A microwave imaging method fusing born iterations and compressed sensing

Abstract

This invention relates to a microwave imaging method integrating Born iteration and compressed sensing, comprising: establishing a two-dimensional electromagnetic inverse scattering integral equation model, discretizing the imaging region, setting iteration and prior parameters, and initializing the contrast and total field as background values ​​and incident fields, respectively; based on the total field of the previous iteration, constructing linearized scattering equations for multiple incident angles, defining single-view inversion as an independent task, and integrating them into a multi-task set sharing sparse priors; employing the MT-BCS algorithm to jointly solve the observation equations using shared hyperparameters, and outputting the updated contrast distribution; solving the state equation based on the new contrast to complete the total field update; outputting the imaging result if the convergence condition or the maximum number of iterations is met; otherwise, continuing iteration. This invention applies joint sparsity constraints through a multi-task joint inference mechanism, mining the geometric structure consistency of multi-view data, and overcoming the shortcomings of traditional single-task methods such as low signal-to-noise ratio, low reconstruction accuracy when measurement data is limited, and severe artifacts.

Description

Technical Field

[0001] This invention belongs to the field of microwave imaging and electromagnetic inverse scattering technology, specifically relating to a microwave imaging method that integrates Born iteration and compressed sensing. Background Technology

[0002] Microwave imaging, as a non-invasive detection technology, reconstructs the distribution of target physical parameters by retrieving scattered field data, and is widely used in fields such as industrial non-destructive testing, underground resource exploration, biomedical breast cancer screening, and public safety security inspection. The electromagnetic inverse scattering problem is the core of microwave imaging systems; the inversion accuracy, convergence speed, and noise robustness of its solution algorithm directly determine the practical application value of the imaging system.

[0003] The electromagnetic inverse scattering problem is inherently a highly nonlinear and severely ill-posed problem. Existing mainstream solution algorithms have obvious drawbacks: deterministic iterative algorithms are prone to getting trapped in local minima; intelligent optimization algorithms have high computational costs and slow convergence speeds; deep learning methods depend on the size and quality of the training dataset, limiting their generalization ability; conventional compressed sensing methods are based on linear approximation models, ignore the structural correlation of multi-view observation data, adopt an independent processing mode, and have poor reconstruction quality in low signal-to-noise ratio environments. Summary of the Invention

[0004] The technical problem of this invention is: to address the shortcomings of existing microwave imaging algorithms in nonlinear inverse scattering solutions, multi-view data utilization, computational efficiency, and robustness, this invention proposes a hybrid microwave imaging method combining Born iteration and compressed sensing, which balances imaging accuracy, computational efficiency, and noise resistance robustness, and solves the problems of high nonlinear complexity, low signal-to-noise ratio, and poor reconstruction accuracy under undersampling conditions in imaging strong scatterers.

[0005] The purpose of this invention is to solve the above-mentioned problems by decoupling the nonlinear inverse scattering problem through the Born iteration strategy and mining the correlation of multi-view data structures using a multi-task Bayesian learning framework. A microwave imaging method integrating Born iteration and compressed sensing is proposed, comprising the following steps: S1: Construct and initialize the imaging model, establish a two-dimensional electromagnetic inverse scattering integral equation model, discretize the imaging area into grid pixels, set the maximum number of iterations, convergence threshold and prior parameters, initialize the contrast distribution of the target to be reconstructed to the background value, and initialize the total field distribution in the imaging area to the incident field distribution. S2: Construct multi-task linear observation equations, enter the iterative loop, and based on the internal total field estimate of the previous iteration, construct linearized scattering data equations for multiple emission sources with different incident angles respectively. Define the single-view inversion problem as an independent task and integrate all view inversion tasks into a multi-task set with shared sparse priors. S3: Multi-task joint inversion and contrast update. The multi-task Bayesian compressed sensing MT-BCS algorithm is used to share the same set of hyperparameters controlling sparsity among all views, jointly solve the multi-task linear observation equation, and output the updated target contrast distribution. S4: Update the internal total field distribution and solve the state equation based on the updated target contrast distribution to complete the update of the internal total field distribution of the imaging region; S5: Iterative convergence judgment, determine whether the preset convergence condition is met or the maximum number of iterations is reached; if met, output the final contrast distribution image; if not met, take the total field distribution obtained in step S4 as a known quantity and return to step S2 to continue iterating.

