An electromagnetic inverse scattering method, device and storage medium combining SOM and complex phase

Abstract

The invention relates to an electromagnetic inverse scattering method, device and storage medium combining SOM and complex phase, belonging to the field of electromagnetic inversion technology, and solving the problem of how to reconstruct the dielectric constant of a target scatterer. The invention establishes a data equation and a physical model of a state equation for electromagnetic inverse scattering, expresses the physical model of electromagnetic inverse scattering using the method of moments, and uses a subspace optimization method to decompose the induced current into a definite current and a fuzzy current, thereby providing richer and more accurate scattering information and helping to enhance the stability of reconstruction. The invention utilizes the complex phase information in the Litov approximation method to obtain a linear relationship between the dielectric target contrast and the complex phase, effectively improving the sensitivity of electromagnetic waves to the internal structure of the scatterer. The invention introduces a CNN network for reconstruction, realizes rapid data processing, greatly accelerates the speed of forward and reverse propagation, and thus realizes real-time imaging.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic inversion, and relates to an electromagnetic inverse scattering method, a device and a storage medium combining SOM and complex phase. Background Art

[0002] Electromagnetic inverse scattering technology reconstructs electromagnetic parameters such as the target's shape, position, and corresponding dielectric constant based on the scattering properties of the target object. Currently, mainstream electromagnetic inverse scattering methods fall into four categories: approximate linear methods, iterative optimization methods, black-box methods based on deep learning, and inversion methods that combine imaging and deep learning. However, these existing methods all have drawbacks. For example, approximate linear methods have difficulty handling strong scattering targets; iterative optimization methods have complex parameter settings; deep learning black-box methods directly process scattering data, obscuring the physical concepts of the process; and neural networks can reconstruct more refined results by combining deep learning methods with preliminary pre-imaging results. However, in actual experiments, the field equations constructed from measured scattering data are underdetermined, a phenomenon known as pathological electromagnetic inverse scattering. Furthermore, the field equations constructed using conventional Green's functions affect the retention of high-frequency information, limiting the fineness of the neural network's final imaging.

[0003] When it comes to solving ill-posed problems, the induced current is non-unique because the number of unknowns in the field equation matrix exceeds the number of constructible equations. Existing techniques (such as the Bern approximation and backpropagation) ignore this issue when dealing with strong scatterers and complex targets, resulting in unstable solutions and high sensitivity to noise.

[0004] When it comes to improving detail, the construction of field equations relies primarily on the electromagnetic wave simulation properties of Green's functions, such as attenuation and phase shifts. This leads to significant signal attenuation when processing high-frequency signals. Existing algorithms, which mostly rely on Green's functions, are difficult to construct case-by-case for complex situations, often making it difficult to reconstruct high-resolution internal details.

[0005] In terms of real-time imaging capabilities, traditional methods rely on iteration and complex mathematical operations when processing large-scale data, which often leads to slow processing speeds and cannot meet the needs of real-time imaging. Summary of the Invention

[0006] The technical problem to be solved by the present invention is how to achieve dielectric constant reconstruction of a target scatterer.

[0007] The present invention solves the above technical problems through the following technical solutions:

[0008] An electromagnetic inverse scattering method combining SOM and complex phase includes the following steps:

[0009] S1. Establish the physical model of the data equation and state equation of electromagnetic inverse scattering;

[0010] S2. The physical model of electromagnetic inverse scattering is expressed using the method of moments;

[0011] S3, using subspace optimization method to decompose the induced current into definite current and fuzzy current;

[0012] S4. Using the complex phase information in the Litov approximation method, a linear relationship between the medium target contrast and the complex phase is obtained;

[0013] S5. Introduce CNN network for reconstruction.

[0014] Furthermore, the mathematical expression of the data equation in step S1 is as follows:

[0015]

[0016] in, for The scattered field, and are domain points and source points respectively, represents the wave number in free space, represents the target domain of the scatterer, represents the Green's function, is the contrast function, express The total electric field.

[0017] Furthermore, the mathematical expression of the state equation in step S1 is as follows:

[0018]

[0019] in, Represents the incident electric field data.

[0020] Furthermore, the physical model of electromagnetic inverse scattering described in step S2 is expressed as follows using the moment method:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] Wherein, the subscript p represents the incident signal of the p-th transmitting antenna. , , , are the vectorization of the incident electric field, total electric field, induced current and scattered field, respectively. Yes N d ×N d The diagonal matrix of scattered intensity, N d The number of evenly divided target domains, N r is the number of receiving antennas;

[0027] The above expressions have the following relationship:

[0028]

[0029] Will Substitute into the above formula, we get:

[0030]

[0031]

[0032] in, is an N d ×N d dimensional matrix and is an N r ×N d dimensional matrix.

