A virtual focus-based inverse scattering imaging method

Abstract

This invention discloses a virtual focusing-based inverse scattering imaging method, comprising the following steps: arranging multiple transmitting and receiving antennas outside the imaging region, the imaging region containing a non-uniform background and a scattering object to be measured; transmitting a plane wave into the imaging region and acquiring scattered field data; dividing the imaging region into several sub-regions and pre-setting virtual focal points; calculating the synthesized focusing weights; performing beamforming weighting processing on the scattered field data to obtain virtual focused scattered field data, and synthesizing virtual focused incident fields corresponding to each virtual focal point; and inverting and reconstructing to obtain the dielectric constant distribution of the scattering object to be measured. This method effectively suppresses wavefront distortion and multiple scattering effects caused by non-uniform backgrounds, significantly reducing the nonlinearity and ill-conditioned nature of the inverse scattering problem. It is particularly suitable for addressing the strong nonlinear challenges faced by inverse scattering imaging under non-uniform backgrounds, providing a stable and reliable numerical linearization method for high-precision imaging under non-uniform backgrounds.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic backscattering imaging technology, and more specifically to a backscattering imaging method based on virtual focusing. Background Technology

[0002] Electromagnetic backscattering imaging, a crucial technique for retrieving the electromagnetic properties of a target object from the scattered field data generated by the interaction between electromagnetic waves and the target, is widely used in microwave remote sensing, medical imaging, and nondestructive testing. However, the imaging accuracy of this technique has long been limited by the inherent strong nonlinearity and ill-conditioned nature of the inverse scattering problem. In many complex practical applications (such as through-wall imaging, biomedical diagnostics, and underground exploration), the scattering object is typically embedded in a non-uniform background medium. Under these complex conditions, deep coupling occurs between the electromagnetic wave, the scattering object, and the surrounding background medium, further exacerbating the physical nonlinearity of the inverse scattering problem and making accurate imaging even more difficult.

[0003] To address the aforementioned challenges, existing inverse scattering imaging strategies are mainly divided into two categories: algorithm-driven and physics-driven.

[0004] The first type of algorithm-driven methods (such as the traditional distortion Born iteration method, contrast source inversion method, subspace optimization method, etc.) focus on the design of pure mathematical inversion algorithms. In terms of the incident field form, conventional plane waves are usually used to irradiate the target. Since the electromagnetic waves are not constrained at the physical level, when encountering strong scatterers with non-uniform backgrounds, they often face severe multiple scattering interference, are very easy to get trapped in local optima, and the reconstruction accuracy drops significantly.

[0005] The second category of physics-driven methods aims to improve the conditions of the inverse scattering problem from a physical perspective. These methods achieve spatial separation and focusing by actively modulating the incident or scattered field using hardware devices (such as superlenses, parabolic reflectors, or phased array antennas). By confining the effect of electromagnetic waves to a specific local sub-region, this method can effectively improve the behavior of discrete inverse scattering operators, suppress multiple scattering at the physical level, and thus alleviate nonlinear problems.

[0006] However, existing physical focusing strategies still face two major technical limitations in practical applications: First, when faced with complex non-uniform backgrounds, the background medium can cause severe wavefront distortion, leading to focus shift and energy dissipation at the originally set physical focus point, resulting in a sharp decline or even failure of the focusing performance of the physical hardware; Second, achieving physical focusing requires additional complex hardware architectures (such as phased array systems requiring a large number of phase shifters or specially designed reflective lenses), which not only significantly increases the design complexity and manufacturing cost of the system, but also increases the difficulty of system calibration, making it difficult to apply on a large scale. Summary of the Invention

[0007] To address the issues of aggravated multiple scattering caused by non-uniform backgrounds and reliance on complex hardware for physical focusing in the prior art, this invention provides a virtual focusing-based inverse scattering imaging method. This method eliminates the dependence on complex phased array hardware and specially designed reflective lenses for physical focusing, while effectively suppressing wavefront distortion and multiple scattering effects caused by non-uniform backgrounds. It significantly reduces the nonlinearity and ill-conditioned nature of the inverse scattering problem, making it particularly suitable for solving the strong nonlinear challenges faced by inverse scattering imaging under non-uniform backgrounds. This provides a stable and reliable numerical linearization method for high-precision imaging under non-uniform backgrounds.

