Image reconstruction method and image quality evaluation method for nuclear waste bin

Abstract

The invention provides an image reconstruction method and an image quality evaluation method for a nuclear waste bin, and relates to the field of nuclear waste bin detection. An image reconstruction method includes transmitting a nuclear waste bin using a TGS to obtain measurement data; an ADMM algorithm is adopted to carry out iterative calculation on measurement data, a graph reconstruction problem is decomposed into a plurality of sub-problems, the plurality of sub-problems comprise a state constraint problem and a parabolic optimal control problem, in each iteration, the state constraint problem and the parabolic optimal control problem are decoupled, original variables and dual variables in the ADMM algorithm are alternately updated, and the optimal control problem is obtained. A subproblem in the ADMM algorithm is solved by using a CG algorithm; and the image reconstruction efficiency and precision are improved. The evaluation method comprises the steps that sparse sampling is carried out on the first model and the second model by rotating the scanning angle once every n degrees to obtain projection data, image reconstruction is carried out on the first model and the second model by adopting an ADMM algorithm and an image reconstruction method to obtain a reconstruction value of each voxel, and the quality of image reconstruction can be evaluated.

Description

Technical Field

[0001] The present application relates to the field of nuclear waste barrel detection, and in particular, to a method for image reconstruction and image quality evaluation of nuclear waste barrels. Background Art

[0002] At present, nuclear energy has become one of the most widely used clean energy sources in the world. However, its use is often accompanied by the generation of a large amount of nuclear waste. Nuclear waste is radioactive waste, which refers to waste containing or contaminated by radionuclides, with an activity greater than the specified clean level [1]. It is generated in various links of the nuclear industry, such as reactors, decommissioned nuclear facilities, nuclear technology and medical waste, and nuclear weapons testing. At present, solid nuclear waste is usually sealed in containers of different sizes in accordance with the standard nuclear waste container regulations: EJ1076-2014 "Steel Boxes for Low and Medium Level Radioactive Solid Waste Containers", such as 200L nuclear waste steel drums.

[0003] Since the composition label information of old barreled nuclear waste is vague and key information such as the types and distribution of radionuclides in the barrels is missing, further testing of the nuclides in the barreled nuclear waste is required. In the existing technology, most of the measurements are made using tomographic gamma scanning technology. However, the research on tomographic gamma scanning technology mainly focuses on detection devices, scanning modes, and voxel division methods. Although some progress has been made, how to improve detection efficiency and accuracy, as well as improve the imaging quality of reconstructed images, are still urgent issues to be solved in this field. Summary of the invention

[0004] The purpose of this application is to provide an image reconstruction method and an image quality evaluation method for nuclear waste barrels, which can improve detection efficiency and accuracy.

[0005] This application is implemented as follows:

[0006] In a first aspect, the present application provides a method for reconstructing an image of a nuclear waste barrel, comprising the following steps:

[0007] Divide nuclear waste barrels into voxels;

[0008] Use TGS to penetrate the nuclear waste barrel to obtain the measurement data of each voxel in the nuclear waste barrel;

[0009] The ADMM algorithm is used to iteratively calculate the measured data, and the graph reconstruction problem is decomposed into multiple sub-problems, wherein the multiple sub-problems include state constraints and parabolic optimal control problems. In each iteration, the state constraints and the parabolic optimal control problem are decoupled, the primal variables and the dual variables in the ADMM algorithm are alternately updated, and the CG algorithm is used to solve the sub-problems in the ADMM algorithm;

[0010] Whether the stopping condition is met is determined according to the iterative convergence criterion. If so, the iteration is stopped to obtain the linear attenuation coefficient of each voxel in the nuclear waste barrel, and the transmission image is reconstructed according to the linear attenuation coefficient.