[0006] Furthermore, step S1 includes: performing non-uniform grid discretization processing on the imaging area, using a finer grid for areas where the target may exist, and using a sparser grid for the background area, in order to balance imaging accuracy and computational efficiency.

[0007] Preferably, step S2 includes discretizing the integral equation using the method of moments to construct a multi-task linear observation equation, expressed as: ; In the formula, Indicates the first One perspective, This is the measured scattered field vector from this perspective. Let be the contrast vector to be reconstructed. It is an additive noise vector. The perception matrix is ​​determined by the Green's function of the background medium and the total field distribution of the previous iteration.

[0008] Preferably, step S3 includes the following sub-steps: 1) Establish a probabilistic model: Assume that the contrast vectors of all viewpoints share the same set of hyperparameters, and apply the Gamma distribution prior to the shared hyperparameters and the noise accuracy of each viewpoint; 2) Constructing the objective function: Based on the Bayesian inference framework, a joint marginal likelihood function containing data from all perspectives is constructed; 3) Iterative solution: Maximize the joint marginal likelihood function, and iteratively update the shared hyperparameters and the noise accuracy of each viewpoint through analytical formulas until convergence; 4) Calculate the posterior mean: Based on the converged hyperparameters, calculate the posterior mean of the contrast distribution, which is used as the contrast update value for the current Born iteration step.

[0009] Furthermore, in step S3, the shared hyperparameters are updated during the iterative solution process by aggregating information from all perspectives. The update calculation formula is: ; In the formula, Indicates the corresponding number Shared hyperparameters for each pixel, Indicates the total number of viewpoints. Indicates the first The second iteration The pixel in the first Posterior mean from each perspective Indicates the first The posterior covariance matrix of the nth iteration The diagonal elements quantify the uncertainty of the estimated value of the pixel.

[0010] Preferably, step S3 includes introducing user-defined shape parameters using the Gamma prior distribution. With ratio parameter The adaptive adjustment algorithm for noise estimation accuracy is based on the prior distribution of noise accuracy, which satisfies the following formula: ; In the formula, Indicates the first Noise accuracy at each viewpoint, the and It is used to adjust the shape and scale of the prior distribution, thereby constraining the estimation of noise accuracy during the iteration process and preventing overfitting due to insufficient measurement data or model errors.

[0011] Furthermore, step S3 also includes: introducing an adaptive pruning strategy during the iterative solution process, where the shared hyperparameters corresponding to a certain pixel are adjusted accordingly. When the threshold is exceeded, the pixel is marked as background and its contrast value is fixed at 0, so that it will no longer participate in subsequent iterations and updates, in order to further reduce computational complexity.

[0012] Preferably, in step S4, the internal total field distribution is updated by solving the following state equation: ; In the formula, Indicates the first The total field of the next iteration Indicates the incident field. This indicates the contrast ratio after the update in step S3. ( ) represents the Green's function matrix within the imaging region.

[0013] Preferably, in step S5, the convergence condition includes at least one of the following: 1) The relative rate of change in contrast is lower than the preset threshold; 2) The relative rate of change of the total field is lower than the preset threshold; 3) Reach the preset maximum number of iterations.

[0014] Compared with the prior art, the beneficial effects of the present invention include: 1) The present invention proposes a hybrid microwave imaging method combining Born iteration and compressed sensing. By applying joint sparsity constraints through a multi-task joint inference mechanism, it can explore the geometric structure consistency of multi-view data, overcome the shortcomings of traditional single-task methods such as low signal-to-noise ratio, low reconstruction accuracy when measurement data is limited, and severe artifacts, and improve the imaging quality of complex scattering environments.

[0015] 2) The present invention proposes a hybrid microwave imaging method combining Born iteration and compressed sensing, which incorporates adaptive Gamma prior distribution and analytical Bayesian inference strategy. This method eliminates the need for massive search iterations, significantly reduces computational complexity, and solves the problem of high time consumption in intelligent optimization algorithms.

