A three-dimensional electromagnetic inverse scattering method based on a diffusion model and BCGS-FFT based on physical constraints

Abstract

The present invention relates to the field of electromagnetic inverse scattering technology, and specifically to a three-dimensional electromagnetic inverse scattering method based on a diffusion model and BCGS-FFT with physical constraints. The invention proposes a new three-dimensional electromagnetic inverse scattering reconstruction method by combining BCGS-FFT, a physical model (CF-BPA and CC-SOM) and a diffusion model: by introducing BCGS-FFT physical constraints consistent with the data generation stage in the reverse diffusion stage, the physical consistency of the three-dimensional reconstruction process is ensured, thereby effectively reducing the physical distortion problem; the gradual denoising process of the diffusion model significantly improves the noise suppression capability in the three-dimensional reconstruction, and combined with the preliminary inversion results of the physical model, the error accumulation in the entire three-dimensional reconstruction process is reduced, the method has higher accuracy and stability, and the adaptability is also greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic inverse scattering, and in particular to a three-dimensional electromagnetic inverse scattering method based on a diffusion model and BCGS-FFT of physical constraints. Background Art

[0002] Electromagnetic inverse scattering technology is a method that reconstructs the electrical parameters and geometric structure of a target object by analyzing the scattering characteristics of electromagnetic waves around the target object. It is widely used in radar inversion, radar imaging, non-destructive testing and other fields. At present, the research and application of electromagnetic inverse scattering methods are mainly focused on two-dimensional (2D) scenarios. The two-dimensional method has a good effect when dealing with simple structures and low-complexity targets. However, with the increasing complexity of actual application requirements, the applicability of the two-dimensional method in a three-dimensional (3D) environment is significantly limited.

[0003] In the field of three-dimensional electromagnetic inverse scattering, there are relatively few studies and applications. The main reason is that the computational complexity of three-dimensional problems has increased significantly, and it is necessary to process a large amount of data and a higher-dimensional parameter space. Existing three-dimensional electromagnetic inverse scattering methods still face many challenges in terms of computational efficiency, reconstruction accuracy and robustness. For example, although the three-dimensional inverse scattering method based on iterative optimization can reconstruct the three-dimensional structure of the target more accurately, it has a huge amount of calculation and a slow convergence speed, which makes it difficult to meet real-time requirements; the three-dimensional inverse scattering model based on deep learning improves the reconstruction speed in some scenarios, but in high-noise environments and complex target shapes, its reconstruction accuracy and stability still need to be improved.

[0004] In addition, the existing three-dimensional inverse scattering method has certain limitations in balancing computational efficiency and reconstruction accuracy, and it is difficult to meet the requirements of high precision and high efficiency at the same time. Therefore, there is an urgent need for a new three-dimensional electromagnetic inverse scattering reconstruction method that can efficiently integrate advanced numerical algorithms and machine learning techniques and introduce physical models and constraints to improve the reconstruction accuracy and computational efficiency and meet the diverse and high-demand needs in practical applications. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a three-dimensional electromagnetic inverse scattering method based on a diffusion model and BCGS-FFT based on physical constraints, which can ensure the physical consistency of the three-dimensional reconstruction process, effectively reduce the physical distortion problem, and significantly improve the noise suppression capability in the three-dimensional reconstruction, and reduce the error accumulation in the entire three-dimensional reconstruction process, with higher accuracy and stability, while greatly improving adaptability.

[0006] To achieve the above object, the present invention provides the following technical solution: a three-dimensional electromagnetic inverse scattering method based on a diffusion model of physical constraints and BCGS-FFT, the method comprising the following steps:

[0007] S1. Generate scattering data for model training and inversion by simulating the propagation and scattering of electromagnetic waves in the target area, use the second-order Green's function to describe the interaction of electromagnetic waves, combine BCGS-FFT for efficient solution, and perform data generation layout based on multi-source and multi-receiver;

[0008] S2. Forward diffusion, from the preliminary generated scattering data and incident field data Start by gradually adding random noise , generate forward diffusion data at different time steps;

[0009] S3. Preliminary inversion of the physical model: based on the prior knowledge of the physical model, the preliminary geometric shape and dielectric constant distribution of the target object are extracted from the data after forward diffusion;

[0010] S4. Backward diffusion, by using the diffusion model, starts from the noise data after forward diffusion and gradually removes the noise.

