A gamma radiation source positioning method based on a sparse solution algorithm

Abstract

This invention discloses a gamma radiation source localization method based on a sparse solution algorithm, comprising: acquiring a series of nuclear radiation measurement data D at different locations within a target area; acquiring a scene model of the target area and voxelizing it to obtain a voxel model, wherein each voxel in the voxel model serves as a gamma source term; constructing a response matrix H of the gamma voxel source term at the location of the nuclear radiation measurement data, wherein the elements in the response matrix H are... h ji , h ji The unit strength of the first i Individual gamma source in the first j The expected nuclear radiation data at each measurement point; construct the system of equations H·S=D for the gamma voxel source term intensity value S, where the source term intensity value, n The number of voxels in the voxel model. s i For the first i The source intensity of voxels; the intensity values ​​of each gamma voxel source term are obtained by solving the equation system using a sparse solution algorithm. s i Based on the intensity values ​​of each gamma voxel source term, the location of the gamma radiation source is visualized in the voxel model.

Description

Technical Field

[0001] This invention relates to the field of radiation source localization, and specifically to a method for localizing gamma radiation sources based on a sparse solution algorithm. Background Technology

[0002] Based on the transport relationships of gamma particles and measurement data from nuclear detectors, establishing and solving equations concerning the source term model parameters forms the basic framework for gamma radiation source localization methods. Currently, the most common radiation source localization technique involves discretizing the region where the source term might exist into smaller source terms and using the Maximum Likelihood Expectation-Maximization (MLEM) algorithm to solve for the intensity values ​​of each smaller source term, thus reflecting the radiation source location. Compared to directly modeling the source term coordinates, this technique, by discretizing the source term region, is more suitable for locating complex geometries in 3D scenes and multiple source terms; while the MLEM algorithm utilizes the characteristic that kernel counts follow a Poisson distribution and can satisfy the non-negativity of the source intensity solution.

[0003] While discrete source term regions can handle more complex radiation source modeling, they also drastically increase the number of radiation source model parameters, typically far exceeding the amount of nuclear radiation measurement data. This further leads to severe overfitting problems in solving radiation source parameters. The problem with existing techniques is that commonly used algorithms such as MLEM cannot handle overfitting, resulting in severe artifacts in the solution and poor accuracy and resolution in gamma radiation source localization. Summary of the Invention

[0004] To achieve the above and other related objectives, this invention discloses a gamma radiation source localization method based on a sparse solution algorithm, comprising: Obtain nuclear radiation measurement data D at different locations within the target area, where , d j For the first j Nuclear radiation measurement data at each measurement point m The number of measurement points; Obtain the scene model of the target area and voxelize it to obtain a voxel model. Each voxel in the voxel model is used as a gamma source term. Construct the response matrix H of the gamma voxel source term at the location of the nuclear radiation measurement data. The elements of the response matrix H are... h ji , h ji The unit strength of the first i Individual gamma source in the first j The expected nuclear radiation data at each measurement point; Construct a system of equations H·S=D concerning the source term intensity value S of the gamma voxel, where the source term intensity value... , nThis represents the number of voxels in the voxel model. s i For the first i Source intensity of individual elements; The intensity values ​​of each gamma voxel source term are obtained by solving the system of equations using a sparse solution algorithm. s i ; Based on the intensity values ​​of each gamma voxel source term, the location of the gamma radiation source is visualized in the voxel model.

[0005] Preferably, the nuclear radiation measurement data D is the gamma particle count rate or gamma dose rate.

[0006] Preferably, the voxel model is a scene voxel model composed of cubic pixels, which is transformed from the target area scene model. The target area scene model is obtained through 3D scanning or constructed according to design drawings.

[0007] Preferably, the response matrix elements h ji The calculation formula is: ; in For the first i Individual gamma source center for the first j The angular response at each measurement point L ji For the first i Individual gamma source center and the first j The distance between the measurement points.