[0016] 3) The present invention proposes a hybrid microwave imaging method combining Born iteration and compressed sensing. Adaptive parameter adjustment improves the algorithm's tolerance to initial noise estimation errors, breaks through the limitation that the traditional Born approximation is only applicable to weak scatterers, realizes high-precision imaging of high-contrast medium targets, and improves engineering practicality. Attached Figure Description

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] Figure 1 This is a geometric schematic diagram of the microwave backscattering imaging system according to an embodiment of the present invention; Figure 2 This is a contrast distribution diagram of the iterative process of the square scatterer in an embodiment of the present invention; Figure 3 This is a graph showing the changes in reconstruction error and single-step iteration time as a function of the number of iterations in an embodiment of the present invention. Figure 4 This is a schematic diagram of the total field error distribution during the iterative process in an embodiment of the present invention; Figure 5 This is a graph showing the hyperparameter calibration and sensitivity analysis of an embodiment of the present invention; Figure 6 This is a comparison chart of inversion results under different parameter configurations in embodiments of the present invention; Figure 7 This is a graph showing the variation of target reconstruction error with signal-to-noise ratio for different contrast ratios in an embodiment of the present invention. Figure 8 This is a comparison of the imaging effects of the present invention and the traditional linear inversion method BA-CSM on L-shaped scatterers; Figure 9 The figures show the reconstruction error curves of the embodiments of the present invention and the traditional linear inversion method under different signal-to-noise ratios. Figure 10This is a comparison curve of the total reconstruction error under different contrast conditions between the embodiments of the present invention and the traditional linear inversion method; Figure 11 This is a schematic diagram comparing the reconstruction error distribution of the embodiment of the present invention and the global optimization algorithm IMM-PSO under different parameter spaces. Figure 12 This is a schematic diagram of the error curves of the embodiment of the present invention and the global optimization algorithm IMM-PSO under different contrast conditions; Figure 13 This is a schematic diagram illustrating the reconstruction contrast distribution under extreme noise and ideal conditions using the global optimization algorithm IMM-PSO in an embodiment of the present invention. Figure 14 This is a schematic diagram of the contrast distribution for imaging multiple target objects according to an embodiment of the present invention; Figure 15 This is a schematic diagram of the reconstruction error curves under different sparsity in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] like Figure 1 As shown, a microwave imaging method integrating Born iteration and compressed sensing includes the following steps: S1: Construct and initialize the imaging model. Establish a two-dimensional electromagnetic inverse scattering integral equation model, discretize the imaging region into grid pixels, set the maximum number of iterations, convergence threshold, and prior parameters, and initialize the contrast distribution of the target to be reconstructed to the background value, and initialize the total field distribution within the imaging region to the incident field distribution. A geometric schematic diagram of the microwave inverse scattering imaging system is shown below. Figure 1 As shown.

[0021] The imaging region is discretized using a non-uniform grid. A finer grid is used for areas where the target may exist, while a sparser grid is used for the background area, in order to balance imaging accuracy and computational efficiency.

[0022] S2: Construct multi-task linear observation equations, enter the iterative loop, and based on the internal total field estimate of the previous iteration, construct linearized scattering data equations for multiple emission sources with different incident angles. Define the single-view inversion problem as an independent task and integrate all view inversion tasks into a multi-task set with shared sparse priors.

[0023] Step S2 involves discretizing the integral equation using the method of moments to construct a multi-task linear observation equation, expressed as: ; In the formula, Indicates the first One perspective, This is the measured scattered field vector from this perspective. Let be the contrast vector to be reconstructed. It is an additive noise vector. The perception matrix is ​​determined by the Green's function of the background medium and the total field distribution of the previous iteration.

[0024] S3: Multi-task joint inversion and contrast update. The multi-task Bayesian compressed sensing MT-BCS algorithm is adopted, which shares the same set of hyperparameters controlling sparsity among all views, jointly solves the multi-task linear observation equation, and outputs the updated target contrast distribution.

