A cosmic ray muon scattering imaging reconstruction method based on path integral

Abstract

This invention discloses a path integral-based imaging reconstruction method for cosmic ray muon scattering, comprising the following steps: 1) Detecting the position information of cosmic ray muons using a detector, and sending the position information, emission direction, and incident direction of the muons to a path integral module; 2) The path integral module determines the traversal path of the muons in the material within the test space based on the position information, emission direction, and incident direction of the muons, and generates multiple traversal paths within the test space. It then traverses multiple paths around each traversal path, selects path-related pixels, accumulates the probability distribution of the selected pixels, and calculates the displacement of the cosmic ray muons after traversing the material based on the position information of the muons. Finally, it solves for the scattering density that maximizes the probability product of the path, scattering angle, and displacement based on the probability distribution and sends it to the reconstruction module; 3) The reconstruction module reconstructs the image of the test material within the test space based on the scattering density information of the muons.

Description

Technical Field

[0001] This invention relates to the field of nuclear imaging, and more particularly to a method for imaging cosmic ray muon scattering using path integrals. Background Technology

[0002] Cosmic ray muon scattering imaging utilizes the fact that muons at Earth's sea level have an average energy of approximately 3–4 GeV and a flux reaching 10,000 m. -2 min -1 It possesses the characteristics of penetrating dense strata thousands of meters thick and being difficult to shield, enabling it to image the target. It typically employs a double-sided "sandwich" structure detector, which is relatively complex. The object to be measured is placed in the middle of the double-sided detector, and the change in the deflection angle of muons before and after passing through the material is detected. The root mean square of the deflection angle is then calculated to identify the atomic number and contour of the material inside the target. Scattering imaging is generally suitable for imaging small, high atomic number (Z) dense objects, such as nuclear materials, border security checks, and nuclear reactor cores.

[0003] The cosmic ray muon scattering imaging system consists of a detector module, front-end electronics, digital electronics, and a reconstruction algorithm. The detector module and front-end electronics are primarily responsible for the energy deposition and conversion output of cosmic ray muons. The digital electronics are mainly responsible for signal triggering and analog-to-digital conversion. The reconstruction algorithm is mainly responsible for the reconstruction and visualization of muon scattering imaging. The basic principle of cosmic ray muon scattering imaging is that muons interact with the detector material through ionization or Coulomb scattering, depositing energy in the detector. After conversion, the energy signals and trigger signals of each channel are output by the detector's front-end electronics. These are then processed by the digital electronics through analog-to-digital conversion, and finally input to the host computer. The reconstruction algorithm then completes the data processing, reconstruction, and visualization, obtaining the scattering density distribution of the material under test, and further determining the radiation length of the material, thus distinguishing between low-Z, medium-Z, and high-Z materials.

[0004] Based on the principles and application scenarios of cosmic ray muon scattering imaging, the ability to distinguish matter and the imaging time are two key performance aspects. The main sources affecting these performances are: (1) The low flux of cosmic ray muons at sea level fundamentally leads to a longer imaging time. (2) In terms of hardware, the insufficient position resolution of the detector limits the ability to distinguish matter at low, medium, and high Z levels in muon imaging. The detector area also limits the speed of muon imaging. (3) In terms of software reconstruction, different reconstruction algorithms result in varying imaging quality and time. In summary, aside from the influence of muon flux and the effects of detector and electronic hardware, algorithmic reconstruction is also an active area in cosmic ray muon scattering imaging.