[0008] Preferably, the intensity values ​​of each gamma voxel source term obtained by solving the system of equations include: Using a nonnegative lasso regression algorithm, adding a regularization term yields the optimization problem, which includes: ; in λ >0 is the regularization parameter for controlling the compression amount of the control coefficient. λ The settings shall be made by those skilled in the art according to actual needs; The source intensity of each voxel is updated sequentially using the coordinate descent method. At each step, only the source intensity of one voxel is optimized, while the source intensities of other voxels remain unchanged. s i The update formula is as follows: ; in f ( z , λ ) is the soft thresholding operation in lasso regression, defined as: ; Update all one by one s i Until convergence.

[0009] Preferably, the location of the visualized gamma radiation source includes: In the voxel model, voxel colors are mapped according to the intensity values ​​of the gamma voxel source term, and the formula for calculating the mapped color is as follows: In the formula r i , g i , b i For the first i RGB values ​​of voxels C It is a constant scaling factor.

[0010] Secondly, the present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0011] By adopting the above technical solution and using a sparse solution algorithm to limit the number of non-zero elements in the solution of voxel gamma source intensity, the overfitting problem that is common and difficult to deal with in the existing technology can be effectively overcome, and gamma radiation source localization results with higher resolution and fewer artifacts can be obtained. Attached Figure Description

[0012] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. The drawings are provided for a better understanding of the invention and are not intended to limit the scope of this disclosure. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein: Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the target area and dose rate measurement points in an embodiment of the present invention; Figure 3 This is a schematic diagram of the target area scene model and scene voxel model according to an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the solution results of the embodiment of the present invention with the solution results obtained using the MLEM algorithm. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Reference Figure 1 This invention provides a method for locating gamma radiation sources based on a sparse solution algorithm, comprising: Obtain nuclear radiation measurement data D at different locations within the target area, where , d j For the first j Nuclear radiation measurement data at each measurement point m The number of measurement points; Obtain the scene model of the target area and voxelize it to obtain a voxel model. Each voxel in the voxel model is used as a gamma source term. Construct the response matrix H of the gamma voxel source term at the location of the nuclear radiation measurement data. The elements of the response matrix H are... h ji , h ji The unit strength of the first i Individual gamma source in the first j The expected nuclear radiation data at each measurement point; Construct a system of equations H·S=D concerning the source term intensity value S of the gamma voxel, where the source term intensity value... , n This represents the number of voxels in the voxel model. s i For the first i Source intensity of individual elements; The intensity values ​​of each gamma voxel source term are obtained by solving the system of equations using a sparse solution algorithm. s i ; Based on the intensity values ​​of each gamma voxel source term, the location of the gamma radiation source is visualized in the voxel model.

[0015] Preferred, refer to Figure 2 In this embodiment of the invention, the target area is a room containing four gamma source terms (201-204); the nuclear radiation measurement data D is the gamma particle count rate or gamma dose rate. In this embodiment of the invention, the nuclear radiation measurement data D is the dose rate value measured at a series of measurement locations 205 in the room. D is: ; in d j For the firstj Dose rate measurements at each measurement point.

[0016] Preferred, refer to Figure 3 The voxel model is a scene voxel model that is transformed from the target area scene model into a scene voxel model composed of cubic pixels. The target area scene model is obtained by 3D scanning or constructed according to design drawings. In this embodiment of the invention, the target area scene model is obtained by 3D scanning. The voxel model is composed of cubes with a side length of 20 cm, and each cube is used as a gamma source term.

[0017] The size of the response matrix H is m × n Assuming isotropic angular response and considering only the inverse square law of dose rate, without considering the shielding and attenuation of gamma rays by scene materials, this approach closely approximates physical laws while significantly simplifying computational complexity and reducing computation time. This facilitates the practical application of the proposed method. (Response matrix elements...) h ji The calculation formula is: ; in For the first i Individual gamma source center for the first j The angular response at each measurement point L ji For the first i Individual gamma source center and the first j The distance between the measurement points.