[0025] Step S3 includes the following sub-steps: 1) Establish a probabilistic model: Assume that the contrast vectors of all viewpoints share the same set of hyperparameters, and apply the Gamma distribution prior to the shared hyperparameters and the noise accuracy of each viewpoint; 2) Constructing the objective function: Based on the Bayesian inference framework, a joint marginal likelihood function containing data from all perspectives is constructed; 3) Iterative solution: Maximize the joint marginal likelihood function, and iteratively update the shared hyperparameters and the noise accuracy of each viewpoint through analytical formulas until convergence; 4) Calculate the posterior mean: Based on the converged hyperparameters, calculate the posterior mean of the contrast distribution, which is used as the contrast update value for the current Born iteration step.

[0026] During the iterative solution process, the shared hyperparameters are updated by aggregating information from all perspectives. The update calculation formula is as follows: ; In the formula, Indicates the corresponding number Shared hyperparameters for each pixel, Indicates the total number of viewpoints. Indicates the first The second iteration The pixel in the first Posterior mean from each perspective Indicates the first The posterior covariance matrix of the nth iteration The diagonal elements quantify the uncertainty of the estimated value of the pixel.

[0027] Step S3 includes introducing user-defined shape parameters using the Gamma prior distribution. With ratio parameter The adaptive adjustment algorithm for noise estimation accuracy is based on the prior distribution of noise accuracy, which satisfies the following formula: ; In the formula, Indicates the first Noise accuracy at each viewpoint, the and It is used to adjust the shape and scale of the prior distribution, thereby constraining the estimation of noise accuracy during the iteration process and preventing overfitting due to insufficient measurement data or model errors.

[0028] An adaptive pruning strategy is introduced during the iterative solution process. When the shared hyperparameter α corresponding to a certain pixel is... i When the threshold is exceeded, the pixel is marked as background and its contrast value is fixed at 0, so that it will no longer participate in subsequent iterations and updates, in order to further reduce computational complexity.

[0029] S4: Update the internal total field distribution and solve the state equation based on the updated target contrast distribution to complete the update of the internal total field distribution of the imaging region.

[0030] Step S4, the internal total field distribution is updated by solving the following state equations: ; In the formula, Indicates the first The total field of the next iteration Indicates the incident field. This indicates the contrast ratio after the update in step S3. ( ) represents the Green's function matrix within the imaging region.

[0031] S5: Iterative convergence judgment, determine whether the preset convergence condition is met or the maximum number of iterations is reached; if met, output the final contrast distribution image; if not met, take the total field distribution obtained in step S4 as a known quantity and return to step S2 to continue iterating.

[0032] In step S5, the convergence condition includes at least one of the following: 1) The relative rate of change in contrast is lower than a preset threshold, expressed as: ; In the formula, , The first , The contrast component obtained in the next iteration. This is the preset contrast convergence threshold.

[0033] 2) The relative rate of change of the total field is lower than the preset threshold, expressed as: ; In the formula, , The first , The result of the iteration is the first The total field components from each perspective This is the preset total field convergence threshold.

[0034] 3) Reach the preset maximum number of iterations.

[0035] This invention comprehensively verifies the reconstruction performance, computational efficiency, and environmental adaptability of a microwave imaging method integrating Born iteration and compressed sensing through numerical experiments. Four representative experimental scenarios were designed for comprehensive evaluation in the numerical experiments: 1) Experimental Scenario 1: A square scatterer is selected to verify the convergence behavior of the algorithm. Prior hyperparameters are determined in the C-shaped scatterer scenario for benchmark verification and parameter calibration.

[0036] 2) Experimental Scenario Two: Select a non-central L-shaped scatterer and change the target contrast. The performance of this invention is compared with that of the linear inversion method BA-CSM to verify the algorithm's ability to handle strong scattering effects and to verify its nonlinear processing capabilities.

[0037] 3) Experimental Scenario 3: Select a C-type scatterer, and compare the performance of the present invention with the global optimization algorithm IMM-PSO by changing the target contrast and signal-to-noise ratio (SNR). Verify the stability and computational efficiency advantages of the algorithm under extreme noise, and use it to verify noise robustness and efficiency.