[0011] Based on the first aspect, the ADMM algorithm is used to iteratively calculate the measurement data, and the graph reconstruction problem is decomposed into multiple sub-problems, wherein the multiple sub-problems include state constraints and parabolic optimal control problems. In each iteration, the state constraints and the parabolic optimal control problem are decoupled, the primal variables and the dual variables in the ADMM algorithm are alternately updated, and the steps of using the CG algorithm to solve the sub-problems in the ADMM algorithm include:

[0012] Set the initial value {u 0 ,λ 0}, where U and Y are the squares of different dual functions, U×Y is the inner product within the relevant range, {u 0 ,λ 0} is the initial value in the augmented Lagrangian functional, u 0 , 0 is the initial value of the multiplier; the initial value is the selected starting point of the iteration;

[0013] If k>0, {u 0 ,λ 0}→z k+1 →u k+1 →λ k+1 , where → represents iterative update of variables, z k+1 Decouple the optimal control problem after iteration about z, u k+1 Decouple the optimal control problem after iteration about u, λ k+1 Decoupling the optimal control problem after iteration with respect to λ;

[0014] Let z k+1 =argminL β (u k ,z;λ k ),u k+1 =argminL β (v,z k+1 ; k ), where u k represents the initial change of u, z is a variable, λ k represents the initial variable of λ;

[0015] Recalculate And use the CG algorithm to update u k+1 and k+1 , Among them, P K is Max{a,min{b,y}}, yk is the value of the kth iteration, β is the penalty parameter, is the assumed value, is the result of iterating the assumed value of the w variable, y k+1 is the multiplier updated using the CG algorithm; To use the CG algorithm to update the multiplier before, Step length

[0016] Update the Lagrange multiplier λ k+1 =λ k -z k+1 .

[0017] Based on the first aspect, the step of dividing the nuclear waste barrel into a plurality of voxels includes:

[0018] The Monte Carlo simulation method is used to establish a voxel grid nuclear waste barrel model. The voxel grid nuclear waste barrel model is layered, and any layer of voxel grid is divided into M×N voxels, where M and N are natural numbers greater than or equal to 2.

[0019] Based on the first aspect, the specific steps of using TGS to transmit the nuclear waste barrel to obtain the measurement data of each voxel in the nuclear waste barrel include:

[0020] Establish the transmission measurement equation:

[0021] In the formula, I i is the intensity of the attenuated γ-ray;

[0022] I0 is the initial γ-ray intensity;

[0023] μ j is the linear attenuation coefficient of the j-th voxel;

[0024] x ij is the track length of the γ-ray passing through the j-th voxel when the i-th position is measured;

[0025] Let P i is the transmittance of the i-th measurement position, then

[0026] P i =C i / C max ;

[0027] In the formula, C i It represents the full energy peak count rate of γ photons measured by the detector at the i-th measurement position when there is an attenuating medium.

[0028] C max It indicates the peak count rate of gamma photons measured by the detector when there is no attenuation medium.

[0029] Definition Si is the projection data of the i-th measurement position:

[0030]

[0031] It can be expressed in matrix form:

[0032] A i =B i ×D i ;

[0033] According to the above formula, the equation of each measurement point can be obtained, so as to obtain the transmission measurement equation of the i-th layer, and the initial transmission image can be obtained according to the transmission measurement equation; where A i represents the projection matrix of the i-th layer, S i represents the projection data at the i-th measurement position, and T is represented as the transpose in linear algebra;

[0034] A i =(S1,S2,…,S i ,…,S I ) T ;

[0035] B i represents the trajectory matrix of the i-th layer, B i ∈R N×M , N is the total number of transmission measurements, R represents a natural matrix, and N×M is the size of the natural matrix;

[0036] D i represents the linear attenuation coefficient matrix of the i-th layer, μ is the linear attenuation coefficient, μ J Indicates the linear attenuation coefficient of the Jth voxel in this layer,

[0037] D i =(μ1,μ2,…,μ j ,…,μ J ) T .