[0018] Preferably, the sparse solution algorithm used in the embodiments of the present invention is a non-negative lasso regression algorithm, including: Using a nonnegative lasso regression algorithm, adding a regularization term yields the optimization problem, which includes: ; in λ >0 is the regularization parameter for controlling the compression amount of the control coefficient. λ ; The source intensity of each voxel is updated sequentially using the coordinate descent method. At each step, only the source intensity of one voxel is optimized, while the source intensities of other voxels remain unchanged; the source intensity s i The update formula is as follows: ; in f ( z , λ ) is the soft thresholding operation in lasso regression, defined as: ; Update all one by one si Until convergence.

[0019] Preferably, the location of the visualized gamma radiation source includes: In the voxel model, voxel colors are mapped according to the intensity values ​​of the gamma voxel source term, and the formula for calculating the mapped color is as follows: In the formula r i , g i , b i For the first i RGB values ​​of voxels C It is a constant scaling factor.

[0020] Reference Figure 4 The comparison between the results of the gamma source localization obtained by the non-negative lasso regression algorithm and the results obtained by the MLEM algorithm in the embodiments of the present invention shows that the solution method used in the embodiments of the present invention has higher accuracy.

[0021] Secondly, the present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0022] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined.

[0023] For the sake of simplicity, the method embodiments are described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to the embodiments of the present invention.

[0024] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0025] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating gamma radiation sources based on a sparse solution algorithm, characterized in that, include: Obtain nuclear radiation measurement data D at different locations within the target area, where , d j For the first j Nuclear radiation measurement data at each measurement point m The number of measurement points; Obtain the scene model of the target area and voxelize it to obtain a voxel model. Each voxel in the voxel model is used as a gamma source term. Construct the response matrix H of the gamma voxel source term at the location of the nuclear radiation measurement data. The elements of the response matrix H are... h ji , h ji The unit strength of the first i Individual gamma source in the first j The expected nuclear radiation data at each measurement point; Construct a system of equations H·S = D for the source term intensity value S of the gamma voxel, where the source term intensity value... , n This represents the number of voxels in the voxel model. s i For the first i Source intensity of individual elements; The intensity values ​​of each gamma voxel source term are obtained by solving the system of equations using a sparse solution algorithm. s i ; Based on the intensity values ​​of each gamma voxel source term, the location of the gamma radiation source is visualized in the voxel model.

2. The method according to claim 1, characterized in that, The nuclear radiation measurement data D is the gamma particle count rate or gamma dose rate.

3. The method according to claim 1, characterized in that, The voxel model is a scene voxel model composed of cubic pixels, which is transformed from the target area scene model. The target area scene model is obtained through 3D scanning or constructed based on design drawings.

4. The method according to claim 1, characterized in that, The response matrix elements h ji The calculation formula is: ； in For the first i Individual gamma source center for the first j The angular response at each measurement point L ji For the first i Individual gamma source center and the first j The distance between the measurement points.

5. The method according to claim 1, characterized in that, Solving the system of equations yields the intensity values ​​of each gamma voxel source term, including: Using a nonnegative lasso regression algorithm, adding a regularization term yields the optimization problem, which includes: ； in λ > 0 is the regularization parameter for controlling the compression amount of the control coefficient. λ ; The source intensity of each voxel is updated sequentially using the coordinate descent method. At each step, only the source intensity of one voxel is optimized, while the source intensities of other voxels remain unchanged; the source intensity s i The update formula is as follows: ； in f ( z , λ ) is the soft thresholding operation in lasso regression, defined as: ； Update all one by one s i Until convergence.

6. The method according to claim 1, characterized in that, The locations of the visualized gamma radiation sources include: In the voxel model, voxel colors are mapped according to the intensity values ​​of the gamma voxel source term, and the formula for calculating the mapped color is as follows: In the formula r i , g i , b i For the first i RGB values ​​of voxels C It is a constant scaling factor.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method described in any one of claims 1-6.

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