[0033] Furthermore, the method of decomposing the induced current into the definite current and the fuzzy current by using the subspace optimization method in step S3 is as follows:

[0034] Green operator G S Perform singular value decomposition:

[0035]

[0036] Where superscript H denotes conjugate transpose, U and V are unitary matrices, and the column vectors of V form a complete subspace;

[0037] Arrange the singular values in order of size: ;

[0038] According to the arrangement of singular values, the induced current is divided into the determined current J det and fuzzy current J amb :

[0039]

[0040] Substitute the above formula into ,have to:

[0041]

[0042] Similarly, , where the current J is determined detThe vector V corresponding to the first L largest singular values S Composition, fuzzy current J amb By the remaining N d -L column vectors V N L is the regularization parameter.

[0043] Furthermore, the method for obtaining the linear relationship between the medium target contrast and the complex phase by using the complex phase information in the Litov approximation method in step S4 is as follows:

[0044] The complex phase of the total electric field and the complex phase of the incident field Introduced, the following expression is obtained:

[0045]

[0046] make , it is deduced that there is a linear relationship between the medium target contrast and the complex phase as follows:

[0047] .

[0048] Furthermore, the method of introducing the CNN network for reconstruction in step S5 is as follows:

[0049] 1) Input data preprocessing;

[0050] 2) Network processing fusion architecture: Using a three-channel parallel input and re-fusion mode to determine the current Jdet, fuzzy current Jamb and complex phase difference Effective features are extracted through three convolutional neural networks. The fuzzy current component is connected to a denoising component to filter out secondary information and noise interference. The complex phase difference component is used as a weak correction component to determine the current frame information. Fusion adopts a channel splicing method and adaptively adjusts the proportion of each branch component through an attention mechanism. The overall network adopts an encoding and decoding structure, reducing the feature map at multiple scales and then reconstructing and amplifying it at multiple scales. Skip connections are used to take into account both deep and shallow features.

[0051] 3) Network training output: The preprocessed data is fed into the CNN network. During the training process, the final output is made close to the corresponding reference contrast. After the set number of iterations, the loss function converges and the optimal parameter model is retained. During testing, the preprocessed data is fed into the network to directly obtain the optimal contrast.

[0052] Furthermore, the method of preprocessing the input data is as follows:

[0053] First, perform singular value decomposition on the Green operator GS of the scattered data: , the singular values are sorted from large to small, the singular vectors VS corresponding to the first L singular values constitute the definite subspace, and the rest constitute the fuzzy subspace VN;

[0054] Secondly, the deterministic subspace VS is used to estimate the deterministic current Jdet by projecting the measured scattered field into the deterministic subspace, i.e.: , where the coefficient s is expressed as: ;

[0055] Again, combining the fuzzy subspace VN and Litov complex phase difference To estimate the fuzzy current Jamb, that is: , where the expression of coefficient a is: ;

[0056] The input of the final CNN network includes the determined current Jdet, the fuzzy current Jamb and the complex phase difference .

[0057] A device includes a memory and a processor, wherein the memory is used to store a program for supporting the processor to execute the electromagnetic inverse scattering method combining SOM and complex phase, and the processor is configured to execute the program stored in the memory.

[0058] A storage medium stores a computer program, which, when executed by a processor, executes the steps of the electromagnetic inverse scattering method combining SOM and complex phase.

[0059] The advantages of the present invention are:

[0060] This invention combines the subspace optimization method (SOM) with the complex phase of the Litov approximation (RA). The subspace optimization method decomposes the induced current into a deterministic current and a fuzzy current, taking into account the non-uniqueness of the induced current and ensuring information integrity. Furthermore, the complex phase difference of the Litov approximation exhibits a certain linear relationship with the contrast, providing richer and more accurate scattering information and helping to enhance the stability of the reconstruction. Utilizing the complex phase information in the Litov approximation effectively increases the sensitivity of electromagnetic waves to the internal structure of the scatterer. Furthermore, the inclusion of a neural network further enhances the ability to reconstruct the details of complex internal structures through its nonlinear properties. The introduction of a neural network enables faster data processing. The parallel processing capabilities and optimized network structure of the CNN significantly accelerate forward and backward propagation, thereby achieving real-time imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a flow chart of an electromagnetic inverse scattering method combining SOM and complex phase according to the first embodiment of the present invention.