[0011] The state closest to the original scattering data is recovered, where the conditional probability of back diffusion is: , the update formula of the reverse diffusion process is: ,

[0012] In the formula, represents the input x at time step t （t） Under the condition of （t-1） An estimated value of represents the contrast function obtained by preliminary inversion of the physical model, is the noise of standard normal distribution, To control the denoising strength at each time step, is the identity matrix, and θ is the parameter of the network model.

[0013] Furthermore, the data generation in S1 includes the following steps:

[0014] S101. Load point cloud data from storage file and use quad Indicates, where x, y, z represent three-dimensional coordinates, Represents the dielectric constant. At the same time, based on the mapping of the quaternion point cloud data to the discrete grid, the dielectric constant distribution in the entire grid is constructed, and then the contrast function is constructed. ;

[0015] S102. Using point cloud data as input, the second-order Green's function is used to describe the propagation characteristics of the electromagnetic field in the medium to generate three-dimensional scattering data for model training. The scattering field described by the second-order Green's function By the incident field and contrast function Perform convolution calculation to express:

[0016] ;

[0017] in, is the second-order Green's function, indicating the position About Location The electric field contribution of represents the contrast function, express The dielectric constant of the location;

[0018] S103. Solve the total electric field inside and outside the target object ;

[0019] S104. Perform data generation layout based on multi-source and multi-receiver, wherein multiple transmitters and receivers are located in the positive and negative directions of the x, y, and z axes, respectively.

[0020] Furthermore, S101 loads the point cloud data from the storage file and performs standardization processing, including: if the number of points contained in the point cloud is insufficient, filling by repeating the points; if the number of points exceeds, performing downsampling processing by random sampling.

[0021] Furthermore, the convolution calculation of the S102 second-order Green's function is accelerated by fast Fourier transform FFT, and the frequency domain representation of the second-order Green's function is: , is the unit wave vector direction, is the wave number, is the imaginary part used to avoid numerical singularities, is the wave vector, which is used to describe the propagation direction of the wave in space, and i represents the imaginary unit.

[0022] Further, S103 the total electric field inside and outside the target object The calculation is accelerated by using the biconjugate gradient stabilization method BCGS combined with fast Fourier transform FFT.

[0023] Furthermore, the process of S2 forward diffusion is expressed by conditional probability: , It means the mean , the variance is The normal distribution of Depends on x (t-1) and β t The distribution of the scattered field data at the final time step t is: , where x （t-1） 、x （t） represents the data at time steps t-1 and t, To control the intensity of the noise added at each time step, is random noise that follows a standard normal distribution.

[0024] Furthermore, in step S3, the coherence factor back-projection algorithm CF-BPA and the cross-correlation subspace optimization method CC-SOM are used to perform preliminary inversion of the physical model.

[0025] Furthermore, the steps of preliminary inversion using the coherence factor backprojection algorithm CF-BPA and the cross-correlation subspace optimization method CC-SOM are as follows:

[0026] S301. Scattering data with high noise generated by forward diffusion process For input data, CF-BPA is used for geometric recovery, and the recovery formula is: ,in, Represents the estimated value of the contrast function, which is used to describe the geometric position of the target; is the final scattered field received at receiver i, is the incident field at emitter j, represents complex conjugate;

[0027] S302. A coherence factor CF is introduced to suppress the influence of noise, where CF is defined as: , N rx Represents the number of receiving antennas, that is, the number of antenna elements in the receiving antenna array; N tx represents the number of transmitting antennas, that is, the number of antenna elements in the transmitting antenna array; r i represents the position of the i-th receiving antenna; r j represents the position of the jth transmitting antenna;

[0028] S303. Combine the geometric recovery formula and the coherence factor to obtain the geometric shape estimation of the target area ;

[0029] S304. Dielectric constant optimization using cross-correlation subspace optimization method CC-SOM Make an estimate.

