Sparse inversion method of radioactive source based on voxel grid and geometric radiation coupling matrix

Abstract

The application discloses a radio source sparse inversion method based on a voxel grid and a geometric-radiation coupling matrix, and aims at the problem that the existing radio source inversion method is difficult to balance among the calculation efficiency, physical consistency and sparsity constraint, and realizes high-precision joint inversion of the radio source position, intensity and medium parameters through the joint inversion framework of ADMM fast sparse solution and PINN physical correction on the basis of constructing the geometric-radiation coupling matrix. The ADMM fast sparse solution + PINN physical correction framework provided by the application provides an effective path for solving the ill-posed inverse problem of the geometric-radiation coupling matrix, ADMM is responsible for efficiently processing linear mapping and sparse constraint, PINN is responsible for compensating the complex physical effects which cannot be completely described by the linear model, and the two cooperate to significantly improve the inversion accuracy and stability.

Description

Technical Field

[0001] This invention belongs to the field of environmental radiation monitoring technology, specifically relating to the design of a sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices. Background Technology

[0002] In critical scenarios such as nuclear facility decommissioning, environmental radiation monitoring, and nuclear safety emergency response, the location and intensity inversion of radioactive sources is a core technical problem and a key technical requirement for ensuring personnel safety and developing scientific response plans. This problem is essentially a typical ill-conditioned inverse problem involving inferring the distribution of radiation sources from the detector response, characterized by high dimensionality, unsteadiness, and strong uncertainty. Currently, existing technologies mainly include the following methods: First, voxel-based linear inversion methods typically construct the response matrix between voxels and the detector and solve it using methods such as least squares and gradient descent. However, when the number of voxels increases significantly, these methods suffer from high computational complexity, large storage overhead, and susceptibility to local optima, making them unsuitable for large-scale 3D scenes. Second, while sparse inversion methods incorporating L1 regularization (such as Lasso) can utilize prior information about the sparse spatial distribution of radiation sources, these methods only constrain the structure of the solution from a mathematical perspective and fail to effectively integrate the physical mechanisms of radiation transmission (such as absorption and scattering), potentially leading to inversion results that deviate from actual physical laws. Furthermore, deep learning-based methods achieve rapid inversion by learning the mapping relationship between "source distribution and detector response," but these methods heavily rely on large-scale labeled data and lack generalization ability under varying medium parameters or unknown environments, making them unsuitable for complex real-world scenarios.

[0003] In recent years, methods based on geometry-radiation coupling matrices have improved modeling accuracy to some extent by explicitly modeling the physical relationship between voxels and detectors. However, these coupling matrices typically exhibit high dimensionality, sparsity, ill-conditioned nature, and non-square matrix characteristics, making stable and efficient solution acquisition a pressing issue. Therefore, ensuring computational efficiency while simultaneously maintaining the sparsity and physical consistency of the solution is a key challenge currently facing the technology. Summary of the Invention

[0004] The purpose of this invention is to solve the problem that existing radioactive source inversion methods are difficult to balance between computational efficiency, physical consistency and sparsity constraints. A radioactive source sparse inversion method based on voxel grid and geometric radiation coupling matrix is ​​proposed to achieve high-precision joint inversion of radioactive source location, intensity and medium parameters.

[0005] The technical solution of this invention is: a sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices, comprising the following steps: S1. Discretize the radiation environment region to be measured in three-dimensional space, divide it into several voxels, and obtain a voxel grid.

[0006] S2. Calculate the response contribution coefficient of each voxel to each detector, and construct the geometry-radiation coupling matrix based on the response contribution coefficient.

[0007] S3. Construct a sparse inversion optimization model based on the geometry-radiation coupling matrix.

[0008] S4. Use ADMM to solve the sparse inversion optimization model to obtain the sparse solution.

[0009] S5. Using sparsity as the initial condition, PINN is used to correct the physical consistency of the sparse inversion optimization model.

[0010] S6. Perform joint inversion using the modified sparse inversion optimization model and output the inversion results.

[0011] Furthermore, each voxel in step S1 It contains a vector of properties to be solved, including the intensity of the radiation source. Medium absorption coefficient and medium scattering coefficient , , This indicates the number of voxels within the voxel grid.

[0012] Furthermore, each voxel in step S2 For each detector response contribution coefficient The calculation formula is: in Voxel representation and detector The solid angle subtended, , Indicates the number of detectors. Indicates the path of ray propagation. Represents a spatial position vector. Represents the medium in spatial coordinates The linear absorption coefficient at that point.