[0038] In a second aspect, the present application provides an image quality evaluation method, which is applied to the above method, and the evaluation method includes:

[0039] Transmission source uses 137 Cs and 60 Co is used as a simulated point source, with characteristic energies of 0.661MeV, 1.17MeV, and 1.33MeV;

[0040] Build the first model and the second model, divide the first model and the second model into 10×10 voxels respectively, and number them from 1 to 100 in sequence;

[0041] In the first model, the voxel positions 22, 23, 32, and 33 were filled with polyethylene, the voxel position 18 was filled with aluminum, and the voxel positions 55, 56, 57 and 65, 66, and 67 were filled with concrete; in the second model, the voxel positions 12, 13, 22, and 23 were filled with polyethylene, the voxel positions 16 and 46 were filled with aluminum, the voxel positions 39, 49, 88, and 89 were filled with water, and the voxel positions 63, 64, 73, and 74 were filled with concrete, and the remaining voxel positions were replaced with air, and it was recorded that the concrete, aluminum, polyethylene, and water all had reference values;

[0042] The scanning angle is rotated once every n° to perform sparse sampling on the first model and the second model to obtain projection data, and the ADMM algorithm and the above-mentioned image reconstruction method are used to reconstruct the image of the first model and the second model to obtain the reconstruction value of each voxel;

[0043] The relative error of each voxel after image reconstruction using the ADMM algorithm and the relative error of each voxel after image reconstruction using the method described in any one of claims 1 to 4 are obtained according to the reference value and the reconstruction value.

[0044] Based on the second method, it also includes using one or more of mean square error MSE, peak signal-to-noise ratio PSNR and multi-scale structural similarity MS-SSIM of image quality to evaluate the reconstruction value of each voxel.

[0045] Compared with the prior art, the present invention has at least the following advantages or beneficial effects:

[0046] The ADMM algorithm and the CG algorithm are used to process the measurement data obtained by TGS transmission of nuclear waste barrels to improve the efficiency and accuracy of image reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0048] In the first model, the voxel positions 22, 23, 32, and 33 are filled with polyethylene, the voxel position 18 is filled with aluminum, and the voxel positions 55, 56, 57 and 65, 66, and 67 are filled with concrete; in the second model, the voxel positions 12, 13, 22, and 23 are filled with polyethylene, the voxel positions 16 and 46 are filled with aluminum, the voxel positions 39, 49, 88, and 89 are filled with water, and the voxel positions 63, 64, 73, and 74 are filled with concrete

[0049] Figure 1A schematic diagram of using TGS to penetrate a nuclear waste barrel in one embodiment of the present application;

[0050] Figure 2 A schematic diagram of a first model filled with concrete, aluminum, polyethylene and water in one embodiment of the present application;

[0051] Figure 3 A schematic diagram of a second model filled with concrete, aluminum, polyethylene and water in one embodiment of the present application;

[0052] Figure 4 An image obtained by reconstructing the first model using the ADMM algorithm in one embodiment of the present application;

[0053] Figure 5 An image obtained by reconstructing the second model using the ADMM algorithm in one embodiment of the present application;

[0054] Figure 6 An image obtained by reconstructing the first model using an image reconstruction method in one embodiment of the present application;

[0055] Figure 7 This is an image obtained by reconstructing the second model using an image reconstruction method in one embodiment of the present application. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.

[0057] In conjunction with the accompanying drawings, some embodiments of the present application are described in detail below. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0058] After long-term research and practice, the applicant of this application found that the research content of TGS transmission image reconstruction technology in the prior art mainly focuses on detection devices and scanning modes, voxel division methods, etc. How to strengthen the research of TGS technology and further improve the efficiency and accuracy of nuclear waste barrel detection and the imaging quality of reconstructed images is still an urgent problem to be solved in the field of nuclear waste treatment.

[0059] In view of this, an embodiment of the present application provides a method for image reconstruction of a nuclear waste barrel, which can improve the efficiency and accuracy of image reconstruction. The method includes the following steps:

[0060] S101: Divide the nuclear waste barrel into several voxels;

[0061] In this step, the nuclear waste barrel is divided into multiple layers according to the actual size of the nuclear waste barrel, and each layer is further divided into multiple voxel grids. For example, the nuclear waste barrel is divided into 5 layers, each layer is divided into 10×10 voxel grids, and the size of each voxel is 10cm×10cm. Please refer to Figure 1 , Figure 1 It is a top view, and the middle of the picture is the surface layer (first layer) of the nuclear waste barrel, which is divided into a 10×10 voxel grid.