[0030] Further, in step S304, the cross-correlation subspace optimization method CC-SOM defines an objective function based on cross-correlation to estimate the contrast function : ,in is the dielectric constant at position r; the optimization goal is: ,in, is the second-order Green's function, which represents the electric field contribution of position r' to position r. The optimization method is the subspace optimization method.

[0031] Furthermore, S4 back-diffusion is also combined with the physical model for consistency constraints, including: introducing BCGS-FFT consistent with the data generation stage in each step of the back-diffusion for physical constraints, and defining a consistent loss function during the training of the back-diffusion model to constrain the consistency of the loss function;

[0032] Among them, the scattered field calculation equation of physical constraints is: , is the second-order Green function, which is consistent with the data generation stage; the consistency loss function is: , is the denoising loss, which is used to measure the effect of the back diffusion model in the denoising process. The scattering field predicted by the calculation is the loss of physical consistency. The scattered field is compared with the initial measurement The error is defined as: , is the weight of controlling the physical consistency loss in the total loss.

[0033] Furthermore, the reverse diffusion process of S4 combined with the physical model is:

[0034] Initial state, t=T, final state x after reverse diffusion from forward diffusion （T） At the beginning, the preliminary inversion results of the physical model are used as prior knowledge to extract the target information from the random noise;

[0035] Stepwise denoising t=T,T-1,…,1, at each back-diffusion time step t, through the neural network model The denoised value of the predicted data is then corrected using BCGS-FFT to obtain the next step of the scattered field data x （t-1） .

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] 1. The present invention realizes high-precision inversion of the three-dimensional geometric shape and dielectric constant of the target object through the synergistic effect of different technologies.

[0038] 2. The present invention uses BCGS-FFT to generate three-dimensional scattering data, which can efficiently calculate the propagation and scattering of electromagnetic waves in the target area, ensuring the high accuracy and physical rationality of the data.

[0039] 3. The present invention combines forward diffusion with reverse diffusion. Forward diffusion generates noise data of different time steps by gradually adding noise to simulate the degradation process of scattering data. Reverse diffusion gradually removes noise and restores the electromagnetic characteristics of the target from high-noise data, greatly enhancing the noise suppression capability and inversion accuracy.

[0040] 4. The present invention performs preliminary inversion of the physical model through CF-BPA and CC-SOM, quickly estimates the geometric shape and dielectric constant distribution of the target, provides reasonable initial conditions for reverse diffusion, and reduces the complexity of inversion and error accumulation.

[0041] 5. The present invention introduces the physical constraints of BCGS-FFT in the reverse diffusion process to ensure that each step of denoising complies with the physical laws of electromagnetic wave propagation, thereby ensuring the physical consistency and scientific rationality of the inversion results. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the process flow of the three-dimensional electromagnetic inverse scattering method of the present invention. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] like Figure 1 As shown in the figure, the present invention adopts a fusion strategy of BCGS-FFT, diffusion model, physical model (CF-BPA and CC-SOM) and physical constraints to give full play to the advantages of each technology in its best field. BCGS-FFT is used to simulate the three-dimensional electromagnetic scattering field and generate high-precision scattering data. Its fast solution capability accurately describes the electromagnetic characteristics of the target and provides reliable initial conditions for subsequent inversion. The preliminary inversion capability of the physical model (CF-BPA and CC-SOM) is used to extract the geometric shape and electrical characteristics of the target from the generated data, especially the dielectric constant, so that the preliminary inversion has good accuracy and rationality. The diffusion model is used for the reverse diffusion process of step-by-step denoising. Through an efficient denoising mechanism, the high-precision target geometry and dielectric constant are gradually restored in the noisy data. At the same time, combined with the physical constraints of BCGS-FFT, the physical consistency of the generation and inversion stages is ensured. Through this fusion strategy, the present invention solves key problems in three-dimensional electromagnetic inverse scattering reconstruction and high-precision inversion of dielectric constants, such as noise suppression, target feature extraction, physical consistency of inversion, and reconstruction accuracy in complex environments, thereby achieving more accurate and reliable three-dimensional target reconstruction and dielectric constant inversion.