[0013] Furthermore, in step S2, the geometry-radiation coupling matrix Contribution coefficients of all responses The combined values ​​are obtained and compared with the detector measurements. The linear mapping relationship between them is: in This represents the source distribution vector to be inverted. It represents the set of real numbers.

[0014] Furthermore, the objective function of the sparse inversion optimization model in step S3 is: in Represents the regularization parameter. Describing the L1 norm, This represents the L2 norm.

[0015] Furthermore, step S4 includes the following sub-steps: S41. Introducing auxiliary variables The objective function of the sparse inversion optimization model is transformed into the standard ADMM form: Its corresponding augmented Lagrangian function is: in This represents the augmented Lagrange function. Represents the dual variable. Indicates the penalty parameter; S42. Iteratively update the source distribution vector within the framework of the augmented Lagrange function. Auxiliary variables and dual variables Until convergence, a sparse solution is obtained. .

[0016] Furthermore, the convergence condition in step S42 is: in This indicates the convergence tolerance.

[0017] Furthermore, step S5 includes the following sub-steps: S51, using the source distribution vector As input, the detector response prediction value To output, construct a neural network. As a forward solver for PINN.

[0018] S52, Change the current sparse solution Inputting the PINN forward solver yields the predicted detector response: S53. Calculate the predicted value of the detector response. Compared with the measured value of the detector residual : S54, residual Feedback is sent to the ADMM framework in step S4 to dynamically adjust the data fidelity items. The corrected data fidelity item is obtained. .

[0019] S55. Correct the data fidelity item Substituting into the ADMM framework, the corrected source distribution is obtained by solving. .

[0020] S56. Repeat steps S51 to S55 until the preset physical consistency threshold is met, and obtain the corrected sparse inversion optimization model.

[0021] Furthermore, the loss function of the PINN forward solver in step S51 for: in Indicates the detector response prediction value Compared with the measured value of the detector The mean square error, This represents the residual of the radiative transfer equation at several sampling points. This represents the physical constraint weight coefficient.

[0022] Furthermore, the inversion results output in step S6 include the spatial coordinates of the radioactive source, the intensity value of the radioactive source, and the distribution of the medium absorption coefficient and the medium scattering coefficient obtained through PINN correction.

[0023] The beneficial effects of this invention are: (1) Significantly improved computational efficiency: This invention uses the ADMM algorithm to solve the L1 regularization problem, decomposing the original problem into subproblems that are easy to solve, avoiding the dimensionality curse faced by traditional methods when directly inverting large-scale matrices or gradient descent. The linear convergence characteristic of ADMM ensures that it can still achieve fast solution under large-scale voxel grids.

[0024] (2) Sparsity and physical consistency are unified: This invention ensures the physical authenticity and rationality of the inversion results by unifying and integrating L1 sparsity constraints and RTE physical constraints, strictly guarantees the sparsity of the inversion results, and conforms to the prior knowledge that the radioactive source is sparsely distributed in space.

[0025] (3) Strong robustness: This invention does not rely on a large amount of training data. By using the PINN forward solver based on RTE, the physical model is embedded in the inversion process. Even when the medium distribution is unknown or uncertain, it can still jointly invert the accurate source distribution and medium parameters.

[0026] (4) Achieving stable solution of ill-conditioned problems: The ADMM fast solution + PINN physical correction framework proposed in this invention provides an effective path for solving the ill-conditioned inversion problem of geometry-radiation coupling matrix. ADMM is responsible for efficiently handling linear mapping and sparse constraints, while PINN is responsible for compensating for complex physical effects that the linear model cannot fully describe. The two work together to significantly improve the accuracy and stability of the inversion.

[0027] (5) More comprehensive information output: The final output of this invention not only includes the location and intensity of the radioactive source, but also the distribution of the absorption coefficient and scattering coefficient of the medium, providing more comprehensive decision support information for nuclear facility decommissioning and radiation environment assessment. Attached Figure Description

[0028] Figure 1 The diagram shows a flowchart of a sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices provided by an embodiment of the present invention. Detailed Implementation

[0029] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0030] This invention provides a sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices, such as... Figure 1 As shown, the process includes the following steps S1 to S6: S1. Discretize the radiation environment region to be measured in three-dimensional space, divide it into several voxels, and obtain a voxel grid.