[0005] Most current reconstruction imaging algorithms are based on the nearest neighbor model algorithm (PoCA). This algorithm assumes that muons are scattered only once in the material and calculates the coordinates of the scattering point by calculating the intersection of the backward extensions of the incident and outgoing trajectories of the muons. This algorithm considers the area near the scattering point to be a strong scattering region. The deflection angle information of the muons before and after passing through the material can be calculated and assigned to the scattering point region to estimate the scattering density of the region. By combining a large amount of muon data, three-dimensional image reconstruction can be completed. This algorithm is based on the assumption that muons are scattered only once in the material, but these assumptions may not hold true, which may reduce the quality of the generated image. The following problems exist with this algorithm: (1) This algorithm assumes that scattering only occurs once near the scattering point and assigns the value of the deflection angle entirely to the scattering point region, which is inconsistent with the actual situation. Figure 1 As shown. (2) In three-dimensional space, two straight lines may not necessarily intersect. Generally, some methods are needed to connect the incident and outgoing tracks, such as using the midpoint of the common perpendicular as the scattering point. This will cause the strong scattering region to deviate, such as Figure 2 As shown. (3) The algorithm assumes that the propagation path of muons in the material is a straight line. For some homogeneous materials, the deflection of muons in the material is a continuous process of minimizing curvature. Therefore, using the nearest neighbor method to calculate the muon path in the material is not the optimal solution.

[0006] The statistical iterative reconstruction algorithm MSLD-EM is an improvement on the PoCA algorithm. It avoids the shortcomings of the PoCA algorithm's single-scattering assumption and the problem of assigning scattering information only to strong scattering regions. It assumes that muon scattering in the material is the result of the combined effect of voxels along the path. By combining the deflection angle information of muons before and after passing through the material with the voxels along the path, it fully utilizes information such as deflection angle and displacement for reconstruction, ultimately improving image quality. However, the calculation of muon path information in the MLSD-EM algorithm is still based on the nearest neighbor model, selecting the path from the incident point to the PoCA point to the exit point. Although the Seton algorithm is subsequently used to calculate the path proportion within each voxel, the path calculation problem present in the PoCA algorithm is still unavoidable in the MLSD-EM algorithm because the path selection is still based on the nearest neighbor model.

[0007] As mentioned above, the MLSD-EM algorithm has significantly improved reconstruction results compared to the PoCA algorithm. In the MLSD-EM algorithm, the key focus is on replacing the nearest neighbor model and calculating the penetration path of muons in the object under test. For the input and output trajectories of muons, a path integral algorithm is used to calculate the most probable path. Geant4 simulations are used to perform weighted calculations of all paths, quantifying the probabilities of all paths and transforming the probability maximization problem into minimizing the curvature integral function, ultimately yielding the route with the highest probability. Unlike the nearest neighbor model, the path integral method, by considering the influence of scattering materials, is compatible with any prior assumptions about the distribution of scattering materials and can handle the problem of non-intersecting input and output trajectories of muons. Summary of the Invention

[0008] To address the problems existing in current muon scattering imaging, this invention aims to provide a path integral-based reconstruction method for cosmic ray muon scattering imaging. This invention combines the calculation of muon traversal paths in materials with the principle of path integrals. The path integral method considers the total contribution of all possible paths a particle can take in space; these paths can be viewed as the particle's temporal wandering, from the initial point to the destination. Each path has a corresponding phase factor, and by integrating the possible paths, the behavior and properties of the quantum system can be obtained. This invention analyzes the advantages of applying path integrals to the calculation of muon scattering paths in the tested material, proposing a method to replace the original nearest-neighbor model, providing a new muon path calculation method for cosmic ray muon scattering reconstruction. Integrating this method into the existing MSLD-EM algorithm reconstruction avoids the calculation offset problem of scattering points in the nearest-neighbor model, thus calculating a more realistic muon path through the material. This method is compatible with the tested material, improves the quality of reconstructed images from cosmic ray muon scattering imaging, and fully leverages the advantages of muon scattering imaging.

[0009] This invention provides a novel method for calculating the passage path of muons in materials, and further provides a method for cosmic ray muon scattering imaging reconstruction based on this path. The method is characterized by including a detector, a path integration algorithm, and a reconstruction algorithm. The position information of the muons detected by the detector serves as the input information for the path integration algorithm. The path integration algorithm calculates the path information and displacement information of the muons based on the input information, which are then used as the input information for the MLSD-EM algorithm.

[0010] The detector is used to detect the position information of the muon, calculate the exit and incident directions of the muon from the position information, and send the information to the path integral algorithm.