[0045] 1. Data generation:

[0046] The electromagnetic inverse scattering problem involves inferring the electromagnetic properties of an object, including its geometry, dielectric constant, etc., from the scattered field of electromagnetic waves. This process requires simulating the propagation and scattering of electromagnetic waves in the target area to generate scattering data for model training and inversion. The present invention uses the second-order Green's function to describe the interaction of electromagnetic waves and combines BCGS-FFT for efficient solution to ensure the accuracy and physical rationality of data generation.

[0047] 1.1 Scattering phenomenon:

[0048] When electromagnetic waves encounter a target object, they will scatter because the electromagnetic properties of the object are different from those of the background medium. The properties of the scattered electromagnetic waves, such as amplitude, phase, direction, etc., can reflect the geometric and physical properties of the object. The scattering phenomenon can be described by the total field of the electromagnetic waves in the target area. Including the incident field and the scattered field, its expression is: in, is the incident electric field, is the scattered field caused by the object.

[0049] 1.2 Generation of scattering data:

[0050] The key to data generation is to generate three-dimensional scattering data for model training by simulating the interaction between electromagnetic waves and target objects. The specific process is as follows:

[0051] 1) Point cloud data:

[0052] Use quaternion point cloud data as input. Each point cloud sample consists of four parameters, namely the three-dimensional coordinates (x, y, z) and the dielectric constant , used to describe the position and electromagnetic properties of objects in three-dimensional space.

[0053] 2) Application of second-order Green's function:

[0054] The calculation of the scattered field is based on the second-order Green's function, which is used to describe the propagation characteristics of the electromagnetic field in the medium. Specifically, the Green's function is used to calculate the electric field contribution of each scatterer to other locations in the grid. It can be calculated by convolving the incident field with the contrast function, and its expression is:

[0055] ,in, is the second-order Green's function, indicating the position The electric field contribution to the position, Contrast function, which is used to describe the difference in electromagnetic properties between an object and the background medium.

[0056] 3) Fast Fourier Transform (FFT) of Green's function:

[0057] In the solution process, FFT (Fast Fourier Transform) is used to accelerate the convolution calculation of Green's function and the incident field. The Green's function is represented in the frequency domain as , through FFT operation, the convolution operation is converted into multiplication in the frequency domain, which significantly improves the computational efficiency. The frequency domain representation of the second-order Green's function is: in, is the unit wave vector direction, is the wave number, is the imaginary part used to avoid numerical singularities.

[0058] 1.3 BCGS-FFT method:

[0059] In order to solve the total electric field inside and outside the target object, the BCGS (biconjugate gradient stabilization method) combined with FFT is used to accelerate the calculation process. BCGS is an iterative method for solving large sparse matrices. Combined with FFT, it can efficiently calculate the electric field effect of the scatterer on the entire grid. Total electric field The solution is obtained by iteratively updating the electric field distribution until the specified convergence condition is met, thereby obtaining a high-precision electromagnetic characteristics description of the target.

[0060] 1.4 Multi-source multi-sink layout:

[0061] In the data generation process, multiple transmitters and receivers are used, located in the positive and negative directions of the x, y, and z axes. The layout of these transmitters and receivers can ensure full coverage of the target area and capture the scattering characteristics of the target in different directions. The position of each transmitter and receiver is r tx and r rx , their relative positions determine the direction and amplitude of the incident field and the received scattered field.

[0062] 1.5 Generation and processing of point cloud data:

[0063] 1) Standardization of point cloud data:

[0064] After loading the point cloud data from the storage file, normalization is performed to ensure that each sample has the same number of scattered points. For example, if the point cloud contains insufficient points, it is filled by duplicating the points; if the number of points exceeds, it is downsampled by random sampling to ensure consistency of all data samples.

[0065] 2) Mapping of point cloud to mesh:

[0066] Each point of the point cloud data is mapped onto a discrete grid and used to construct the dielectric constant distribution in the entire grid, i.e., the contrast function This distribution describes the differences in the electromagnetic properties of the scatterer throughout the three-dimensional space and is used in subsequent scattered field calculations.

