV according to the present invention;

[0058] Figure 13(a) shows the reconstruction results of the attenuation coefficient of concrete under an energy of 1.17 MeV according to the present invention;

[0059] Figure 13(b) shows the reconstruction results of the attenuation coefficient of polyethylene at an energy of 1.17 MeV according to the present invention;

[0060] Figure 13(c) shows the reconstruction results of the attenuation coefficient of the hybrid material at an energy of 1.17 MeV according to the present invention;

[0061] Figure 14(a) shows the reconstruction results of the attenuation coefficient of concrete under an energy of 1.33 MeV according to the present invention;

[0062] Figure 14(b) shows the reconstruction results of the attenuation coefficient of polyethylene at an energy of 1.33 MeV according to the present invention;

[0063] Figure 14(c) shows the reconstruction results of the attenuation coefficient of the hybrid material at an energy of 1.33 MeV according to the present invention. Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0065] The chromatographic gamma scanning method of the present invention includes:

[0066] S1. Establish a voxel model of the sample nuclear waste square container.

[0067] The TGS transmission measurement system is primarily used for quantitative measurement of the radioactive material content in non-homogeneous solid nuclear waste or nuclear waste containers, and to obtain the attenuation coefficient and activity distribution of the radioactive material within the container. In TGS measurements, to obtain more accurate reconstruction information, the sample in the nuclear waste container needs to be tested in equally spaced layers. It is crucial that each layer uses the same transmission scanning mode, and that the projection data, system matrix acquisition, and image reconstruction algorithm are identical, thereby calculating the linear attenuation coefficient and radioactive source activity of the material within the container. The TGS transmission measurement system mainly consists of a radioactive source collimator, a nuclear waste container, a detector shield, and an HPGe detector. Figure 1 As shown.

[0068] The HPGe used in this invention is a P-type coaxial GEM20P4-70 detector, which employs cylindrical lead material as a collimator to reduce background. During measurement, the center of the detector probe, the voxel center of the sample model, and the center of the transmission source are kept on the same straight line.

[0069] In traditional research methods, the physical model of the TGS transmission measurement system is simplified, treating the HPGe detector as a point and the radiation source as a point as well. The model of the radiation source and HPGe detector is a point-to-point model. This model is an idealized model, which can only obtain one projection line. When solving the track matrix in the subsequent process, there is only one line segment. This model has certain differences from the actual detection system, and the measurement error is uncontrollable.

[0070] In this invention, the HPGe detector has a certain width. The transmission source is treated as a point, establishing an idealized "angle" model. That is, the transmission source is considered a point source located at the center of the sample voxel. The width of the X-ray beam gradually increases from the transmission source to the HPGe detector, and the overall X-ray beam is triangular. Figure 1 As shown in the figure. This model is more in line with reality. When solving the track matrix, many line segments are selected in the ray beam for solving. The effective line segments in the clipping region are summed and the average value is taken to approximate the track length of the γ-ray passing through the voxel. Compared with the traditional "point-to-point" ideal model, the "angle" model is closer to the actual measurement conditions and can reduce measurement errors.

[0071] The transmission source uses common 137 Cs point source and point source 60 Co was used as the experimental source for simulation, with energies of 0.661 MeV, 1.17 MeV, and 1.33 MeV, respectively. Based on the actual level of steel containers for low- and medium-level radioactive solid waste in my country, a voxel model of a square container for sample nuclear waste was established. Each layer of this model has... Voxels, each voxel is 12 in size 12 12 (cm).

[0072] S2. Perform layer-by-layer scanning measurements on the voxel model to obtain scanning data.

[0073] To obtain sufficient measurement data, voxel information is collected as much as possible by measuring different positions and angles during each layer scan to obtain the medium filling material of the sample model. TGS transmission measurement adopts a combination of three scanning methods: step scan, rotation scan, and vertical scan, and scans layer by layer. Before each scan, it is confirmed that the transmission source and the detector are on the same straight line. The transmission source is placed outside the packaging body. The transmission source also uses a cylindrical collimator so that the transmission source can emit rays within a small solid angle. Figure 2-5The diagrams show the scanning test schematics of the test medium with rotation angles of 0°, 45°, 90°, and 135° in the simulated transmission experiment.