[0031] In this embodiment of the invention, each voxel It contains a vector of properties to be solved, including the intensity of the radiation source. Medium absorption coefficient and medium scattering coefficient , , This indicates the number of voxels within the voxel grid.

[0032] S2. Calculate the response contribution coefficient of each voxel to each detector, and construct the geometry-radiation coupling matrix based on the response contribution coefficient.

[0033] In this embodiment of the invention, based on the radiative transport physics equations (such as the Boltzmann transport equation or its simplified form), considering the exponential decay law of absorption and the solid angle geometric factor, the calculation is performed for each voxel. For each detector response contribution coefficient The calculation formula is: in Voxel representation and detector The solid angle subtended is integral along the total attenuation of the ray path from the voxel center to the detector. , Indicates the number of detectors. Indicates the path of ray propagation, that is, from the first... The position of the individual element center to the first The straight-line propagation path at the center of each detector. Spatial position vectors are usually represented by coordinates. Represents the medium in spatial coordinates The linear absorption coefficient at a given point is the ability of the medium to absorb radiation.

[0034] In this embodiment of the invention, the geometry-radial coupling matrix Contribution coefficients of all responses The combined values ​​are obtained and compared with the detector measurements. The linear mapping relationship between them is: in This represents the source distribution vector to be inverted, containing the source intensity of each voxel. Represents the set of real numbers, i.e., a matrix. All elements in the set are real numbers.

[0035] S3. Construct a sparse inversion optimization model based on the geometry-radiation coupling matrix.

[0036] In this embodiment of the invention, based on the prior sparsity of the radioactive source distribution, the radioactive source inversion problem is transformed into an optimization problem with sparsity constraints, and the objective function is: in Represents the regularization parameter. Describing the L1 norm, This represents the L2 norm. The first term in the objective function. For data fidelity, the second item This is an L1 regularization term used to improve the sparsity of the solution.

[0037] S4. Use ADMM (Alternating Direction Multiplier Method) to solve the sparse inversion optimization model and obtain the sparse solution.

[0038] Step S4 includes the following sub-steps S41~S42: S41. Introducing auxiliary variables The objective function of the sparse inversion optimization model is transformed into the standard ADMM form: Its corresponding augmented Lagrangian function is: in This represents the augmented Lagrange function. Represents the dual variable. Indicates the penalty parameter; S42. Iteratively update the source distribution vector within the framework of the augmented Lagrange function. Auxiliary variables and dual variables Until convergence, a sparse solution is obtained. The iteration format is: superscript Indicates the first Next iteration, superscript Indicates the first The next iteration.

[0039] In this embodiment of the invention, the source distribution vector During the update, it's equivalent to solving a linear least squares problem, which can be efficiently solved using methods such as the conjugate gradient method, with auxiliary variables... During the update, a soft threshold operation is performed.

[0040] In this embodiment of the invention, sparse solution Most voxel sources have a source intensity of 0, with only a few voxels, such as the source location, having a non-zero value.

[0041] In this embodiment of the invention, the convergence condition is: in This indicates the convergence tolerance.

[0042] S5. Using sparsity as the initial condition, PINN (Physical Information Neural Network) is used to correct the physical consistency of the sparse inversion optimization model.

[0043] Step S5 includes the following sub-steps S51 to S56: S51, using the source distribution vector As input, the detector response prediction value To output, construct a neural network. As a forward solver for PINN.

[0044] In this embodiment of the invention, the loss function of the PINN forward solver for: in Indicates the detector response prediction value Compared with the measured value of the detector The mean square error (MSE). This represents the residual of the radiative transfer equation at several sampling points. This represents the weighting coefficients of the physical constraints, used to balance the relative contributions of data-driven terms and physical equation residuals during PINN training. Loss function. It not only includes the error between the network output and the measured data, but more importantly, it embeds the residual terms of the radiative transfer equation (RTE) to ensure that the network output strictly follows the physical laws.

[0045] S52, Change the current sparse solution Inputting the PINN forward solver yields the predicted detector response: S53. Calculate the predicted value of the detector response. Compared with the measured value of the detector residual : S54, residual Feedback is sent to the ADMM framework in step S4 to dynamically adjust the data fidelity items. The corrected data fidelity item is obtained. .

[0046] S55. Correct the data fidelity item Substituting into the ADMM framework, the corrected source distribution is obtained by solving. .