[0038] 4) Experimental Scenario 4: Select a complex scenario containing multiple discrete targets to verify the algorithm's ability to mine multi-view structural correlations and its adaptability to changes in target sparsity, for the verification of multi-target and structural correlations.

[0039] Experimental Scenario 1: Inversion test on a square scatterer, the results are as follows Figure 2 As shown, the complete reconstruction process of the algorithm from initialization to final convergence is illustrated. With each iteration, the algorithm continuously corrects the internal total field using the updated contrast, causing the contrast amplitude of the reconstructed target to steadily increase and gradually approach the true value. In the later stages of iteration, the reconstructed profile stabilizes, and the target boundary becomes clear, verifying the convergence and robustness of the algorithm in handling strong scattering problems.

[0040] like Figure 3As shown, to quantify this convergence process, the total reconstruction error exhibits a significant decreasing trend ( , Furthermore, the external error remained at an extremely low level throughout the entire iteration process. This is thanks to the joint sparsity constraint under the multi-task Bayesian framework, which effectively integrates complementary information from multiple perspectives, greatly suppressing random noise and artifacts in the background region.

[0041] like Figure 4 As shown, at the angle of incidence From this perspective, the total field error steadily improves during the iteration process and eventually converges to an extremely low level.

[0042] like Figure 5 and Figure 6 As shown, a parameter scan of the C-type scatterer was performed to determine the optimal hyperparameter configuration. Experimental results demonstrate that this invention maintains high-precision imaging over a wide parameter range. Finally, the selected... Even under conditions of strong noise and suboptimal parameters, the geometric features of the target are still well recovered, proving that the algorithm of this invention still has excellent engineering applicability without the need for fine parameter tuning.

[0043] Based on this, to verify the consistency of the algorithm under different scattering intensities, three different contrast ratios were selected ( The C-type scatterer was tested: like Figure 7 As shown, the reconstruction error decreases significantly with increasing signal-to-noise ratio and eventually converges to a stable value, verifying the consistency of this invention under different scattering intensities. Even for... The strong scatterer, the total reconstruction error always remains at The level indicates that the method of the present invention effectively overcomes the nonlinear difficulties caused by strong scattering and has good engineering applicability.

[0044] Experimental Scenario 2: To verify the ability of this invention to process strong scatterers, it is compared with the traditional linear inversion method BA-CSM based on the first-order Born approximation.

[0045] like Figure 8 As shown, an L-shaped medium target located off-center in the imaging region was constructed, with the contrast set to [value missing]. At noise levels of 20dB SNR and 10dB, the BA-CSM method failed to correctly reconstruct the target shape, resulting in a severe underestimation of the inversion value, far below the true value of 2.0. In contrast, this invention effectively corrects the nonlinear error caused by multiple scattering through an iterative update strategy. Even under 10dB noise interference, this method can still accurately reconstruct the geometric contour and precise location of the L-shaped target, with the inversion value closely approximating the true value.

[0046] like Figure 9 As shown, for The L-shaped scatterer is used to illustrate the curves of the reconstruction error indices of this invention and BA-CSM as a function of signal-to-noise ratio. It can be seen that the total error curve of this invention is consistently significantly lower than that of BA-CSM.

[0047] like Figure 10 As shown, the reconstruction error of the present invention and the BA-CSM method are compared with the change in contrast. As the contrast increases, the reconstruction error of BA-CSM shows a significant upward trend, confirming the limitations of the Born approximation in processing strong scatterers.

[0048] This method overcomes the limitation of the traditional Born approximation, which is only applicable to weak scatterers, and maintains significant robustness and accuracy when dealing with scatterers with high contrast.

[0049] Experimental Scenario 3: Compare this invention with the classic global optimization algorithm, the Iterative Multi-Scale Particle Swarm Optimization (IMM-PSO).

[0050] like Figure 11 The figure shows a heatmap of the total reconstruction error distribution when imaging a C-type target using two different methods. The horizontal axis corresponds to the contrast ratio. The vertical axis corresponds to the signal-to-noise ratio. dB. The method of this invention maintains extremely high reconstruction accuracy under most parameter combinations, and the total error is always kept at an extremely low level. However, the error of IMM-PSO increases significantly in high contrast or low signal-to-noise ratio regions.