[0074] The scanning method for each voxel layer is as follows:

[0075] S21. Select 5 equally spaced measurement points, measure three times at each measurement position, take the average value as the measurement value, and then calculate the projection data.

[0076] S22. Using the geometric center of the voxel model as the rotation center, rotate the voxel model clockwise by 0 degrees, 45 degrees, 90 degrees, and 135 degrees. After each rotation, select 5 equally spaced measurement points, measure three times at each measurement position, and take the average value as the measurement value. Then calculate the projection data.

[0077] Once the entire layer is scanned, the calibration for that layer is complete. Repeating this process until all sample models are scanned yields the scan data. Although each layer is relatively independent, the calculation method for each layer is consistent; therefore, only the measurement results from any one layer need to be used for simulation verification.

[0078] According to the attenuation law of rays in matter (i.e., Lambert-Beer's law), the attenuation law in complex mixed inhomogeneous materials can be expressed by the following formula:

[0079] (1)

[0080] in n This indicates that there are n Such materials, μ mi Indicates the first i The linear attenuation coefficient of this material c i Indicates the first i The weight percentage of a material in a mixture.

[0081] When gamma rays pass through matter, they are attenuated; the formula for transmittance can be expressed as:

[0082] (2)

[0083] Indicates the first i Transmittance of photons at each measurement location C i This indicates that after the ray passes through the sample model, the detector reaches the [missing information] on the [missing information]. i The photon count rate at each measurement location after attenuation C i0 Indicates the detector at the i The count rate of photons that have not passed through attenuating matter, measured at each location, is defined as...P i For the first i Projected data for each measurement location:

[0084] (3)

[0085] (4)

[0086] (5)

[0087] Based on the attenuation law, the equation for each measurement point can be derived, thus obtaining the first equation. i The measurement equation of the layer, where x i Indicates the first i The track matrix of the layer rays, A i Indicates the first i Layer projection data matrix, B i Indicates the first The attenuation coefficient matrix of the layer, if S i If the matrix is ​​square, then equation (5) has a unique solution:

[0088] (6)

[0089] Scanning the first layer of the established voxel model yields 20 count rates, and the resulting count vector is denoted as... I k To calculate the transmittance, the sample packaging was removed and three more measurements were taken. The average count rate was used as the initial count of the radioactive source. I 0 Then, according to equation (2), the projected data vector can be obtained as shown in equation (7):

[0090] (7)

[0091] (8)

[0092] Then, the attenuation coefficient is solved according to equation (6), and 20 sets of linear equations can be established based on the scanning results.

[0093] S3. Solve for the track matrix of the TGS transmission imaging:

[0094] S31. Divide the two-dimensional plane into 9 regions using the four sides of the rectangular clipping window, and encode them using 4-bit binary code C. t C b C r C lLabel each region: the three regions above the cropping window are 1001, 1000, and 1010 from left to right; the left region of the cropping window is 0001; the right region is 0010; the inner region of the cropping window is 0000; and the three regions below the cropping window are 0101, 0100, and 0110 from left to right. Figure 6 As shown.

[0095] S32. Denote the codes at both ends of the line segment to be clipped as code1 and code2 respectively, and determine the relationship between code1 and code2 and the clipping window:

[0096] The first type of relationship: If code1=code2=0, the line segment is fully visible and inside the clipping window, so it is selected;

[0097] The second relationship: If code1&code2≠0, & is a bitwise AND operation, the line segment is completely invisible and outside the clipping window, so it is discarded.

[0098] There is also a third relationship, which is neither that code1=code2=0 nor that code1&code2≠0.

[0099] The traditional Cohen-Sutherland pruning algorithm has the advantage that the first and second cases can be separated, eliminating the need for intersection operations; however, the computational cost is high in the third case. For example... Figure 6 As shown, line segments P7 and P8 do not satisfy the first and second relationships. According to the traditional algorithm, they need to be intersected. However, line segments P7 and P8 are outside the window, so intersecting them is meaningless.