[0062] S102: Use TGS to penetrate the nuclear waste barrel to obtain measurement data of each voxel in the nuclear waste barrel;

[0063] In this step, please refer to Figure 1 In the middle of the figure is a nuclear waste barrel, the left side of the nuclear waste barrel is the transmission source, and the right side is the detector. The centers of the transmission source, voxel grid and detector are all on the same horizontal plane. At the same time, the transmission source is regarded as a point source to form a source-detector "angle" model, so that the transmission source and the detector rotate around the nuclear waste barrel. The rays generated by the transmission source at multiple angles pass through the nuclear waste barrel and are received by the detector, thereby obtaining the measurement data of each voxel in the nuclear waste barrel.

[0064] S103: Adopt ADMM algorithm to iteratively calculate the measured data, decompose the graph reconstruction problem into multiple sub-problems, the multiple sub-problems include state constraints and parabolic optimal control problems, decouple the state constraints and parabolic optimal control problems in each iteration, alternately update the original variables and dual variables in ADMM algorithm, and use CG algorithm to solve the sub-problems in ADMM algorithm; in this step, for the sake of ease of understanding, ADMM algorithm is an iterative method for solving optimization problems, especially for distributed or large-scale optimization problems. It works by decomposing the original problem into multiple smaller and more easily handled sub-problems and alternately solving these sub-problems. ADMM updates two sets of variables in each iteration: original variables (corresponding to the solution of the optimization problem) and dual variables (Lagrange multipliers associated with constraints). The measured data obtained in step S102 contains some incomplete and noisy data. Graph reconstruction is the process of restoring a complete image or graph from incomplete and noisy measured data. This is a typical inverse problem, which requires solving a complex optimization problem. In order to simplify this complex optimization problem, ADMM algorithm decomposes it into multiple sub-problems. These sub-problems are divided based on different parts of the data, different spatial scales, or different types of constraints. The specific division method is not limited in this embodiment. For ease of understanding, the state constraint problem refers to a constraint in which the change of the database state is only related to whether the changed database state is correct, but is unrelated to the state of other data. In the process of image reconstruction of nuclear waste barrels, the state constraint involves restrictions on the state of each voxel in the nuclear waste barrel, and these constraints are based on previous measurement data, physical models or safety standards. Parabolic optimal control problem: a specific type of optimal control problem described by parabolic partial differential equations. The parabolic optimal control problem involves the optimization of the iterative process to minimize the reconstruction error or improve the reconstruction efficiency. In each iteration, the state constraint and the parabolic optimal control problem in the original problem are processed separately. This can reduce the complexity of the problem and make each sub-problem easier to solve. The original variable is a variable representing the image information, and the dual variable is a Lagrange multiplier. In each iteration, the algorithm will alternately update the original variable and the dual variable, and use the CG algorithm to solve the sub-problem until the convergence condition is met. In each iteration, the original variable is first updated based on the current value of the dual variable, and then the dual variable is updated based on the updated value of the original variable. This alternating update method helps to gradually approach the solution of the optimization problem. These sub-problems can be transformed into problems of solving a system of linear equations or minimizing a quadratic function. Solving such problems with the CG algorithm improves efficiency.

[0065] S104: judging whether the stopping condition is satisfied according to the iterative convergence criterion, and stopping the iteration if the condition is satisfied, so as to obtain the linear attenuation coefficient of each voxel in the nuclear waste barrel, and reconstructing the transmission image according to the linear attenuation coefficient.

[0066] In this step, the convergence criteria are not limited, including the number of iterations, the change in the solution is less than a certain threshold, the change in the objective function value is less than a certain threshold, etc. Once the convergence criteria determine that the stop condition is met, the iterative process will stop. At this time, the algorithm will output the result of the current iteration as the final solution. The linear attenuation coefficient of each voxel (volume element, which can be understood as a small cube or sphere in three-dimensional space) in the nuclear waste barrel is obtained through the final solution. The linear attenuation coefficient is a physical quantity used to describe the absorption or scattering ability of a substance to radiation. After obtaining the linear attenuation coefficient of each voxel, these coefficients can be used to reconstruct a transmission image. The transmission image helps researchers understand the structure and radiation distribution inside the waste barrel.

