Three-dimensional electromagnetic inverse scattering imaging inversion method, device and system based on non-convex regularization and medium
By adopting the non-convex regularization method in electromagnetic inverse scattering imaging technology, and using Fourier-based extended regularization and L2/3 regularization to construct the optimal model, the problems of nonlinearity and discomfort qualities in electromagnetic inverse scattering imaging are solved, and the clarity of inversion imaging is improved.
Patent Information
- Application Number
- CN202510038237.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-10
- Publication Date
- 2025-05-02
AI Technical Summary
There are nonlinear and unfit qualitative problems in electromagnetic inverse scattering imaging technology, resulting in low clarity of inversion imaging, especially in the case of noise pollution and inaccurate measurements.
The three-dimensional electromagnetic inverse scattering imaging method based on non-convex regularization is adopted, and the optimal model is constructed through the Fourier-based extension regularization shrinkage integral model and L2/3 regularization, and the alternating iterative solution is used to solve the problem by alternating direction multipliers method, and finally the inversion imaging is obtained.
It improves the clarity of inversion imaging, is suitable for electromagnetic inverse scattering inversion reconstruction, can better deal with noise and nonlinear problems and improve image quality.
Smart Images
Figure CN119919586A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to but is not limited to the field of image processing technology, and in particular to a three-dimensional electromagnetic inverse scattering imaging inversion method, device, system and medium based on non-convex regularization. Background Art
[0002] Electromagnetic inverse scattering imaging is a non-invasive imaging method that uses known incident field and scattered field information to invert the shape, position, and constitutive properties (such as dielectric constant and conductivity) of the target object to achieve imaging. This technology is an important branch of the field of electromagnetics and is widely used in medicine, civil, industry, and military fields.
[0003] For the inverse scattering problem, the solution must exist and be unique. Since most of the inverse scattering data are obtained through instrument measurement, there will be noise pollution, measurement instrument errors, inaccurate measurements and other factors in the measurement process, which will lead to unstable measurement data and discontinuous data. Therefore, the inverse scattering problem is ill-posed. In addition, the inverse scattering problem is also nonlinear. This is because the inverse scattering problem involves the relationship between the scattering field and the scatterer parameters. Obviously, this relationship is not linear. The main reason is that there is a multiple scattering effect. There are many scattering particles in the scatterer. When the dielectric constant of the scatterer doubles, the scattering field does not simply double. Secondly, the expensive phase measurement instrument causes the measurement data in the inverse scattering problem to lack phase information. The lack of phase information further deepens the nonlinearity of the problem.
[0004] The nonlinearity and ill-posedness of the inverse scattering problem are the two biggest challenges. The goal is to invert high-quality images from the noisy scattered field data and incident field data. How to solve the nonlinearity and ill-posedness to improve the clarity of the inversion imaging is a problem that the industry has been eager to solve. Summary of the invention
[0005] The following is a summary of the subject matter described in detail herein. This summary is not intended to limit the scope of the claims.
[0006] The embodiments of the present application provide a three-dimensional electromagnetic inverse scattering imaging inversion method, device, system and medium based on non-convex regularization to improve the clarity of inversion imaging.
[0007] In a first aspect, an embodiment of the present application provides a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization, comprising the following steps:
[0008] S100, determining the inversion imaging model based on the shrinkage integral model regularized by Fourier basis expansion;
[0009] In S100, the inversion imaging model is determined based on the shrinkage integral model regularized by Fourier basis expansion, including: the determined shrinkage integral model, whose data equation and state equation are:
[0010]
[0011] in, is the scattered field, is the incident field, I l is a source of comparison, is the integral operator with the dyadic Green's function G as the integral kernel, R(r) is the modified contrast function, β(r) is the auxiliary parameter, χ(r) is the contrast function, D is the region of interest, S is the receiver area, l Representative l Second incidence.
[0012] The full contrast source is expanded using the discrete Fourier basis using the Fourier basis regularization. The specific expression is:
[0013]
[0014] in, is a source of comparison, is the vectorized discrete Fourier basis, IDFT represents the inverse discrete Fourier transform performed by the 3D fast Fourier transform algorithm, is the 3D Fourier coefficient tensor.
[0015] The inversion imaging model is determined based on the shrinkage integral model of Fourier basis expansion regularization. The inversion imaging model is:
[0016]
[0017] in, and The distribution represents the data equation residuals and the state equation residuals, and τ>0 is the weight factor.