[0011] The path integral module, a path integral-like module, is used to calculate the path of muons through the material. It iterates through and calculates all possible paths between the incident and exit points, such as... Figure 2 Since the PoCA path calculated by the nearest neighbor model is relatively close to the actual traversal path of muons in the material, except that the selection of voxels along the path is inaccurate, the traversal interval can be limited to the space surrounding the PoCA path calculated by the nearest neighbor model to reduce computational cost. Figure 3 Calculate the probability distribution of possible paths, extract the available finite numbers from the infinitesimal probabilities generated by the diffusion calculation, and complete the selection calculation of the crossing path;

[0012] The reconstruction module, based on the traditional MLSD-EM algorithm, introduces a path integral module to replace the original nearest neighbor model for calculating muon path information. The muon positions received by the detector and the traversal path information calculated by the path integral module are input into the MLSD-EM algorithm to complete muon scattering reconstruction and graphical display.

[0013] Furthermore, the MLSD-EM algorithm is used to receive the direction and path information of muons for image reconstruction. The image reconstruction process includes data input, data processing, iterative process, image filtering and display, etc.

[0014] Furthermore, the data processing method calculates the deflection angle and displacement of each muon event after its interaction with the material based on the input data. It then uses path integration to traverse all paths between the incident and exit points and performs weighted calculations of all paths using Geant4 simulation to quantify the probabilities of all paths.

[0015] Furthermore, the iterative algorithm and scattering density, based on the quantized path probability solution, maximize the scattering density distribution that maximizes the probability product of the path, scattering angle, and displacement, and minimize the corresponding curvature integral function, complete the calculation of the scattering density, calculate the new path probability based on the scattering density, and then iteratively complete the calculation of the new scattering density, thereby completing the iteration and reconstruction.

[0016] Furthermore, the image filtering display involves performing median and mean filtering on the final calculated scattering density data before reconstructing the image for display, thereby reducing background noise and ultimately completing the image display.

[0017] The advantages of this invention are as follows:

[0018] Compared with existing technical solutions, this invention no longer uses the traditional nearest neighbor model to calculate the muon's trajectories in the test material. Instead, it utilizes path integral technology, which avoids the assumption of the traditional nearest neighbor model that the muon scatters only once in the material, thus better aligning with the principle of muon-material interaction. It also avoids the problem of non-intersection between the incident and exit trajectories of muons in the three-dimensional imaging space, reducing the trajectory displacement of muons in the material and improving image quality. The path integral-based calculation process also avoids the linearization of the muon's penetration trajectory in the material, more closely matching the muon's motion trajectory within the material. This invention proposes a method for calculating the trajectories of cosmic ray muons in materials using path integral, applicable to cosmic ray muon scattering reconstruction algorithms, and has wide application and potential for improving the image quality of cosmic ray muon scattering imaging. Attached Figure Description

[0019] Figure 1 This is a 3D comparison diagram showing the difference between the simulated real path of the muon in the material and the path calculated using the nearest neighbor model.

[0020] Figure 2 The PoCA path calculated for the nearest neighbor model in two-dimensional space is compared with the real path in the graph.

[0021] Figure 3 This is a schematic diagram illustrating the possible pixel calculations for the penetration paths of cosmic ray muons in the material being tested.

[0022] Figure 4 A schematic diagram of the setup for detecting muon information in cosmic rays. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0024] This invention relates to a path integral-based imaging reconstruction method for cosmic ray muon scattering. Its key feature is the use of a novel method for calculating the penetration path of muons in materials, improving upon the traditional nearest-neighbor model for muon path calculation. Furthermore, it proposes a method combining path integral with the MLSD-EM algorithm for cosmic ray muon scattering reconstruction. The specific implementation of this reconstruction method is as follows:

[0025] S1: As Figure 4As shown, the position information of cosmic ray muons detected by four layers of detectors is illustrated. The positions of the first to fourth layers of detectors are P1(X1,Y1,Z1), P2(X2,Y2,Z2), P3(X3,Y3,Z3), and P4(X4,Y4,Z4), respectively. Based on the detected muon position information, the incident direction Din and the exit direction Dout of the muons are calculated using vector calculations. The deflection angle of the muons in the material is then calculated based on these direction vectors.