[0067] In some embodiments of the present invention, the step of using the ADMM algorithm to iteratively calculate the measurement data, decomposing the graph reconstruction problem into multiple sub-problems, wherein the multiple sub-problems include state constraints and parabolic optimal control problems, decoupling the state constraints and the parabolic optimal control problems in each iteration, alternately updating the primal variables and the dual variables in the ADMM algorithm, and using the CG algorithm to solve the sub-problems in the ADMM algorithm includes:

[0068] Set the initial value {u 0 ,λ 0}, where U and Y are the squares of different dual functions, U×Y is the inner product within the relevant range, {u 0 ,λ 0} is the initial value in the augmented Lagrangian functional, u 0 , 0 is the initial value of the multiplier; the initial value is the selected starting point of the iteration;

[0069] If k>0, {u 0 ,λ 0}→z k+1 →u k+1 →λ k+1 , where → represents iterative update of variables, z k+1 Decouple the optimal control problem after iteration about z, u k+1 Decouple the optimal control problem after iteration about u, λ k+1 Decoupling the optimal control problem after iteration with respect to λ;

[0070] Let z k+1 =argminL β (u k ,z;λ k ),u k+1 =argminL β (v,z k+1 ; k), where u k represents the initial change of u, z is a variable, λ k represents the initial variable of λ;

[0071] Recalculate And use the CG algorithm to update u k+1 and k+1 , Among them, P K is Max{a,min{b,y}}, y k is the value of the kth iteration, β is the penalty parameter, is the assumed value, is the result of iterating the assumed value of the w variable, y k+1 is the multiplier updated using the CG algorithm; To use the CG algorithm to update the multiplier before, is the step length;

[0072] Update the Lagrange multiplier λ k+1 =λ k -z k+1 .

[0073] In some embodiments of the present invention, the step of dividing the nuclear waste barrel into a plurality of voxels comprises:

[0074] The Monte Carlo simulation method is used to establish a voxel grid nuclear waste barrel model. The voxel grid nuclear waste barrel model is layered, and any layer of voxel grid is divided into M×N voxels, where M and N are natural numbers greater than or equal to 2.

[0075] In this embodiment, each layer of voxel grid is preferably divided into 10×10 voxels, and the size of each voxel is 10 cm×10 cm.

[0076] In some embodiments of the present invention, the specific steps of using TGS to penetrate a nuclear waste barrel to obtain measurement data of each voxel in the nuclear waste barrel include:

[0077] Establish the transmission measurement equation:

[0078] In the formula, I i is the intensity of the attenuated γ-ray;

[0079] I0 is the initial γ-ray intensity;

[0080] μ j is the linear attenuation coefficient of the j-th voxel;

[0081] x ij is the track length of the γ-ray passing through the j-th voxel when the i-th position is measured;

[0082] Let Pi is the transmittance of the i-th measurement position, then

[0083] P i =C i / C max ;

[0084] In the formula, C i It represents the full energy peak count rate of γ photons measured by the detector at the i-th measurement position when there is an attenuating medium.

[0085] C max It indicates the peak count rate of gamma photons measured by the detector when there is no attenuation medium.

[0086] Definition S i is the projection data of the i-th measurement position:

[0087]

[0088] It can be expressed in matrix form:

[0089] A i =B i ×D i ;

[0090] According to the above formula, the equation of each measurement point can be obtained, so as to obtain the transmission measurement equation of the i-th layer, and the initial transmission image can be obtained according to the transmission measurement equation; where A i represents the projection matrix of the i-th layer, S i represents the projection data at the i-th measurement position, and T is represented as the transpose in linear algebra;

[0091] A i =(S1,S2,…,S i ,…,S I ) T ;

[0092] B i represents the trajectory matrix of the i-th layer, B i ∈R N×M , N is the total number of transmission measurements, R represents a natural matrix, and N×M is the size of the natural matrix;

[0093] D i represents the linear attenuation coefficient matrix of the i-th layer, μ is the linear attenuation coefficient, μ J Indicates the linear attenuation coefficient of the Jth voxel in this layer,

[0094] D i =(μ1,μ2,…,μ j ,…,μ J ) T .