[0067] 2. Forward diffusion:

[0068] After the data generation is completed, the generated three-dimensional scattering data needs to be forward diffused. The forward diffusion process starts from a certain initial scattering field data, gradually adds noise, and makes the scattering data gradually degenerate into pure noise. The purpose of forward diffusion is to provide the noise data required for the diffusion model training, and at the same time provide a reasonable basis for the reverse diffusion process. The following is a detailed description of the forward diffusion process:

[0069] 2.1 Goals and definitions of forward diffusion:

[0070] 1) The forward diffusion process generates scattering data from the initial and incident field data Start by gradually adding random noise , generate diffusion data at different time steps.

[0071] 2) At each time step t, the goal of forward diffusion is to gradually transform the original scattered field data into completely random noise, which can provide rich samples for model training and help the model learn the relationship between noise and object characteristics.

[0072] 2.2 Forward diffusion formula:

[0073] 1) The forward diffusion process can be represented by a conditional probability, that is, the data x at time step t−1 （t-1） Data x at time step t （t） Relationship:

[0074] in, Indicates the mean , the variance is The normal distribution of Depends on x (t-1) and β t The distribution of To control the intensity of the noise added at each time step.

[0075] 2) Corresponding to the total electric field generated in the previous step , including the superposition of the incident field and the scattered field. In the forward diffusion process, Noise is gradually added to generate electric field data at different times until the final field distribution is completely degraded into noise.

[0076] 3) Representation of scattered field data in forward diffusion: For the scattered field data at time step t, it can be expressed as: in, is random noise that obeys the standard normal distribution. In this way, the original electric field data is superimposed with noise at each step, and the signal component of the electric field is gradually covered by the noise.

[0077] 2.3 Gradual degradation of scattered field data:

[0078] 1) Initial state t=0:

[0079] The starting point of forward diffusion is the scattered field data from the previous step , which is composed of the superposition of the incident field and the scattered field. That is:

[0080] 2) Time step t>0:

[0081] At each time step t, we gradually add random noise to the data, making the electric field signal gradually chaotic, as described below: in, The value of increases gradually, which means that in the process of diffusion, the intensity of the noise gradually increases, causing the data to change from ordered to disordered, and gradually degenerate from the physical field to pure noise.

[0082] 2.4 The physical meaning of noise:

[0083] In the forward diffusion process of electromagnetic scattering data, the addition of noise can be understood as the various uncertainties encountered in the simulation measurement, such as interference of electromagnetic waves during propagation, environmental noise, and errors caused by measurement equipment. By gradually adding noise to the original scattered field data, the diffusion model can learn how to recover the original target information from the noise-contaminated data, thereby improving the robustness and accuracy of the model under low signal-to-noise ratio conditions.

[0084] 3. Preliminary inversion of physical model:

[0085] After the forward diffusion is completed, the next step is to perform a preliminary inversion of the physical model. The purpose of this process is to provide a preliminary reasonable physical state for the reverse diffusion process, thereby improving the accuracy and convergence speed of the inversion. The physical model estimates the geometric shape and electrical properties (such as dielectric constant) of the target object through preliminary processing of the three-dimensional scattering data. In the present invention, CF-BPA (coherence factor back projection algorithm) and CC-SOM (cross-correlation subspace optimization method) are used for the preliminary inversion of the physical model.

[0086] 3.1 Objectives of the physical model:

[0087] The initial inversion process of the physical model aims to extract the preliminary geometry and dielectric constant distribution of the target object from the data after forward diffusion, so as to provide a reasonable starting condition for the reverse diffusion process. By combining the prior knowledge of the physical model, the difficulty of reverse diffusion can be effectively reduced and local optimality can be avoided.

[0088] 3.2 Steps of preliminary inversion of physical model:

[0089] 1) Input data:

[0090] The initial inversion of the physical model is used to obtain the final output data x of the forward diffusion process. （T） As input, these data have been processed by adding noise multiple times, and contain the scattering information of the target object and its mixture with the environmental noise. The input data is the scattered field data, that is, the scattering data with more noise generated by the forward diffusion process. .

[0091] 2) Geometry recovery (CF-BPA):

[0092] First, use CF-BPA (Coherence Factor Back-Projection Algorithm) for geometry recovery. The goal of CF-BPA is to extract the geometry of the target object from the noisy scattering data. The formula for geometry recovery is:

[0093] in, Represents the estimated value of the contrast function, which is used to describe the geometric position of the target; For receiver The final scattered field received at For the transmitter The incident field at represents complex conjugate.