[0062] Figure 2This is a simulation data rendering of the electromagnetic inverse scattering method combining SOM and complex phase according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with 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. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0064] The technical solution of the present invention is further described below with reference to the accompanying drawings and specific embodiments:

[0065] Example 1

[0066] like Figure 1 As shown, the electromagnetic inverse scattering method combining SOM and complex phase according to an embodiment of the present invention includes the following contents:

[0067] 1. Electromagnetic inverse scattering physical model

[0068] It is known that the forward process of electromagnetic inverse scattering can be represented by two equations - the data equation and the state equation. The data equation calculates the scattered field generated by the incident wave encountering the target scatterer, and the state equation indicates that the total electric field received by the receiver is composed of the incident field and the scattered field.

[0069] The mathematical expression of the data equation is as follows:

[0070]

[0071] in, for The scattered field, and are the domain point and the source point, which represent the position vector of the receiver and the source point of the target domain respectively, represents the wave number in free space, represents the target domain of the scatterer, Represents the Green's function, which is used to describe the value of the electromagnetic field generated by the source point at the receiving point. is the contrast function, defined as , is the dielectric constant, and the contrast function reflects the difference in electromagnetic properties between the object and the surrounding environment. express The total electric field.

[0072] The mathematical expression of the state equation is as follows:

[0073]

[0074] in, Represents the incident electric field data.

[0075] Total electric field and the induced current The following relationship exists:

[0076]

[0077] 2. Moment method representation of electromagnetic inverse scattering

[0078] In the actual experiment, the incident electric field and the total electric field are vectorized. Nt transmitting antennas and Nr receiving antennas are evenly arranged around the circumference of the dielectric target, dividing the surrounding space into uniform regions. At the same time, the dielectric target area D is divided into Nd square grids of equal size, and the center points of the divided blocks are discretized. The vector expression is as follows:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Wherein, the subscript p represents the incident signal of the p-th transmitting antenna. , , , are the vectorization of the incident electric field, total electric field, induced current and scattered field, respectively. Yes N d ×N d The diagonal matrix of scattered intensity, N d The number of evenly divided target domains, N r is the number of receiving antennas;

[0085] The above expressions have the following relationship:

[0086]

[0087] Will Substituting into the above formula, we can get:

[0088]

[0089]

[0090] in, is an N d ×N d dimensional matrix and is an N r ×N d dimensional matrix.

[0091] 3. Subspace Optimization Method (SOM)

[0092] The subspace optimization method first performs singular value decomposition on the Green operator GS, which is mainly used to identify and separate important information from secondary or noise information in scattering data.

[0093]

[0094] Where superscript H denotes conjugate transpose, U and V are unitary matrices, and the column vectors of V form a complete subspace;

[0095] Arrange the singular values in order of size: .

[0096] According to the arrangement of singular values, the induced current can be divided into the definite current Jdet and the fuzzy current Jamb:

[0097]

[0098] Bring in ,

[0099]

[0100] Similarly,

[0101] The determined current Jdet is composed of the first L largest singular value corresponding vectors VS, and the fuzzy current Jamb is composed of the remaining Nd-L column vectors VN. L is the regularization parameter used to balance the accuracy and stability of the solution.

[0102] 4. Litov Approximation (RA)

[0103] The Litov approximation transforms the complex phase of the total electric field into and the complex phase of the incident field Introduced, the following expression is obtained:

[0104]

[0105] make , it can be deduced that:

[0106]

[0107] From the above formula, it can be seen that there is a linear relationship between the contrast of the medium target and the complex phase. Compared with other traditional preprocessing imaging methods, the Litov approximation method is more accurate at higher frequencies.

[0108] 5. CNN Reconstruction

[0109] (1) Input data preprocessing

[0110] First, perform singular value decomposition on the Green operator GS of the scattered data: , the singular values are sorted from large to small, the singular vectors VS corresponding to the first L singular values constitute the definite subspace, and the rest constitute the fuzzy subspace VN.

[0111] The deterministic subspace VS is used to estimate the deterministic current Jdet, which is usually achieved by projecting the measured scattered field into the deterministic subspace, namely: , where s is the coefficient obtained by solving the following optimization problem: .

[0112] Combining fuzzy subspace VN and Litov complex phase difference The fuzzy current Jamb is estimated in the following way: , where a is a coefficient obtained by solving the following optimization problem: .

[0113] The final CNN input includes the determined current Jdet, the fuzzy current Jamb and the complex phase difference .