[0095] The embodiment of the present invention further provides an image quality evaluation method, which is applied to the above-mentioned image reconstruction method. The evaluation method includes:

[0096] S201: Transmission source adopts 137 Cs and 60 Co is used as a simulated point source, with characteristic energies of 0.661MeV, 1.17MeV, and 1.33MeV;

[0097] S202: constructing a first model and a second model, dividing the first model and the second model into 10×10 voxels respectively, and numbering them in sequence from 1 to 100;

[0098] Please refer to Figure 2 and Figure 3 , the first model and the second model are divided into 10×10 voxels respectively, and are numbered 1-100 from left to right and from top to bottom.

[0099] S203: in the first model, the voxel positions 22, 23, 32, and 33 are filled with polyethylene, the voxel position 18 is filled with aluminum, and the voxel positions 55, 56, 57 and 65, 66, and 67 are filled with concrete; in the second model, the voxel positions 12, 13, 22, and 23 are filled with polyethylene, the voxel positions 16 and 46 are filled with aluminum, the voxel positions 39, 49, 88, and 89 are filled with water, the voxel positions 63, 64, 73, and 74 are filled with concrete, and the remaining voxel positions are replaced with air, and it is recorded that the concrete, aluminum, polyethylene, and water all have reference values;

[0100] Please refer to Figure 2 and Figure 3 , Figure 2 Schematic diagram of filling the first model with concrete, aluminum, polyethylene, and water; Figure 3 Schematic diagram of the second model filled with concrete, aluminum, polyethylene and water; the reference values ​​of the linear attenuation coefficients of the four filling medium materials with different densities at three characteristic energies of two transmission sources of 137Cs and 60Co, 0.661MeV, 1.17MeV, and 1.33MeV are shown in Table 1 below:

[0101] Table 1 Reference values ​​of linear attenuation coefficients of radioactive source dielectric materials

[0102]

[0103] S204: performing sparse sampling on the first model and the second model by rotating the scanning angle once every n° to obtain projection data, and reconstructing the first model and the second model by using the ADMM algorithm and the above-mentioned image reconstruction method to obtain a reconstruction value of each voxel;

[0104] In this step, a large amount of information data is collected by measuring 10 positions and rotating every 13° to obtain the medium filling material of the sample model. Specifically, we ignore the attenuation effect of air on gamma rays, and the voxel grid that is not filled with medium material is replaced by air with a linear attenuation coefficient of 0. The scanning angle is rotated every 13° to obtain sparse sampling of the two models to obtain projection data, and the transmission images of the two models are reconstructed using the ADMM algorithm and the image reconstruction method of the present application. When the transmission source energy is 0.661Mev, the transmission image imaging effect is as follows: Figure 4-Figure 7 shown. Figure 4 An image obtained by reconstructing the first model using the ADMM algorithm; Figure 5 The image is obtained by reconstructing the second model using the ADMM algorithm; Figure 6 An image obtained by reconstructing the first model using an image reconstruction method; Figure 7 The image is obtained by reconstructing the second model using an image reconstruction method.

[0105] S205: Obtaining the relative error of each voxel after image reconstruction using the ADMM algorithm and the relative error of each voxel after image reconstruction using the above-mentioned image reconstruction method according to the reference value and the reconstruction value.

[0106] After the experiment of transmitting a 137Cs point source with a characteristic energy of 0.661 MeV, a total of 100 voxel reconstruction values ​​were obtained. Then, the reconstruction value results of the two models were compared with the reference value of the linear attenuation coefficient of the filling dielectric material under the corresponding characteristic energy, and the relative error analysis was performed. The results are listed in Table 2 below:

[0107] Table 2 Comparison of the reconstruction values ​​and relative errors of different algorithms at the medium filling position under the two models

[0108]

[0109] It can be seen from Table 2 that when the transmission characteristic energy is 0.661MeV, in the first model, using the ADMM algorithm, the relative error range between the reconstructed value and the reference value is: 0.327% to 21.933%, and using the image reconstruction method of the present application, the relative error range between the reconstructed value and the reference value is: 1.778% to 20.141%. In the second model, the ADMM algorithm is: 1.003% to 42.932%, and the image reconstruction method of the present application is: 2.407% to 55.088%. It can be obtained that the relative error between the linear attenuation coefficient reconstruction value and the reference value of the image reconstruction method of the present application under the first model is small. In the second model, due to the complex filling medium material, the error analysis comparison of the two algorithms is not obvious.