[0018] S200, based on the inversion imaging model and L 2 / 3 Regularization constructs the optimal model for inversion imaging;
[0019] In S200, the inversion imaging model and L 2 / 3 Regularization builds an optimization model for inversion imaging, including:
[0020] Based on the inversion imaging model and the L 2 / 3 Regularization constructs a non-convex regularized shrinkage integral model, and uses the non-convex regularized shrinkage integral model as an optimization model for inversion imaging;
[0021] The non-convex regularized shrinkage integral model is
[0022]
[0023] in, Indicates L 2 / 3 Norm.
[0024] S300, obtaining electromagnetic field data to be inverted, inputting the electromagnetic field data to be inverted into the optimization model, and solving the optimization model by alternating iteration using an alternating direction multiplier method to obtain an inverted image.
[0025] In S300, the electromagnetic field data to be inverted is input into the optimization model, and the optimization model is solved by alternating iteration using an alternating direction multiplier method to obtain an inverted image, including:
[0026] S310, initializing the number of iterations, stop criteria, regularization parameter μ, auxiliary parameter β and weight factor τ;
[0027] S320, inputting the electromagnetic field data to be inverted into the optimization model, and converting the optimization model into the following minimization model:
[0028]
[0029]
[0030] S330, expressing the augmented Lagrangian function of the minimization model as
[0031]
[0032] Among them, δ is the quadratic penalty coefficient;
[0033] S340, solving in sequence to obtain the minimum The solution and minimization The solution of and the solution that minimizes R;
[0034] S350, accumulating the number of iterations and the stopping criteria of the current generation, and determining whether the preset maximum number of iterations and the stopping criteria have been reached. If so, executing S360; if not, minimizing The solution is used as the data to be inverted, and S320 is executed;
[0035] S360, outputting the solution that minimizes R as the inverted image.
[0036] In S340, the minimization in the minimization model is obtained by sequentially solving The solution and minimization The solution to and the solution that minimizes R include:
[0037] The minimization model contains parameters according to the following formula The terms of the augmented Lagrangian function are extracted and we get:
[0038]
[0039] Solving using the conjugate gradient method Optimize the subproblem and get Optimize the solution of the subproblem:
[0040]
[0041] Among them, d l,n is the step size of the nth iteration, and is the classic Polak-Ribivère-Polyak CG direction, defined as
[0042] in, is the relative Fourier coefficient exist and The derivative at . The expression form is
[0043]
[0044] According to the exact line search, we get the following minimization problem
[0045]
[0046] use The solution of the optimization subproblem updates the formal variables Its sub-problem is
[0047]
[0048] use The solution of the optimization subproblem is used to update the modified contrast function Its sub-problem is
[0049]
[0050] Equivalent to
[0051]
[0052] Then get Optimize the solution of the subproblem:
[0053]
[0054] in,
[0055] In a second aspect, an embodiment of the present application further provides a three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization, wherein the three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization comprises:
[0056] The first module determines the inversion imaging model based on the shrinkage integral model regularized by Fourier basis expansion;
[0057] The second module is based on the inversion imaging model and L 2 / 3 Regularization constructs the optimal model for inversion imaging;
[0058] The third module obtains the electromagnetic field data to be inverted, inputs the electromagnetic field data to be inverted into the optimization model, and solves the optimization model by alternating iteration using the alternating direction multiplier method to obtain the inverted imaging.
[0059] In the third aspect, an embodiment of the present application also provides a three-dimensional electromagnetic inverse scattering imaging inversion system based on non-convex regularization, comprising: a collector, a memory, a processor, a display, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization as described in the first aspect.
[0060] In a fourth aspect, an embodiment of the present application further provides a three-dimensional electromagnetic inverse scattering imaging inversion medium based on non-convex regularization, which is a computer-readable storage medium storing computer executable instructions, and the computer executable instructions are used to execute a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization as described in the first aspect.
[0061] The embodiments of the present application include the following beneficial effects: In the embodiments provided in the present application, the inversion imaging model and L 2 / 3 Combined with regularization, the constructed optimization model parameters are more flexible to adjust, and more suitable for electromagnetic inverse scattering inversion reconstruction and inversion imaging clarity. The optimization model can be solved by alternating iteration using the alternating direction multiplier method to obtain the inverted imaging. The present application can improve the clarity of the inversion imaging.
[0062] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or understood by practicing the present application. The purpose and other advantages of the present application can be realized and obtained by the structures specifically pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0063] The accompanying drawings are used to provide further understanding of the technical solution of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present application and do not constitute a limitation on the technical solution of the present application.