[0051] like Figure 12 and 13 As shown, the performance difference under extreme noise SNR=5dB and ideal environment SNR=50dB was examined in detail. From the error curve, it can be seen that as the contrast increases from 0.5 to 2.0, the error corresponding to the method of this invention increases slightly, but the overall error remains relatively constant. The following; however, the IMM-PSO reconstruction error remained consistently at... In terms of imaging results, regardless of the signal-to-noise ratio and contrast, the present invention can accurately reconstruct the geometry and position of the target. Although slight artifacts appear at low signal-to-noise ratios, the outline of the target body is still clearly discernible. In contrast, although IMM-PSO can roughly locate the target area, it suffers from severe data distortion.

[0052] Experimental Scenario 4: Focus on verifying the adaptability of the algorithm in complex multi-objective scenarios and the impact of sparsity on performance.

[0053] like Figure 14As shown, the image presents a comparison of the imaging reconstructions of multiple scattering targets with different contrasts under a signal-to-noise ratio of 20 dB. The first column shows the true contrast distribution, and the second column shows the reconstruction results of the method of this invention. Even under conditions of strong multiple scattering interference, this invention can still accurately locate all scattering objects and accurately recover the geometry and dielectric parameter distribution of each target, with clear boundaries between targets and no obvious background artifacts.

[0054] like Figure 15 As shown, the trend of reconstruction error with the sparsity S of the scatterer is further analyzed. Regardless of the contrast ratio, the target sparsity decreases with the increase of S, exacerbating the ill-conditioned nature of the inversion problem and leading to a non-linear growth trend in reconstruction error. This result is consistent with the expectations of compressed sensing theory and quantifies the applicability boundary of the algorithm.

[0055] To intuitively evaluate the computational efficiency of the algorithm, the running time of the scatterer imaging experiment mentioned above was recorded and compared with the theoretical computational complexity.

[0056] Table 1 shows Figure 8 The computation time statistics of L-shaped scatterers under different contrast ratios show that, although the Born approximation-compressed sensing method (BA-CSM) has extremely high computational efficiency, the reconstruction results suffer from severe distortion and cannot accurately restore the geometric and dielectric parameter distributions of strongly scattering targets. The method of this invention, by introducing the Born iteration mechanism, successfully achieves high-precision reconstruction of high-contrast targets while moderately increasing computation time, effectively overcoming the nonlinear error defects of traditional linear approximation methods.

[0057] Table 1

[0058] Table 2 provides... Figure 13 The computation time statistics for the C-type scatterer under different signal-to-noise ratios are presented. In terms of computational efficiency, the method of this invention exhibits significant advantages: compared to the globally optimized improved multimodal particle swarm optimization algorithm IMM-PSO, which, as a random search method, requires massive iterations to evaluate the fitness function, resulting in an overall computation time more than 3.5 times that of this invention; while this invention, relying on analytical Bayesian inference and shared sparse priors, significantly reduces computational complexity while ensuring reconstruction accuracy, making it more suitable for engineering real-time imaging scenarios.

[0059] Table 2

[0060] Intelligent optimization algorithms, such as IMM-PSO, have a computational load that directly depends on the square of the total number of grid cells in the imaging region, resulting in extremely high computational costs in large-scale imaging scenarios. In contrast, compressed sensing-based inversion methods fully utilize the sparse priors of the target, and their computational complexity mainly depends on the square of the sparsity. The method of this invention theoretically possesses significant efficiency advantages, and its performance closely matches the actual running time recorded in experiments, fully verifying the advantages of the method in terms of computational efficiency and reconstruction accuracy.