[0110] In some embodiments of the present invention, the reconstruction value of each voxel is evaluated by using one or more of mean square error MSE, peak signal-to-noise ratio PSNR and multi-scale structural similarity MS-SSIM of image quality.

[0111] In this embodiment, three evaluation parameters are introduced to perform multi-level analysis of image reconstruction using different algorithms under two models. The results are shown in Table 3.

[0112] Table 3 Comparison of evaluation parameters of the two models under the ADMM algorithm and the image reconstruction method of this application

[0113]

[0114] It can be seen from Table 3 that in the two models, the image reconstruction method of the present application has an MSE value of 9.73E-06, a PSNR value of 50.12, and a ME-SSIM value of 9.99E-01 for the first model. The performance of the MSE value, PSNR value, and ME-SSIM value are significantly better than that of the ADMM algorithm. Figure 4-7 The reconstruction effect and the data conclusion in Table 2 show that the MSE value of the first model under the image reconstruction method of the present application is significantly lower than that of the second model, and the PSNR value of 50.12 is much higher than 41.25 of the second model. At the same time, the ME-SSIM value is closer to 1, which shows that the image reconstruction method of the present application has a better image reconstruction effect, and the quality of the transmission reconstructed image is better when the filling medium material is relatively simple.

[0115] It will be apparent to those skilled in the art that the present application is not limited to the details of the exemplary embodiments described above, and that the present application can be implemented in other specific forms without departing from the spirit or essential features of the present application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the present application is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present application. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. A method for image reconstruction of a nuclear waste barrel, characterized in that: The following steps are involved: Divide nuclear waste barrels into voxels; Use TGS to penetrate the nuclear waste barrel to obtain the measurement data of each voxel in the nuclear waste barrel; The ADMM algorithm is used to iteratively calculate the measured data, and the graph reconstruction problem is decomposed into multiple sub-problems, wherein the multiple sub-problems include state constraints and parabolic optimal control problems. In each iteration, the state constraints and the parabolic optimal control problem are decoupled, the primal variables and the dual variables in the ADMM algorithm are alternately updated, and the CG algorithm is used to solve the sub-problems in the ADMM algorithm; Whether the stopping condition is met is determined according to the iterative convergence criterion. If so, the iteration is stopped to obtain the linear attenuation coefficient of each voxel in the nuclear waste barrel, and the transmission image is reconstructed according to the linear attenuation coefficient.

2. The method for image reconstruction of a nuclear waste barrel according to claim 1, characterized in that: The step of using the ADMM algorithm to iteratively calculate the measurement data, decomposing the graph reconstruction problem into multiple sub-problems, wherein the multiple sub-problems include state constraints and parabolic optimal control problems, decoupling the state constraints and the parabolic optimal control problems in each iteration, alternately updating the original variables and the dual variables in the ADMM algorithm, and using the CG algorithm to solve the sub-problems in the ADMM algorithm includes: Set the initial value {u 0 ,λ 0 }, where U and Y are the squares of different dual functions, U×Y is the inner product within the relevant range, {u 0 ,λ 0 } is the initial value in the augmented Lagrangian functional, u 0 , 0 is the initial value of the multiplier; If k>0, {u 0 ,λ 0 }→z k+1 →u k+1 →λ k+1 , where → represents iterative update of variables, z k+1 Decouple the optimal control problem after iteration about z, u k+1 Decouple the optimal control problem after iteration about u, λ k+1 Decoupling the optimal control problem after iteration with respect to λ; Let z k+1 =argminL β (u k ,z;λ k ),u k+1 =argminL β (v,z k+1 ; k ), where u k represents the initial change of u, z is a variable, λ k represents the initial variable of λ; Recalculate And use the CG algorithm to update u k+1 and k+1 , Among them, P K is Max{a,min{b,y}}, y k is the value of the kth iteration, β is the penalty parameter, is the assumed value, is the result of iterating the assumed value of the w variable, y k+1 is the multiplier updated using the CG algorithm; To use the CG algorithm to update the multiplier before, is the step length; Update the Lagrange multiplier λ k+1 =λ k -z k+1 .