[0064] Figure 1 It is a flowchart of a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization provided by an embodiment of the present application;
[0065] Figure 2 It is an inversion comparison diagram of two spheres and a U-shaped structure provided by an embodiment of the present application;
[0066] Figure 3 This is an inversion comparison diagram of a coated cube structure provided by an embodiment of the present application;
[0067] Figure 4 is the total field error Err provided by an embodiment of the present application tot Plotted against the number of iterations;
[0068] Figure 5 is a graph showing the relationship between the structural similarity SSIM and the number of iterations provided by an embodiment of the present application;
[0069] Figure 6 It is a structural diagram of a three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization provided by an embodiment of the present application;
[0070] Figure 7 It is a structural diagram of a three-dimensional electromagnetic inverse scattering imaging inversion system based on non-convex regularization provided by an embodiment of the present application. DETAILED DESCRIPTION
[0071] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.
[0072] It should be noted that, although the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first", "second", etc. in the specification, claims or the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.
[0073] refer to Figure 1 The present application provides a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization, the method comprising the following steps:
[0074] S100, determining the inversion imaging model based on the shrinkage integral model regularized by Fourier basis expansion;
[0075] In S100, the inversion imaging model is determined based on the shrinkage integral model regularized by Fourier basis expansion, including: the determined shrinkage integral model, whose data equation and state equation are:
[0076]
[0077]
[0078]
[0079]
[0080] in, is the scattered field, is the incident field, I l is a source of comparison, is the integral operator with the dyadic Green's function G as the integral kernel, R(r) is the modified contrast function, β(r) is the auxiliary parameter, χ(r) is the contrast function, D is the region of interest, S is the receiver area, l Representative l Second incidence.
[0081] The full contrast source is expanded using the discrete Fourier basis using the Fourier basis regularization. The specific expression is:
[0082]
[0083] in, is a source of comparison, is the vectorized discrete Fourier basis, IDFT represents the inverse discrete Fourier transform performed by the 3D fast Fourier transform algorithm, is the 3D Fourier coefficient tensor.
[0084] The inversion imaging model is determined based on the shrinkage integral model of Fourier basis expansion regularization. The inversion imaging model is:
[0085]
[0086] in, and The distribution represents the data equation residuals and the state equation residuals, and τ>0 is the weight factor.
[0087] S200, based on the inversion imaging model and L 2 / 3 Regularization constructs the optimal model for inversion imaging;
[0088] In S200, the inversion imaging model and L2 / 3 Regularization builds an optimization model for inversion imaging, including:
[0089] Based on the inversion imaging model and the L 2 / 3 Regularization constructs a non-convex regularized shrinkage integral model, and uses the non-convex regularized shrinkage integral model as an optimization model for inversion imaging;
[0090] The non-convex regularized shrinkage integral model is
[0091]
[0092] in, Indicates L 2 / 3 Norm.
[0093] S300, obtaining electromagnetic field data to be inverted, inputting the electromagnetic field data to be inverted into the optimization model, and solving the optimization model by alternating iteration using an alternating direction multiplier method to obtain an inverted image.
[0094] In S300, the electromagnetic field data to be inverted is input into the optimization model, and the optimization model is solved by alternating iteration using an alternating direction multiplier method to obtain an inverted image, including:
[0095] S310, initializing the number of iterations, stop criteria, regularization parameter μ, auxiliary parameter β and weight factor τ;
[0096] S320, inputting the electromagnetic field data to be inverted into the optimization model, and converting the optimization model into the following minimization model:
[0097]
[0098]
[0099] S330, expressing the augmented Lagrangian function of the minimization model as
[0100]
[0101] Among them, δ is the quadratic penalty coefficient;
[0102] S340, solving in sequence to obtain the minimum The solution and minimization The solution and minimization of The solution;
[0103] S350, accumulating the number of iterations and the stopping criteria of the current generation, and determining whether the preset maximum number of iterations and the stopping criteria have been reached. If so, executing S360; if not, minimizing The solution is used as the data to be inverted, and S320 is executed;
[0104] S360, minimize The solution is output as the inverted image.