[0094] 3) Introduction of coherence factors:

[0095] The coherence factor (CF) is introduced to suppress the influence of noise. The role of the coherence factor is to enhance the effective scattering signal and reduce the noise artifact by increasing the weight of the coherent superposition signal, so that the geometric shape can be restored more accurately. It is defined as:

[0096]

[0097] 4) Restore the target geometry:

[0098] Combining the above geometric recovery formula and coherence factor, the geometric shape estimation of the target area is obtained ,These estimates are used to determine the distribution of the target in three-dimensional space and provide preliminary structural information for subsequent dielectric constant inversion.

[0099] 3.3 Electrical characteristics estimation (CC-SOM):

[0100] 1) After the geometry restoration is completed, CC-SOM (Cross-Correlation Subspace Optimization Method) is used to further estimate the dielectric constant of the target.

[0101] 2) Optimization of contrast function:

[0102] a) In CC-SOM, a cross-correlation based objective function is defined to estimate the contrast function , that is, the dielectric constant distribution of the target:

[0103] .

[0104] b) The optimization goal is to minimize the received scattered field The error between the model-predicted scattered field is: in, is the second-order Green's function, which represents the electric field contribution of position r' to position r.

[0105] 3) Introduction of subspace optimization:

[0106] CC-SOM uses a subspace optimization method to improve the efficiency and stability of the calculation by restricting the estimation of the contrast function to a low-dimensional subspace for optimization. The output of this process is the dielectric constant distribution of the target object. , used to describe the electromagnetic properties of objects in three-dimensional space.

[0107] 3.4 The significance of the preliminary inversion of the physical model:

[0108] 1) Reasonable initial conditions:

[0109] Through CF-BPA and CC-SOM, a preliminary estimate of the geometric shape and electrical properties of the target object is obtained. Compared with the inversion process starting completely from random noise, such a preliminary inversion provides a more reasonable initial condition, reduces the difficulty of back diffusion, and effectively improves the accuracy of the results.

[0110] 2) Reduce the cumulative error in inversion:

[0111] Performing a preliminary inversion of the physical model before back diffusion can effectively reduce the impact of noise on the reconstruction results and reduce the accumulation of errors during the inversion process. This not only improves the physical consistency of the final inversion results, but also enhances the stability of the entire process.

[0112] 4. Reverse diffusion process:

[0113] After the initial inversion of the physical model, the next step is to further restore the three-dimensional electromagnetic properties of the target object through the back diffusion process. The purpose of back diffusion is to gradually remove noise from the noisy scattering data, restore the high-precision geometry and dielectric constant of the target, and ensure that the final inversion results are consistent with the physical principles.

[0114] 4.1 The goal of reverse diffusion:

[0115] The goal of the reverse diffusion process is to gradually remove the noise from the noise data after forward diffusion, and finally restore it to the state closest to the original scattered data. By using the diffusion model for reverse diffusion, we can learn how to effectively eliminate noise, and at the same time combine the physical constraints of BCGS-FFT to ensure that each step of the denoising process complies with the physical laws of electromagnetic wave propagation.

[0116] 4.2 Back diffusion formula:

[0117] 1) Conditional probability of reverse diffusion:

[0118] In back diffusion, starting from completely random noise, the original scattered data is gradually recovered through a back diffusion process. The conditional probability of back diffusion can be described as: in, represents the input x at time step t （t） Under the condition of （t-1） An estimated value of Represents the contrast function (dielectric constant distribution) obtained through preliminary inversion of the physical model.

[0119] 2) Update formula in the reverse diffusion process:

[0120] At each step t, back diffusion updates the scattered field data by progressively denoising: in, is the noise of standard normal distribution, Controls the strength of denoising at each time step.

[0121] 4.3 Integration with physical models:

[0122] 1) Consistency of physical constraints:

[0123] In each step of the backdiffusion, the BCGS-FFT physical constraints consistent with the data generation stage are introduced to ensure the physical consistency of the inversion process. Specifically, for time step t, the contrast function χ(t)(r) predicted by the backdiffusion model is used to calculate the scattered field Epred(t)(r): in, is the second-order Green's function, which is consistent with the data generation stage.