[0047] S56. Repeat steps S51 to S55 until the preset physical consistency threshold is met, and obtain the corrected sparse inversion optimization model.

[0048] In this embodiment of the invention, the physical consistency threshold is: Less than the set value.

[0049] S6. Perform joint inversion using the modified sparse inversion optimization model and output the inversion results.

[0050] In this embodiment of the invention, the output inversion results include the spatial coordinates of the radioactive source (corresponding to non-zero voxels), the intensity value of the radioactive source, and the distribution of the medium absorption coefficient and medium scattering coefficient obtained through PINN correction.

[0051] In this embodiment of the invention, the final output of the modified sparse inversion optimization model is... , The coordinates of the non-zero voxels represent the spatial coordinates of the radioactive source, and their values ​​represent the source intensity. Meanwhile, PINN updated the medium absorption coefficient in its last iteration. and medium scattering coefficient The distribution of is output as the corrected environmental parameters.

[0052] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices, characterized in that, Includes the following steps: S1. Discretize the radiation environment region to be measured in three-dimensional space, divide it into several voxels, and obtain a voxel grid. S2. Calculate the response contribution coefficient of each voxel for each detector, and construct the geometry-radiation coupling matrix based on the response contribution coefficient; S3. Construct a sparse inversion optimization model based on the geometry-radiation coupling matrix; S4. Use ADMM to solve the sparse inversion optimization model to obtain the sparse solution; S5. Using sparsity as the initial condition, PINN is used to correct the physical consistency of the sparse inversion optimization model. S6. Perform joint inversion using the modified sparse inversion optimization model and output the inversion results.

2. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 1, characterized in that, Each voxel in step S1 It contains a vector of properties to be solved, including the intensity of the radiation source. Medium absorption coefficient and medium scattering coefficient , , This indicates the number of voxels within the voxel grid.

3. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 2, characterized in that, Each voxel in step S2 For each detector response contribution coefficient The calculation formula is: in Voxel representation and detector The solid angle subtended, , Indicates the number of detectors. Indicates the path of ray propagation. Represents a spatial position vector. Represents the medium in spatial coordinates The linear absorption coefficient at that point.

4. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 3, characterized in that, The geometry-radiation coupling matrix in step S2 Contribution coefficients of all responses The combined values ​​are obtained and compared with the detector measurements. The linear mapping relationship between them is: in This represents the source distribution vector to be inverted. It represents the set of real numbers.

5. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 4, characterized in that, The objective function of the sparse inversion optimization model in step S3 is: in Represents the regularization parameter. Describing the L1 norm, This represents the L2 norm.

6. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 5, characterized in that, Step S4 includes the following sub-steps: S41. Introducing auxiliary variables The objective function of the sparse inversion optimization model is transformed into the standard ADMM form: Its corresponding augmented Lagrangian function is: in This represents the augmented Lagrange function. Represents the dual variable. Indicates the penalty parameter; S42. Iteratively update the source distribution vector within the framework of the augmented Lagrange function. Auxiliary variables and dual variables Until convergence, a sparse solution is obtained. .

7. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 6, characterized in that, The convergence condition in step S42 is: in This indicates the convergence tolerance.

8. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 6, characterized in that, Step S5 includes the following sub-steps: S51, using the source distribution vector As input, the detector response prediction value To output, construct a neural network. As a forward solver for PINN; S52, Change the current sparse solution Inputting the PINN forward solver yields the predicted detector response: S53. Calculate the predicted value of the detector response. Compared with the measured value of the detector residual : S54, residual Feedback is sent to the ADMM framework in step S4 to dynamically adjust the data fidelity items. The corrected data fidelity item is obtained. ; S55. Correct the data fidelity item Substituting into the ADMM framework, the corrected source distribution is obtained by solving. ; S56. Repeat steps S51 to S55 until the preset physical consistency threshold is met, and obtain the corrected sparse inversion optimization model.

9. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 8, characterized in that, The loss function of the PINN forward solver in step S51 for: in Indicates the detector response prediction value Compared with the measured value of the detector The mean square error, This represents the residual of the radiative transfer equation at several sampling points. This represents the physical constraint weight coefficient.

10. The sparse inversion method for radioactive sources based on voxel grids and geometric radiation coupling matrices according to claim 1, characterized in that, The inversion results output in step S6 include the spatial coordinates of the radioactive source, the intensity value of the radioactive source, and the distribution of the medium absorption coefficient and the medium scattering coefficient obtained through PINN correction.

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