[0114] (2) Network processing converged architecture

[0115] CNN uses a three-channel parallel input and re-fusion mode to determine the current Jdet, fuzzy current Jamb and complex phase difference Effective features are extracted through three convolutional neural networks. The fuzzy current component is connected to a denoising component to filter out secondary information and noise interference. The complex phase difference component is used as a weak correction component to focus on the current frame information. Fusion uses channel splicing, and an attention mechanism adaptively adjusts the proportions of each component. The overall network adopts an encoder-decoder structure, with feature maps reduced at multiple scales and then reconstructed and amplified at multiple scales. Skip connections are used to consider both deep and shallow features.

[0116] (3) Network training output

[0117] The preprocessed data is fed into the CNN. During training, the final output is trained to approximate the reference contrast (electromagnetic scattering intensity). After completing the set number of iterations, the loss function converges. The optimal parameter model is retained and, during testing, the preprocessed data is fed directly to obtain the optimal contrast.

[0118] like Figure 2 As shown in the figure, it is a simulation data effect diagram of the electromagnetic inverse scattering method combining SOM and complex phase of the present invention. It can be seen from the figure that the final inversion imaging result has the same structural contour as the true value, and the edge is clearer, which can ensure better detection characteristics.

[0119] The present invention combines the subspace optimization method and the pre-processing imaging mode of the Litov approximate complex phase difference to guide the CNN to reconstruct the target dielectric constant. The subspace optimization method takes into account the pathological problem of electromagnetic inverse scattering, and ensures the integrity of the medium target information by determining the decomposition of the current and the fuzzy current. The Litov complex phase difference is introduced to consider the relationship between the total electric field and the incident field, and has a more accurate reconstruction effect for high-frequency information. The hybrid strategy of the two ensures the determination of the current-dominant framework while optimizing the fuzzy current part using the complex phase difference, taking into account the target details. A good pre-processing step plays a good guiding role in the training of CNN, so that the starting point of CNN training is the effective information that expresses the electromagnetic characteristics, ensuring the physical characteristics in the training derivation. The idea of lightweight and accurate reconstruction is implemented in the design of the CNN network framework, and the encoding and decoding structure with the best feature extraction effect is used. A three-branch parallel extraction and fusion design is adopted. At the same time, an external denoising network is used to further filter the fuzzy current part, and the complex phase difference is spliced for correction. The final reconstruction effect can well preserve the specific framework of the scatterer, and the edge details are also rich and clear enough.

[0120] The present invention combines the subspace optimization method and the pre-imaging method of the Litov approximation complex phase difference, in this way providing more effective and streamlined information for CNN training while retaining the information integrity and high-frequency details. A lightweight network architecture with three parallel branches. The network realizes the differentiated extraction and decentralized adaptive fusion of input data, and the external denoising network filters the redundant parts, and overall tries to use the most streamlined structure to achieve the required functions. A complete method and system combining preprocessing with CNN. Combining the chimeric traditional pre-imaging with the neural network provides more effective information for CNN, enhances the physical concepts in CNN derivation, and helps to streamline the network architecture.

[0121] Information Completeness: This method combines subspace optimization with Litov complex phase difference to more comprehensively utilize information in the electromagnetic field. SOM analysis identifies and fuzzifies subspaces, providing a preliminary understanding of scatterers, while Litov complex phase difference provides additional information about the relationship between the incident field and the total field. This method combines the advantages of physical and data-driven models, leveraging not only the physical information provided by traditional electromagnetic theory but also using deep learning to uncover complex patterns hidden in the data, resulting in a more complete reconstruction of information.

[0122] Reconstruction Accuracy: The SOM provides a rough estimate of the scatterer frame, while the Litov complex phase difference more accurately describes the relationship between the incident field and the total field, improving reconstruction accuracy when dealing with high-frequency information. The CNN can further refine these estimates, improving overall reconstruction accuracy.

[0123] Real-time imaging and lightweight: Introducing CNN significantly accelerates the reconstruction process. Given a large amount of training data, CNN can better adapt to various complex scattering scenarios. The network structure of this invention also selects the most efficient and streamlined codec architecture for feature extraction, avoiding unnecessary complex mapping and conserving computing resources.

[0124] Example 2

[0125] A device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the electromagnetic inverse scattering method combining SOM and complex phase in embodiment 1, and the processor is configured to execute the program stored in the memory.

[0126] Example 3

[0127] A storage medium stores a computer program, which, when executed by a processor, executes the steps of the electromagnetic inverse scattering method combining SOM and complex phase in embodiment 1.