[0100] Therefore, this invention re-evaluates the third relationship to further filter out line segments that fall outside the clipping window. The evaluation method is as follows:

[0101] If neither code1=code2=0 nor code1&code2≠0 is satisfied, then draw a perpendicular line from the vertex of the clipping window to the line segment, and then determine the position of the foot of the perpendicular. If the foot of the perpendicular is inside the clipping window, then perform an intersection operation on the line segment; if the foot of the perpendicular is outside the clipping window, then discard it.

[0102] like Figure 7 and Figure 8 As shown, for each endpoint of the clipping window, a perpendicular line is drawn to the line segment. It is then determined whether the foot of the perpendicular x is within the window range. If at least one foot of the perpendicular falls within the window range, it indicates that the line segment passes through the window and can be intersected. If all the feet of the perpendiculars fall outside the window range, it indicates that the line segment is outside the window and is discarded without further calculation.

[0103] Therefore, the Cohen-Sutherland clipping algorithm of this invention does not require intersection calculations for line segments located outside the clipping window, saving unnecessary work and improving solution efficiency.

[0104] The process for determining the position of the perpendicular foot is as follows:

[0105] Let the coordinates of the two endpoints of any line segment AB be ( x a , y a ), ( x b , y b ), window's four vertices ( V BL , V TL , V BR , V TR The coordinates are ( x 1 , y 1 ), ( x 1 , y 2 ), ( x 2 , y 1 ), ( x 2 , y 2 The coordinate of the foot of the perpendicular F is ( x f , y f ).

[0106] V TL to the foot of the line segment:

[0107] (9)

[0108] (10)

[0109] (11)

[0110] From the perpendicular relationship of vectors, we can obtain:

[0111] (12)

[0112] Therefore, we can conclude that:

[0113] (13)

[0114] The foot of the perpendicular F lies on line segment AB. According to the collinearity of vectors, we know that:

[0115] (14)

[0116] (15)

[0117] (16)

[0118] Substituting the formula, we get:

[0119] (17)

[0120] but V TL The coordinates of the foot of the perpendicular are:

[0121] (18)

[0122] (19)

[0123] If the perpendicular foot is inside the clipping window:

[0124] (20)

[0125] Similarly, the coordinates of the foot of the perpendicular from the other vertices of the window to any line segment are:

[0126] (twenty one)

[0127] V BL to the foot of the line segment:

[0128] (twenty two)

[0129] (twenty three)

[0130] V TR to the foot of the line segment:

[0131] (twenty four)

[0132] (25)

[0133] V BR to the foot of the line segment:

[0134] (26)

[0135] (27)

[0136] If the perpendicular coordinates are within the window range ( x 1 , x 2 ), ( y 1 , y 2 If the line segment passes through the window, then the line segment passes through the window.

[0137] The specific flowchart of the cropping algorithm of this invention is as follows: Figure 9 As shown.

[0138] According to the TGS transmission scanning model, since the radiation source and detector use an "angle" model, the path of the gamma ray is almost a straight line. The average of the summations of the effective line segments within the clipped region is used to approximate the track length of the gamma ray passing through the voxel, i.e.: The effects of cutting 2 line segments and 10 line segments are shown in Figure 10(a) and Figure 10(b), respectively.

[0139] To test the pruning efficiency of the two algorithms, experiments were conducted on a Windows 10 computer with an AMD Ryzen 32300U processor (2.0 GHz, 4 cores, 8 threads). A controlled variable method was used to ensure that both methods were performed under identical conditions. Experimental results show that both methods produce the same track matrix when performing voxel segmentation on square kernel waste bins, but their pruning times differ. The pruning times are shown in Table 1 below.

[0140] Table 1 Comparison of running time of the original algorithm and its improved Cohen-Sutherland algorithm.