3. The method for image reconstruction of a nuclear waste barrel according to claim 1, characterized in that: The step of dividing the nuclear waste barrel into a plurality of voxels comprises: The Monte Carlo simulation method is used to establish a voxel grid nuclear waste barrel model. The voxel grid nuclear waste barrel model is layered, and any layer of voxel grid is divided into M×N voxels, where M and N are natural numbers greater than or equal to 2.

4. The method for image reconstruction of a nuclear waste barrel according to claim 1, characterized in that: The specific steps of using TGS to transmit through a nuclear waste barrel to obtain the measurement data of each voxel in the nuclear waste barrel include: Establish the transmission measurement equation: In the formula, I i is the intensity of the attenuated γ-ray; I0 is the initial γ-ray intensity; μ j is the linear attenuation coefficient of the j-th voxel; x ij is the track length of the γ-ray passing through the j-th voxel when the i-th position is measured; Let P i is the transmittance of the i-th measurement position, then P i =C i / C max ; In the formula, C i It represents the full energy peak count rate of γ photons measured by the detector at the i-th measurement position when there is an attenuating medium. C max It indicates the peak count rate of gamma photons measured by the detector when there is no attenuation medium. Definition S i is the projection data of the i-th measurement position: It can be expressed in matrix form: A i =B i ×D i ; According to the above formula, the equation of each measurement point can be obtained, so as to obtain the transmission measurement equation of the i-th layer, and the initial transmission image can be obtained according to the transmission measurement equation; where A i represents the projection matrix of the i-th layer, S i represents the projection data at the i-th measurement position, T is represented as the transpose in linear algebra; A i =(S1,S2,…,S i ,…,S I ) T ; B i represents the trajectory matrix of the i-th layer, B i ∈R N×M , N is the total number of transmission measurements, R represents a natural matrix, and N×M is the size of the natural matrix; D i represents the linear attenuation coefficient matrix of the i-th layer, μ is the linear attenuation coefficient, μ J Indicates the linear attenuation coefficient of the Jth voxel in this layer, D i =(μ1,μ2,…,μ j ,…,m J ) T 。 5. A method for evaluating image quality, characterized in that: The method applied to any one of claims 1 to 4, wherein the evaluation method comprises: Transmission source uses 137 Cs and 60 Co is used as a simulated point source, with characteristic energies of 0.661MeV, 1.17MeV, and 1.33MeV; Build the first model and the second model, divide the first model and the second model into 10×10 voxels respectively, and number them from 1 to 100 in sequence; In the first model, the voxel positions 22, 23, 32, and 33 were filled with polyethylene, the voxel position 18 was filled with aluminum, and the voxel positions 55, 56, 57 and 65, 66, and 67 were filled with concrete; in the second model, the voxel positions 12, 13, 22, and 23 were filled with polyethylene, the voxel positions 16 and 46 were filled with aluminum, the voxel positions 39, 49, 88, and 89 were filled with water, and the voxel positions 63, 64, 73, and 74 were filled with concrete, and the remaining voxel positions were replaced with air, and it was recorded that the concrete, aluminum, polyethylene, and water all had reference values; The scanning angle is rotated once every n° to perform sparse sampling on the first model and the second model to obtain projection data, and the ADMM algorithm and the method described in any one of claims 1 to 4 are used to reconstruct the image of the first model and the second model to obtain the reconstruction value of each voxel; The relative error of each voxel after image reconstruction using the ADMM algorithm and the relative error of each voxel after image reconstruction using the method described in any one of claims 1 to 4 are obtained according to the reference value and the reconstruction value.

6. The image quality evaluation method according to claim 5, characterized in that: It also includes evaluating the reconstruction value of each voxel by using one or more of mean square error MSE, peak signal-to-noise ratio PSNR and multi-scale structural similarity MS-SSIM of image quality.

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