[0061] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A microwave imaging method integrating Born iteration and compressed sensing, characterized in that, Includes the following steps: S1: Construct and initialize the imaging model, establish a two-dimensional electromagnetic inverse scattering integral equation model, discretize the imaging area into grid pixels, set the maximum number of iterations, convergence threshold and prior parameters, initialize the contrast distribution of the target to be reconstructed to the background value, and initialize the total field distribution in the imaging area to the incident field distribution. S2: Construct multi-task linear observation equations, enter the iterative loop, and based on the internal total field estimate of the previous iteration, construct linearized scattering data equations for multiple emission sources with different incident angles respectively. Define the single-view inversion problem as an independent task and integrate all view inversion tasks into a multi-task set with shared sparse priors. S3: Multi-task joint inversion and contrast update. The multi-task Bayesian compressed sensing MT-BCS algorithm is used to share the same set of hyperparameters controlling sparsity among all views, jointly solve the multi-task linear observation equation, and output the updated target contrast distribution. S4: Update the internal total field distribution and solve the state equation based on the updated target contrast distribution to complete the update of the internal total field distribution of the imaging region; S5: Iterative convergence judgment, determine whether the preset convergence condition is met or the maximum number of iterations is reached; if met, output the final contrast distribution image; if not met, take the total field distribution obtained in step S4 as a known quantity and return to step S2 to continue iterating.

2. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, Step S1 includes: performing non-uniform grid discretization processing on the imaging area, using a finer grid for areas where the target may exist, and using a sparser grid for the background area, in order to balance imaging accuracy and computational efficiency.

3. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, Step S2 includes discretizing the integral equation using the method of moments to construct a multi-task linear observation equation, expressed as: ； In the formula, Indicates the first One perspective, This is the measured scattered field vector from this perspective. Let be the contrast vector to be reconstructed. It is an additive noise vector. The perception matrix is ​​determined by the Green's function of the background medium and the total field distribution of the previous iteration.

4. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, Step S3 includes the following sub-steps: 1) Establish a probabilistic model: Assume that the contrast vectors of all viewpoints share the same set of hyperparameters, and apply the Gamma distribution prior to the shared hyperparameters and the noise accuracy of each viewpoint; 2) Constructing the objective function: Based on the Bayesian inference framework, a joint marginal likelihood function containing data from all perspectives is constructed; 3) Iterative solution: Maximize the joint marginal likelihood function, and iteratively update the shared hyperparameters and the noise accuracy of each viewpoint through analytical formulas until convergence; 4) Calculate the posterior mean: Based on the converged hyperparameters, calculate the posterior mean of the contrast distribution, which is used as the contrast update value for the current Born iteration step.

5. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, In step S3, the shared hyperparameters are updated during the iterative solution process by aggregating information from all viewpoints. The update calculation formula is as follows: ； In the formula, Indicates the corresponding number Shared hyperparameters for each pixel, Indicates the total number of viewpoints. Indicates the first The second iteration The pixel in the first Posterior mean from each perspective Indicates the first The posterior covariance matrix of the nth iteration The diagonal elements quantify the uncertainty of the estimated value of the pixel.

6. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, Step S3 includes introducing user-defined shape parameters using the Gamma prior distribution. With ratio parameter The adaptive adjustment algorithm for noise estimation accuracy is based on the prior distribution of noise accuracy, which satisfies the following formula: ； In the formula, Indicates the first Noise accuracy at each viewpoint, the and It is used to adjust the shape and scale of the prior distribution, thereby constraining the estimation of noise accuracy during the iteration process and preventing overfitting due to insufficient measurement data or model errors.

7. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, Step S3 also includes: introducing an adaptive pruning strategy during the iterative solution process, when the shared hyperparameters corresponding to a certain pixel... When the threshold is exceeded, the pixel is marked as background and its contrast value is fixed at 0, so that it will no longer participate in subsequent iterations and updates, in order to further reduce computational complexity.

8. The microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, In step S4, the internal total field distribution is updated by solving the following state equation: ； In the formula, Indicates the first The total field of the next iteration Indicates the incident field. This indicates the contrast ratio after the update in step S3. ( ) represents the Green's function matrix within the imaging region.

9. A microwave imaging method fusing Born iteration and compressed sensing according to claim 1, characterized in that, In step S5, the convergence condition includes at least one of the following: 1) The relative rate of change in contrast is lower than the preset threshold; 2) The relative rate of change of the total field is lower than the preset threshold; 3) Reach the preset maximum number of iterations.

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