[0141]

[0142] As can be seen from the runtime data in Table 1, the improved Cohen-Sutherland algorithm runs faster than the original algorithm when trimming voxel segments. This is because the original algorithm cannot effectively determine whether a segment is outside the window within the trimming area and will repeatedly judge invalid intersection points. By introducing the judgment of the perpendicular foot vector, the calculation of invalid intersection points is avoided, the trimming time is shortened, and thus the computational efficiency is improved.

[0143] S4, Reconstruct the linear attenuation coefficient.

[0144] This invention employs the OSEM algorithm to solve for the projection matrix. The OS algorithm, also known as the ordered subset algorithm, is a commonly used acceleration algorithm in numerical computation. It addresses the problems of low computational efficiency and slow convergence speed encountered in statistical iterative reconstruction of CT images. The OS algorithm divides the projection data into... n There are several subsets, and these subsets of projected data are also called ordered subsets. The OS level of a subset is defined by the number of subset partitions. n The process of reconstructing an image using the OS algorithm is a continuous process of updating and correcting the reconstructed image; the reconstructed image needs to be updated a total of [number missing]. n This is because the OS algorithm can perform a check on each pixel of the image every time it uses the projection data in an ordered subset, and the reconstructed image will be updated accordingly. However, since the projection data is generated by... n It consists of ordered subsets, so the OS algorithm needs to correct each pixel. n The reconstructed image will be updated accordingly. n Once the OS algorithm has used up all the projected data in the ordered subsets at once, it means that one iteration has been completed.

[0145] The OSEM algorithm, also known as the ordered subset maximum expectation algorithm, essentially applies the OS method to the EM algorithm. Each iteration of the EM algorithm consists of two steps: an E-step and an M-step. The E-step calculates the expectation, while the M-step maximizes it. In the EM algorithm, the image correction value is calculated using all projected values. In the OSEM algorithm, the image correction value is calculated from the projected data within each subset. OSEM applies the EM algorithm to every subset of projected data. In the OSEM algorithm, we divide the projection matrix into... n An ordered subset For each subset of projected data, the standard EM algorithm is applied sequentially to maximize the likelihood function, and the reconstructed subset is used as the initial value for the next subset. Similar to the OS algorithm, the OSEM algorithm also repeatedly corrects and updates the image during reconstruction, and the image is updated a total of [number missing] times. n The OSEM algorithm completes the first time. n After the projection data of each subset is corrected for the pixels, the first iteration is considered complete, and the reconstruction result will be used as the initial value for the next iteration. However, compared to the OS algorithm, the OSEM algorithm also adds the maximum likelihood function of the previous subset to the next subset and uses it as the initial value for the next subset in the calculation, thereby increasing the correlation between the reconstructed images.

[0146] (28)

[0147] In the OSEM algorithm, data subsets are usually divided by projection angle. When dividing the projected data into ordered subsets, the OSEM algorithm often allocates them according to the principle of symmetry and balance to ensure that the contribution of each pixel to each subset is roughly equal.

[0148] The specific steps of the OSEM algorithm of this invention are as follows:

[0149] S41, Given unknown quantities x j Assign initial values, (29)

[0150] S42. For the nth subset, calculate the estimated values ​​of all projections within the subset:

[0151] ; (30)

[0152] (31)

[0153] Calculation error;

[0154] According to the formula

[0155] (32)

[0156] Calculate the correction value for the j-th unknown;

[0157] right The value is corrected: ;

[0158] S43. Repeat step S42 until the operation of n subsets is completed, thus completing one round of iteration;

[0159] S44. Using the result of the previous iteration as the initial value, repeat steps S42 and S43 and perform a new round of iteration until a result that meets the convergence requirements is obtained.

[0160] From the perspective of image reconstruction quality, the subset level of the OSEM algorithm has a significant impact. A higher subset level results in faster convergence, but as the number of iterations increases, it can introduce undesirable noise levels in low-activity image regions, leading to image divergence. Conversely, a lower subset level results in slower convergence, prioritizing the recovery of low-frequency elements while losing high-frequency information. In the absence of noise, the convergence speed is directly proportional to the subset size. Therefore, using OSEM for reconstruction, selecting fewer subsets not only increases iteration time but may also result in the loss of some high-frequency information. Conversely, selecting more subsets can cause image divergence during iteration. Thus, different subset levels significantly affect both the convergence speed and the quality of the reconstructed image.