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. An electromagnetic inverse scattering method combining SOM and complex phase, characterized in that: The following steps are involved: S1. Establish the physical model of the data equation and state equation of electromagnetic inverse scattering; S2. The physical model of electromagnetic inverse scattering is expressed using the method of moments; S3, using subspace optimization method to decompose the induced current into definite current and fuzzy current; S4. Using the complex phase information in the Litov approximation method, a linear relationship between the medium target contrast and the complex phase is obtained; S5. Introduce a CNN network for reconstruction. The method of introducing a CNN network for reconstruction is as follows: 1) Input data preprocessing: The method of input data preprocessing is as follows: First, perform singular value decomposition on the Green operator GS of the scattered data: , the singular values are sorted from large to small, the singular vectors VS corresponding to the first L singular values constitute the definite subspace, and the rest constitute the fuzzy subspace VN; Secondly, the deterministic subspace VS is used to estimate the deterministic current Jdet by projecting the measured scattered field into the deterministic subspace, i.e.: , where the coefficient s is expressed as: ; Again, combining the fuzzy subspace VN and Litov complex phase difference To estimate the fuzzy current Jamb, that is: , where the expression of coefficient a is: ; The input of the final CNN network includes the determined current Jdet, the fuzzy current Jamb and the complex phase difference ; 2) Network processing fusion architecture: Using a three-channel parallel input and re-fusion mode to determine the current Jdet, fuzzy current Jamb and complex phase difference Effective features are extracted through three convolutional neural networks. The fuzzy current component is connected to a denoising component to filter out secondary information and noise interference. The complex phase difference component is used as a weak correction component to determine the current frame information. Fusion adopts a channel splicing method and adaptively adjusts the proportion of each branch component through an attention mechanism. The overall network adopts an encoding and decoding structure, reducing the feature map at multiple scales and then reconstructing and amplifying it at multiple scales. Skip connections are used to take into account both deep and shallow features. 3) Network training output: The preprocessed data is fed into the CNN network. During the training process, the final output is made close to the corresponding reference contrast. After the set number of iterations, the loss function converges and the optimal parameter model is retained. During testing, the preprocessed data is fed into the network to directly obtain the optimal contrast.

2. The electromagnetic inverse scattering method combining SOM and complex phase according to claim 1, characterized in that: The mathematical expression of the data equation in step S1 is as follows: in, for The scattered field, and are domain points and source points respectively, represents the wave number in free space, represents the target domain of the scatterer, represents the Green's function, is the contrast function, express The total electric field.

3. The electromagnetic inverse scattering method combining SOM and complex phase according to claim 2, characterized in that: The mathematical expression of the state equation in step S1 is as follows: in, Represents the incident electric field data.

4. The electromagnetic inverse scattering method combining SOM and complex phase according to claim 3, characterized in that: The physical model of electromagnetic inverse scattering described in step S2 is expressed as follows using the moment method: Wherein, the subscript p represents the incident signal of the p-th transmitting antenna. , , , are the vectorization of the incident electric field, total electric field, induced current and scattered field, respectively. Yes N d ×N d The diagonal matrix of scattered intensity, N d The number of evenly divided target domains, N r is the number of receiving antennas; The above expressions have the following relationship: Will Substitute into the above formula, we get: in, is an N d ×N d dimensional matrix and is an N r ×N d dimensional matrix.

5. The electromagnetic inverse scattering method combining SOM and complex phase according to claim 4, characterized in that: The method of decomposing the induced current into the definite current and the fuzzy current by using the subspace optimization method in step S3 is as follows: Green operator G S Perform singular value decomposition: Where superscript H denotes conjugate transpose, U and V are unitary matrices, and the column vectors of V form a complete subspace; Arrange the singular values in order of size: ; According to the arrangement of singular values, the induced current J ind Divided into determining the current J det and fuzzy current J amb : Substitute the above formula into ,have to: Similarly, , where the current J is determined det The vector V corresponding to the first L largest singular values S Composition, fuzzy current J amb By the remaining N d -L column vectors V N L is the regularization parameter.

6. The electromagnetic inverse scattering method combining SOM and complex phase according to claim 5, characterized in that: The method for obtaining the linear relationship between the medium target contrast and the complex phase by using the complex phase information in the Litov approximation method in step S4 is as follows: The complex phase of the total electric field and the complex phase of the incident field Introduced, the following expression is obtained: make , it is deduced that there is a linear relationship between the medium target contrast and the complex phase as follows: 。 7. A device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the electromagnetic inverse scattering method combining SOM and complex phase according to any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the electromagnetic inverse scattering method combining SOM and complex phase according to any one of claims 1 to 6 are performed.

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