[0105] In S340, the minimization in the minimization model is obtained by sequentially solving The solution and minimization The solution and minimization of The solution includes:
[0106] The minimization model contains parameters according to the following formula The terms of the augmented Lagrangian function are extracted and we get:
[0107]
[0108] Solving using the conjugate gradient method Optimize the subproblem and get Optimize the solution of the subproblem:
[0109]
[0110] Among them, d l,n is the step size of the nth iteration, and is the classic Polak-Ribivère-Polyak CG direction, defined as
[0111] in, is the relative Fourier coefficient exist and The derivative at . The expression form is
[0112]
[0113] According to the exact line search, we get the following minimization problem
[0114]
[0115] use The solution of the optimization subproblem updates the formal variables Its sub-problem is
[0116]
[0117] use The solution of the optimization subproblem is used to update the modified contrast function Its sub-problem is
[0118]
[0119] Equivalent to
[0120]
[0121] Then get Optimize the solution of the subproblem:
[0122]
[0123] in,
[0124] In the embodiment provided in the present application, the contraction integral equation (CIE) regularized by Fourier bases-expansion (FBE) can effectively maintain the edge information of the image; the inversion imaging model and L 2 / 3 Regularization is combined to construct an optimization model. The optimization model is solved by alternating iteration using the alternating direction multiplier method, and the unconstrained non-convex problem is transformed into an equality constrained problem, which is equivalent to multi-block iterative optimization, thereby solving the inverted imaging. The optimization model constructed in this application and the corresponding solution method can improve the clarity of the inverted imaging.
[0125] Inverting three-dimensional electromagnetic inverse scattering imaging, first initialize the number of iterations, stop criteria, regularization parameter μ, auxiliary parameter β and weight factor τ; then, input the electromagnetic field data to be inverted into the optimization model, and solve the optimization model: each time the solution is completed, the number of iterations of the current generation and the stop criteria are accumulated once, and the steps of solving the minimization model are continued to be iteratively executed until the preset maximum number of iterations and stop criteria are reached, and The solution to the optimization subproblem is output as an inverted image.
[0126] In some embodiments, the maximum number of iterations is preset to 200 times, and the number of iterations of the stopping criterion is preset to k=2.
[0127] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the inverted image, wherein the evaluation index parameters include a total field error Err tot , structural similarity SSIM;
[0128]
[0129]
[0130] in, represents the true relative permittivity distribution, Represents the reconstruction result. θ>0、 and ξ>0 control the relative importance of the three terms, are the brightness, contrast, and structure components, and the SSIM values of the real and imaginary parts are denoted as SSIM-Re and SSIM-Im, respectively.
[0131] In this embodiment, the total field error Err tot , structural similarity SSIM to evaluate the inverted image quality.
[0132] The following is a classic electromagnetic inverse scattering imaging experiment based on the model proposed in the embodiment of the present application, and verifies the efficiency and feasibility of the non-convex regularized shrinkage integral model (NRCIE). First, the electromagnetic field data to be inverted is obtained, and the electromagnetic field data to be inverted is input into the optimization model to obtain the inverted imaging.
[0133] In some embodiments, the inversion object is selected as two spheres and a U-shaped structure. In some embodiments, the coated cube structure is used as the target object, and the raw data is recorded as After the original data is determined, load the original data to be inverted.
[0134] It should be noted that all target objects are lossy synthetic data and 20% Gaussian noise is added as the inversion target used in the experiment. The purpose of this embodiment is to image the image based on the inversion of electromagnetic field data.
[0135] like Figure 2 As shown, Figure 2 Inversion diagrams of two spheres and a U-shaped lossy structure under different algorithms. Each group of diagrams corresponds to a different algorithm. (a) is the inversion diagram of the FBE-CIE-I method; (b) is the inversion diagram of the FBE-WCIE method; (c) is the inversion diagram of the L 1 / 2 -FBE-WCIE method inversion diagram; (d) is L 2 / 3 -Inversion image of the FBE-WCIE method. It can be seen that the image inverted by the method provided in this paper is better in quality than the image inverted by other methods, and the detail effect is better. The image inverted by the FBE-CIE-I method has too many shadows; the image inverted by the FBE-WCIE method is relatively blurred, which shows the importance of method selection in the experiment; L 1 / 2 - Although the FBE-WCIE method has good results, it does not handle details well.
[0136] like Figure 3 As shown, Figure 3The inversion diagrams of the lossy structure of the coated cube under different algorithms. Figure (a) is the inversion diagram of the FBE-CIE-I method, Figure (b) is the inversion diagram of the FBE-WCIE method, and Figure (c) is the inversion diagram of the L 1 / 2 -FBE-WCIE method inversion diagram, Figure (d) is L 2 / 3 -FBE-WCIE method inversion diagram, the four methods in the reconstruction diagram have good results and have certain application value. Through image analysis, it can be seen that the inversion method provided in this paper is better than the FBE-CIE-I method, FBE-WCIE method and L 1 / 2 -FBE-WCIE method is more efficient.