[0026] Din = (X2-X1, Y2-Y1, Z2-Z1)

[0027] Dout = (X4 - X3, Y4 - Y3, Z4 - Z3)

[0028] S2: As Figure 4 As shown, the nearest neighbor model is calculated based on the detected points P2 and P3, the incident direction Din, and the outgoing direction Dout. The muon PoCA path L1 of point P2-nearest neighbor-P3 is calculated as auxiliary information. This muon PoCA path L1 is used as the traversal space constraint for the probability distribution calculation of the path integral algorithm.

[0029] S3: Based on the detected points P2 and P3, the incident direction Din, and the exit direction Dout, calculations are performed. Based on the calculation results of S2, multiple paths surrounding the PoCA path L1 are traversed, and path-related pixels are selected, accumulating the probability distribution of the selected pixels. For example... Figure 3 The diagram illustrates the calculation of the probability distribution of possible paths, extracting a finite number of usable paths from the infinitesimal probabilities generated by the diffusion calculation, and completing the selection calculation of the crossing path.

[0030] S4: Based on the position information of the muon incident and exit, calculate the displacement of the cosmic ray muon after it passes through the material, and then calculate the relevant projection matrix.

[0031] S5: Based on the calculation results of S1 to S4, all paths between the incident and exit points are traversed using path integrals. Geant4 simulation is used to perform weighted calculations of all paths, quantifying the probabilities of all paths. Based on the quantized path probabilities, the scattering density distribution matrix that maximizes the probability product of the path, scattering angle, and displacement is calculated. Based on this scattering density matrix, the process of S3 to S5 is repeated to recalculate new path probabilities and complete the calculation of a new voxel scattering density matrix. This process is iterated.

[0032] S6: Reconstruct and display the scattering density matrix of each voxel in the iterated imaging space. Before display, filter and smooth the data to reduce scatter plot noise.

[0033] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.

Claims

1. A method for cosmic ray muon scattering imaging reconstruction based on path integral, comprising the following steps: 1) Detect the position information of cosmic ray muons using a detector, and calculate the exit and incident directions of the muons based on the position information; then send the position information, exit direction, and incident direction of the muons to the path integration module; 2) The path integration module determines the traversal space of the muon's path through the material based on the muon's position information, emission direction, and incident direction. Multiple traversal paths are generated within this space, and multiple paths surrounding each path are traversed. Path-related pixels are selected, and the probability distribution of the selected pixels is accumulated. The displacement of the cosmic ray muon after traversing the material is calculated based on the muon's position information. Then, the scattering density that maximizes the probability product of the path, scattering angle, and displacement is calculated based on the probability distribution and sent to the reconstruction module. 3) The reconstruction module performs image reconstruction of the material to be tested in the test space based on the scattering density information of the muons.

2. The method according to claim 1, characterized in that, The method for image reconstruction of the material under test is as follows: 21) For each ray, the path integration module traverses the surrounding constrained imaging space path, and uses path integration to traverse all paths between the incident point and the exit point. It uses Geant4 simulation to perform weighted calculation of all paths, quantizes the probability of all paths, and solves the scattering density distribution based on the quantized path probability to maximize the probability product of the path, scattering angle, and displacement. 22) Reconstruct the image of the material under test based on the scattering density of each voxel obtained in step 21).

3. The method according to claim 2, characterized in that, Before reconstructing and displaying the image, the final calculated scattering density is subjected to median and mean filtering to reduce background noise and finally complete the image display.

4. The method according to claim 1, 2, or 3, characterized in that, The location information of the muon includes the incident point and the exit point of the muon; the path integration module calculates the PoCA path of the muon using the nearest neighbor model based on the incident point, exit point, exit direction and incident direction of the muon as auxiliary information, and determines the traversal space of the muon's path in the material based on the muon PoCA path.

5. The method according to claim 1, 2, or 3, characterized in that, Based on the traversal space of the determined muon path in the material, calculate the probability distribution of possible muon paths, and select the scattering density matrix of each voxel that maximizes the probability product of the path, scattering angle, and displacement.

Images