[0124] 2) Consistency constraints in loss functions:

[0125] When training the back-diffusion model, a consistency loss function is defined to ensure that each step of the back-diffusion complies with the physical constraints. The form of the loss function is: in, Denoising is the denoising loss, which is used to measure the effect of the back diffusion model in the denoising process; For physical consistency loss, the predicted scattered field is calculated The scattered field is compared with the initial measurement The error is defined as: is the weight of controlling the physical consistency loss in the total loss.

[0126] 4.4 The process of reverse diffusion:

[0127] 1) Initial state t=T:

[0128] The final state x after reverse diffusion from forward diffusion （T） Initially, these data contain a high level of random noise. The preliminary inversion results of the physical model (geometry and dielectric constant distribution) serve as prior knowledge to help the back-diffusion model extract target information from the random noise.

[0129] 2) Stepwise denoising t=T,T-1,…,1:

[0130] At each back-diffusion time step t, the neural network model The denoised value of the predicted data is then corrected using BCGS-FFT to obtain the next step of the scattered field data x （t-1） This gradual denoising process ensures that the data gradually recovers from a chaotic state to a physically plausible state, so that the ultimately recovered scattering field is consistent with the initial estimate of the physical model.

[0131] 4.5 The final output of back diffusion:

[0132] 1) Final target feature recovery:

[0133] After the back diffusion is completed, the three-dimensional electromagnetic properties of the target object are obtained, including its geometric shape and dielectric constant distribution. These characteristic data are gradually restored by denoising, combined with the prior information provided by the physical model, so that the final restoration result has high physical rationality and accuracy.

[0134] 2) Physical consistency guarantee:

[0135] By combining BCGS-FFT physical constraints at each time step, the back diffusion process ensures that the recovered electromagnetic properties are consistent with the actual physical propagation laws. The introduction of physical consistency loss effectively reduces the accumulation of errors, making the final restored 3D reconstruction results not only visually close to the real target, but also in line with the physical laws of electromagnetic scattering.

[0136] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A three-dimensional electromagnetic inverse scattering method based on a diffusion model with physical constraints and BCGS-FFT, characterized in that: The method comprises the following steps: S1. Generate scattering data for model training and inversion by simulating the propagation and scattering of electromagnetic waves in the target area, use the second-order Green's function to describe the interaction of electromagnetic waves, combine BCGS-FFT for efficient solution, and perform data generation layout based on multi-source and multi-receiver; S2. Forward diffusion, from the preliminary generated scattering data and incident field data Start by gradually adding random noise , generate forward diffusion data at different time steps; S3. Preliminary inversion of the physical model: based on the prior knowledge of the physical model, the preliminary geometric shape and dielectric constant distribution of the target object are extracted from the data after forward diffusion; S4. Backward diffusion, by using the diffusion model, starts from the noise data after forward diffusion, gradually removes the noise and restores the state closest to the original scattering data, where the conditional probability of backward diffusion is: , the update formula of the reverse diffusion process is: , In the formula, represents the input x at time step t （t） Under the condition of （t-1） An estimated value of represents the contrast function obtained by preliminary inversion of the physical model, is the noise of standard normal distribution, To control the denoising strength at each time step, is the identity matrix, and θ is the parameter of the network model.

2. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 1 is characterized in that: The data generation in S1 includes the following steps: S101. Load point cloud data from storage file and use quad Indicates, where x, y, z represent three-dimensional coordinates, Represents the dielectric constant. At the same time, based on the mapping of the quaternion point cloud data to the discrete grid, the dielectric constant distribution in the entire grid is constructed, and then the contrast function is constructed. ; S102. Using point cloud data as input, the second-order Green's function is used to describe the propagation characteristics of the electromagnetic field in the medium to generate three-dimensional scattering data for model training. The scattering field described by the second-order Green's function By the incident field and contrast function Perform convolution calculation to express: ； in, is the second-order Green's function, indicating the position About Location The electric field contribution of represents the contrast function, express The dielectric constant of the location; S103. Solve the total electric field inside and outside the target object ; S104. Perform data generation layout based on multi-source and multi-receiver, wherein multiple transmitters and receivers are located in the positive and negative directions of the x, y, and z axes, respectively.

3. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 2 is characterized in that: S101 loads point cloud data from a storage file and performs standardization processing, including: if the number of points contained in the point cloud is insufficient, filling it by repeating the points; if the number of points exceeds, performing downsampling processing by random sampling.

4. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 2 is characterized in that: The convolution calculation of the S102 second-order Green's function is accelerated by fast Fourier transform FFT. The frequency domain representation of the second-order Green's function is: , is the unit wave vector direction, is the wave number, is the imaginary part used to avoid numerical singularities, is the wave vector, which is used to describe the propagation direction of the wave in space, and i represents the imaginary unit.

5. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 2 is characterized in that: S103 Total electric field inside and outside the target object The calculation is accelerated by using the biconjugate gradient stabilization method BCGS combined with fast Fourier transform FFT.

6. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 2, characterized in that: The process of S2 forward diffusion is expressed by conditional probability: , Indicates the mean , the variance is The normal distribution of , the final scattered field data at time step t is: , where x （t-1） 、x （t） represents the data at time steps t-1 and t, To control the intensity of the noise added at each time step, is random noise that follows a standard normal distribution.

7. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 2, characterized in that: In step S3, the coherence factor back-projection algorithm CF-BPA and the cross-correlation subspace optimization method CC-SOM are used to perform preliminary inversion of the physical model.

8. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 7 is characterized in that: The steps of preliminary inversion using the coherence factor backprojection algorithm CF-BPA and the cross-correlation subspace optimization method CC-SOM are as follows: S301. Scattering data with high noise generated by forward diffusion process For input data, CF-BPA is used for geometric recovery, and the recovery formula is: ,in, Represents the estimated value of the contrast function, which is used to describe the geometric position of the target; is the final scattered field received at receiver i, is the incident field at emitter j, represents complex conjugate; S302. A coherence factor CF is introduced to suppress the influence of noise, where CF is defined as: , N rx Represents the number of receiving antennas, that is, the number of antenna elements in the receiving antenna array; N tx represents the number of transmitting antennas, that is, the number of antenna elements in the transmitting antenna array; r i represents the position of the i-th receiving antenna; r j represents the position of the jth transmitting antenna; S303. Combine the geometric recovery formula and the coherence factor to obtain the geometric shape estimation of the target area ; S304. Dielectric constant optimization using cross-correlation subspace optimization method CC-SOM Make an estimate.

9. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 8, characterized in that: In step S304, the cross-correlation subspace optimization method CC-SOM defines an objective function based on cross-correlation to estimate the contrast function. : ,in is the dielectric constant at position r; the optimization goal is: ,in, is the second-order Green's function, which represents the electric field contribution of position r' to position r. The optimization method is the subspace optimization method.

10. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 1, characterized in that: S4 back-diffusion is also combined with the physical model for consistency constraints, including: introducing BCGS-FFT consistent with the data generation stage in each step of the back-diffusion for physical constraints, and defining a consistent loss function during the back-diffusion model training to constrain the consistency of the loss function; Among them, the scattered field calculation equation of physical constraints is: , is the second-order Green function, which is consistent with the data generation stage; the consistency loss function is: , is the denoising loss, which is used to measure the effect of the back diffusion model in the denoising process. The scattering field predicted by the calculation is the loss of physical consistency. The scattered field is compared with the initial measurement The error is defined as: , is the weight of controlling the physical consistency loss in the total loss.

11. The three-dimensional electromagnetic inverse scattering method based on the diffusion model and BCGS-FFT of physical constraints according to claim 9, characterized in that: The reverse diffusion process of S4 combined with the physical model is: Initial state, t=T, final state x after reverse diffusion from forward diffusion （T） At the beginning, the preliminary inversion results of the physical model are used as prior knowledge to extract the target information from the random noise; Stepwise denoising t=T,T-1,…,1, at each back-diffusion time step t, through the neural network model The denoised value of the predicted data is then corrected using BCGS-FFT to obtain the next step of the scattered field data x （t-1） .

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