[0161] This invention employs a coding clipping algorithm based on perpendicular vector judgment to quickly clip the length of each voxel within a square bucket, thereby obtaining the trajectory length matrix of the ray within each voxel. Then, the OSEM algorithm is used to reconstruct the attenuation coefficients of each layer within the bucket under transmitted energy. To verify the accuracy of the OSEM algorithm, two experimental models were selected: a single-medium model of concrete and polyethylene, and a mixed model of concrete, polyethylene, and aluminum. The first layer of the square bucket sample model was selected as the research object. Voxels 7, 8, 12, and 13, as shown in Figure 11(a), were entirely filled with concrete or polyethylene. Voxels 2, 8, 9, 13, 14, 17, and 22, as shown in Figure 11(b), were successively filled with polyethylene, concrete, and aluminum. The other voxels were filled with air. Reference values ​​for the attenuation coefficients of the three media materials under different transmitted energies are shown in Table 2.

[0162] Table 2 Reference values ​​of attenuation coefficient of dielectric material at transmission characteristic energy

[0163]

[0164] To accurately verify the effectiveness of the computer graphics cropping algorithm, based on the known true distribution of the sample to be tested and its material attenuation coefficient reference value, three image quality evaluation parameters were introduced: relative mean deviation, root mean square error, and Pearson correlation coefficient, to evaluate the accuracy of the reconstructed values ​​of all 25 voxels in the square bucket.

[0165] The root mean square error (RMSE) is the square root of the ratio of the square of the deviation between the predicted and actual values ​​to the number of observations (N). It measures the degree of deviation between the observed and the true value. The smaller the RMSE, the closer the predicted value is to the reference value, i.e., the higher the accuracy. The formula for calculating the RMSE is as follows:

[0166] (33)

[0167] in represents the difference between the OSEM algorithm reconstructed value and the reference value in the i-th case, and N represents the N cases of the unique identical variable.

[0168] The Pearson correlation coefficient, calculated as the quotient of the covariance and standard deviation of variables X and Y, is a parameter used to measure the strength of the correlation between two variables. Its value ranges from -1 to 1. A value of 1 indicates a perfect positive correlation between the two random variables; a value of -1 indicates a perfect negative correlation; and a value of 0 indicates no correlation between the two random variables. The calculation formula is shown below:

[0169] (34)

[0170] Where n represents the preset number of voxels. X i This represents the calculated value obtained using the encoding algorithm in the i-th case. Y i This represents the reconstructed value obtained using the OSEM algorithm in the i-th case. , These represent the corresponding reference values. The Pearson correlation coefficient quantifies the numerical correlation and reconstruction similarity between the reconstructed image and the real image. The closer the value is to 1, the closer the reconstructed image is to the real image, and the higher its reconstruction quality.

[0171] This invention employs two transmission sources: 137Cs and 60Co. In the first model, voxels 7, 8, 12, and 13 within a square barrel are pre-filled with concrete and polyethylene materials, respectively. In the second model, voxels 2, 8, 9, 13, 14, 17, and 22 are filled with a mixture of polyethylene, cement, and aluminum, respectively. Then, using a coding clipping algorithm based on perpendicular vector judgment, after calculating the trajectory matrix of each voxel, the OSEM algorithm is used to calculate the reconstructed attenuation coefficient values ​​when the clipped line segments within each voxel are 2, 12, 100, and 1000, respectively. The reconstruction results are shown in Figures 12-14.

[0172] The Pearson correlation coefficient, root mean square error, and relative average deviation of high-density concrete, low-density polyethylene, and hybrid materials with increasing cutting segment values ​​at transmission energies of 0.661 MeV, 1.17 MeV, and 1.33 MeV are shown in Tables 3, 4, and 5, respectively.