[0137] like Figure 4 As shown, Figure 4 is the plotted total field error Err tot The relationship curve between the number of iterations, Figure (a) is the total field error Err of Example 1 tot The relationship between the number of iterations and the total field error Err of Example 2 is shown in Figure (b). tot The relationship between and the number of iterations. Figure 4 It can be seen that the total field error Err of the inversion method provided by this application tot The total field error is smaller than that of other methods, and the total field error decreases faster.
[0138] like Figure 5 As shown, Figure 5 Figure 1 is a graph showing the relationship between the structural similarity SSIM and the number of iterations. Figure (a) is a graph showing the relationship between the structural similarity SSIM and the number of iterations for Example 1, and Figure (b) is a graph showing the relationship between the structural similarity SSIM and the number of iterations for Example 2. Figure 5 It can be seen that, whether it is SSIM-Re or SSIM-Im, the inversion method provided in this paper has achieved excellent results, with larger structural similarity values and faster rising curves.
[0139] Referring to Table 1, by comparing the experimental results of all the methods in Table 1, it can be found that the L 2 / 3 -The various indicators of the FBE-WCIE method have been significantly improved, and the comprehensive experimental results are better.
[0140] Table 1: Experimental results of each method;
[0141]
[0142] The above two experiments verify that the NRCIE model provided in this application can be significantly improved. Compared with the existing FBE-CIE-I method and FBE-WCIE method, the NRCIE model has obvious numerical superiority.
[0143] In addition, refer to Figure 6 In some embodiments, a three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization is further provided. A three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization includes:
[0144] The first module determines the inversion imaging model based on the shrinkage integral model regularized by Fourier basis expansion;
[0145] The second module is based on the inversion imaging model and L 2 / 3 Regularization constructs the optimal model for inversion imaging;
[0146] The third module obtains the electromagnetic field data to be inverted, inputs the electromagnetic field data to be inverted into the optimization model, and solves the optimization model by alternating iteration using the alternating direction multiplier method to obtain the inverted imaging.
[0147] The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
[0148] In addition, refer to Figure 7 An embodiment of the present application also provides a three-dimensional electromagnetic inverse scattering imaging inversion system based on non-convex regularization, the system comprising: a collector 11, a memory 12, a processor 13, a display 14, and a computer program stored in the memory 12 and executable on the processor 13.
[0149] The processor 13 and the memory 12 may be connected via a bus or other means.
[0150] The inversion data required to implement a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization in the above-mentioned embodiment is extracted through the collector 11, and the non-transient software program and instructions are stored in the memory 12. When executed by the processor 13, a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization in the above-mentioned embodiment is executed, and finally imaging visualization is realized through the display 14.
[0151] In addition, an embodiment of the present application also provides a three-dimensional electromagnetic inverse scattering imaging inversion medium based on non-convex regularization, and the computer-readable storage medium stores computer executable instructions, and the computer executable instructions are executed by a processor or controller, for example, by a processor in the above-mentioned electronic device embodiment, so that the above-mentioned processor can execute a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization in the above-mentioned embodiment.
[0152] It will be appreciated by those skilled in the art that all or some of the steps and systems in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. Certain physical components may be implemented in software form by a processor (such as a central processing unit, a digital signal processor, or a microprocessor), or may be implemented as hardware or an application-specific integrated circuit. Such software may be distributed on computer-readable media, including computer storage media (non-temporary) and communication media (temporary). According to the knowledge in the art, computer storage media refers to all media used to store volatile and non-volatile information, such as RAM, ROM, flash memory, CD-ROM, DVD, magnetic tape, etc., and includes removable and non-removable forms. In addition, the communication medium generally contains computer-readable instructions and other information, which are transmitted via a carrier or transmission mechanism. The above is a specific description of the preferred implementation of the present application, but the present application is not limited to the above-mentioned implementation modes. Those skilled in the art may also make various equivalent modifications or substitutions without violating the spirit of the present application, and these equivalent modifications or substitutions are all included in the scope defined by the claims of the present application.
Claims
1. A three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization, characterized in that: The following steps are involved: S100, determining the inversion imaging model based on the shrinkage integral model regularized by Fourier basis expansion; S200, based on the inversion imaging model and L 2 / 3 Regularization constructs the optimal model for inversion imaging; S300, obtaining electromagnetic field data to be inverted, inputting the electromagnetic field data to be inverted into the optimization model, and solving the optimization model by alternating iteration using an alternating direction multiplier method to obtain an inverted image.
2. The three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization according to claim 1, characterized in that: In S100, the inversion imaging model is determined based on the shrinkage integral model regularized by Fourier basis expansion, including: The data equation and state equation of the determined shrinkage integral model are: in, is the scattered field, is the incident field, I l is a source of comparison, is the integral operator with the dyadic Green's function G as the integral kernel, R(r) is the modified contrast function, β(r) is the auxiliary parameter, χ(r) is the contrast function, D is the region of interest, S is the receiver area, l Representative l Second incidence. The full contrast source is expanded using the discrete Fourier basis using the Fourier basis regularization. The specific expression is: in, is a source of comparison, is the vectorized discrete Fourier basis, are Fourier coefficients, IDFT represents the inverse discrete Fourier transform performed by the 3D fast Fourier transform algorithm, is the 3D Fourier coefficient tensor. The inversion imaging model is determined based on the shrinkage integral model of Fourier basis expansion regularization. The inversion imaging model is: in, and The distribution represents the data equation residuals and the state equation residuals, and τ>0 is the weight factor.
3. The three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization according to claim 2, characterized in that: In S200, based on the inversion imaging model and L 2 / 3 Regularization builds an optimization model for inversion imaging, including: Based on the inversion imaging model and the L 2 / 3 Regularization constructs a non-convex regularized shrinkage integral model, and uses the non-convex regularized shrinkage integral model as an optimization model for inversion imaging; The non-convex regularized shrinkage integral model is in, Indicates L 2 / 3 Norm.
4. The three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization according to claim 3, characterized in that: In S300, the data to be inverted is input into the optimization model, and the optimization model is solved by alternating iteration using an alternating direction multiplier method to obtain an inverted image, including: S310, initializing the number of iterations, stop criteria, regularization parameter μ, auxiliary parameter β and weight factor τ; S320, inputting the data to be inverted into the optimization model, and converting the optimization model into the following minimization model: S330, expressing the augmented Lagrangian function of the minimization model as Among them, δ is the quadratic penalty coefficient; S340, solving in sequence to obtain the minimum The solution and minimization The solution and minimization of The solution; S350, accumulating the number of iterations and the stopping criteria of the current generation, and determining whether the preset maximum number of iterations and the stopping criteria have been reached. If so, executing S360; if not, minimizing The solution is used as the data to be inverted, and S320 is executed; S360, minimize The solution is output as the inverted image. In S340, the minimization in the minimization model is obtained by sequentially solving The solution and minimization The solution and minimization of The solution includes: The minimization model contains parameters according to the following formula The terms of the augmented Lagrangian function are extracted and we get: Solving using the conjugate gradient method Optimize the subproblem and get Optimize the solution of the subproblem: Among them, d l,n is the step size of the nth iteration, and is the classic Polak-Ribivère-Polyak CG direction, defined as in, is the relative Fourier coefficient exist and The derivative at . The expression form is According to the exact line search, we get the following minimization problem use The solution of the optimization subproblem updates the formal variables Its sub-problem is use The solution of the optimization subproblem is used to update the modified contrast function Its sub-problem is Equivalent to Then get Optimize the solution of the subproblem: in, 5. A three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization, characterized in that: The three-dimensional electromagnetic inverse scattering imaging inversion device based on non-convex regularization comprises: The first module determines the inversion imaging model based on the shrinkage integral model regularized by Fourier basis expansion; The second module is based on the inversion imaging model and L 2 / 3 Regularization constructs the optimal model for inversion imaging; The third module obtains the electromagnetic field data to be inverted, inputs the electromagnetic field data to be inverted into the optimization model, and solves the optimization model by alternating iteration using the alternating direction multiplier method to obtain the inverted imaging.
6. A three-dimensional electromagnetic inverse scattering imaging inversion system based on non-convex regularization, comprising: A collector, a memory, a processor, a display and a computer program stored in the memory and executable on the processor, characterized in that when the processor executes the computer program, a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization as described in any one of claims 1 to 4 is implemented.
7. A three-dimensional electromagnetic inverse scattering imaging inversion medium based on non-convex regularization, which is a computer-readable storage medium storing computer executable instructions, and the computer executable instructions are used to execute a three-dimensional electromagnetic inverse scattering imaging inversion method based on non-convex regularization as described in any one of claims 1 to 4.