[0173]

[0174]

[0175] As shown in Tables 3 and 4, when the pre-set material inside the square bucket is high-density concrete, a single medium, the relative average deviation and root mean square error between the reconstructed attenuation coefficient and the standard reference value gradually decrease with the increase of the number of cut segments within each voxel, and the Pearson correlation coefficient gradually approaches 1. When the pre-set material inside the square bucket is low-density polyethylene, the trend of the reconstructed attenuation coefficient and the reference standard value in the three evaluation parameters is the same as that of the high-density medium material, but the image evaluation quality indicators are worse than when using the high-density medium material. Table 5 shows that when there are multiple pre-set materials inside the square bucket, with the increase of the number of cut segments, the different densities and attenuation coefficients of the different medium materials lead to poorer image evaluation quality indicators in all three aspects due to their mutual influence. This indicates that when the pre-set materials are complex, the accuracy of the image reconstruction effect is poor, possibly due to the mutual scattering effect caused by rays passing through each material. In addition, the attenuation coefficient values ​​reconstructed by both preset models showed a relatively stable trend after 100 segments were cut within the voxel, indicating that when a large number of segments were cut within the voxel, the average value could be used to approximate the track length of the γ-ray passing through the voxel.

[0176] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of tomographic gamma scanning in transmission imaging, characterized by, include S1. Establish a voxel model of the square container for sample nuclear waste; S2. Perform layer-by-layer scanning measurements on the voxel model to obtain scanning data; S3. Solve for the track matrix of the TGS transmission imaging: S31. Divide the two-dimensional plane into 9 regions using the four sides of the rectangular clipping window, and label each region with a 4-bit binary code: the three regions above the clipping window are 1001, 1000, and 1010 from left to right, the region on the left side of the clipping window is 0001, the region on the right side is 0010, the region inside the clipping window is 0000, and the three regions below the clipping window are 0101, 0100, and 0110 from left to right. S32. Denote the codes at both ends of the line segment to be clipped as code1 and code2 respectively, and determine the relationship between code1 and code2 and the clipping window: If code1=code2=0, the line segment is fully visible, so we take it; If code1&code2≠0, & is a bitwise AND operation, the line segment will be completely invisible and should be discarded; If neither code1=code2=0 nor code1&code2≠0 is satisfied, then draw a perpendicular line from the vertex of the clipping window to the line segment, and then determine the position of the foot of the perpendicular. If the foot of the perpendicular is inside the clipping window, then perform an intersection operation on the line segment; if the foot of the perpendicular is outside the clipping window, then discard it. S4, Reconstruct the linear attenuation coefficient.

2. The tomographic gamma scanning method in transmission imaging as described in claim 1, characterized in that, In step S1, the voxel model has 5 Five voxels, each voxel measuring 12cm x 12cm. *12 cm per layer.

3. The transmissive imaging, tomographic gamma scanning method of claim 2 wherein, In step S2, the scanning method for each voxel layer is as follows: S21. Select 5 equally spaced measurement points, measure three times at each measurement position, take the average value as the measurement value, and then calculate the projection data. S22. Using the geometric center of the voxel model as the rotation center, rotate the voxel model clockwise by 0 degrees, 45 degrees, 90 degrees, and 135 degrees. After each rotation, select 5 equally spaced measurement points, measure three times at each measurement position, and take the average value as the measurement value. Then calculate the projection data.

4. The transmission tomographic gamma scanning method of claim 1, wherein, Step S4 includes S41, Given unknown quantities x j Initialize: ; S42, for the nth subset, calculate the estimated value of all projections within the subset: ; According to the formula calculated error; According to the formula The correction value of the jth unknown is calculated; correction is made to the value of x j : ； S43. Repeat step S42 until the operation of n subsets is completed, thus completing one round of iteration; S44. Using the result of the previous iteration as the initial value, repeat steps S42 and S43 and perform a new round of iteration until a result that meets the convergence requirements is obtained.

Images