[0008] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a backscattering imaging method based on virtual focusing, comprising the following steps: S1. Multiple transmitting antennas and multiple receiving antennas are arranged outside the imaging area. The imaging area includes a non-uniform background and a scattering object to be measured disposed therein. Plane waves are transmitted into the imaging area through the multiple transmitting antennas, and scattered field data are collected through the multiple receiving antennas. S2. Divide the imaging area into several sub-regions, and preset virtual focus points in each sub-region; S3. For each virtual focal point, the composite focusing weight required for each transmitting antenna to focus on the virtual focal point is calculated using the non-uniform background Green's function of the imaging region. S4. The scattered field data is subjected to beamforming weighting processing using the synthetic focusing weight to obtain virtual focused scattered field data corresponding to each virtual focus point, and virtual focused incident field corresponding to each virtual focus point is synthesized. S5. Based on the virtual focused scattering field data and the virtual focused incident field, perform inversion reconstruction to obtain the dielectric constant distribution of the scattering body under test.

[0009] Unlike traditional physical-driven methods that rely on phased array hardware to focus the incident field, this invention collects scattered field data under plane wave illumination by deploying conventional transmitting and receiving antennas. In the data post-processing stage, it uses the Green's function of the non-uniform background to calculate the synthetic focusing weight and applies beamforming weights to the scattered field data, synthesizing equivalent virtual focused incident and virtual focused scattered fields in a purely numerical manner. This avoids the problems of physical focusing point shift and energy dissipation caused by wavefront distortion due to non-uniform background, and eliminates the need for complex hardware devices such as phase shifters, superlenses, or reflecting lenses, reducing system complexity, hardware cost, and calibration difficulty. At the same time, by numerically constraining the effect of electromagnetic waves to the local sub-regions where each virtual focus point is located, it effectively suppresses multiple scattering effects outside the target area, reduces the nonlinearity and ill-conditioned nature of the inverse scattering problem, and improves the feasibility and reconstruction accuracy of inverse scattering imaging under non-uniform backgrounds.

[0010] The method of this invention eliminates the dependence on complex phased array hardware and special reflective lenses and other physical focusing equipment. At the same time, it effectively suppresses wavefront distortion and multiple scattering effects caused by non-uniform backgrounds, and significantly reduces the nonlinearity and ill-conditioned nature of the inverse scattering problem. It is especially suitable for solving the strong nonlinear challenges faced by inverse scattering imaging under non-uniform backgrounds, and provides a stable and reliable numerical linearization method for high-precision imaging under non-uniform backgrounds.

[0011] Preferably, in step S3, the synthesized focusing weight is in complex form, generated by combining the phase compensation weight and the amplitude compensation weight, and its complex form is expressed as follows: , in, Indicates the first m The transmitting antenna corresponds to the first... p The composite focus weights in complex form of a preset virtual focus point, This indicates the corresponding magnitude compensation weight. This indicates the corresponding phase compensation weight. m =1,…, M , M This represents the total number of transmitting antennas.

[0012] This invention achieves precise dual calibration of amplitude and phase of each transmitting antenna signal during beamforming by constructing the composite focusing weight as a complex number combining phase compensation weight and amplitude compensation weight. The phase compensation weight is used to correct the wavefront phase distortion caused by the spatial variation of the refractive index of the medium when electromagnetic waves propagate in a non-uniform background, while the amplitude compensation weight is used to suppress energy diffusion caused by the sidelobe level after beamforming. The combination of the two enables the weighted composite field to form an equivalent focusing effect with highly concentrated energy at the preset virtual focus point, while reducing the field strength in the non-focused area. This enhances the signal-to-noise ratio of local sub-region scattering information in inverse scattering inversion and provides a physical linearization scheme for further improving imaging quality.

[0013] As a further preferred embodiment, the phase compensation weight is calculated based on the phase conjugate principle, and the calculation formula is as follows: , Where ∠(·) represents the phase extraction operator, Indicates the first m Each transmitting antenna at the virtual focal point The corresponding non-uniform background Green's function at that location, Represents the position vector of the virtual focal point. Indicates the first m The position vector of each transmitting antenna j It is the imaginary unit.

[0014] This invention utilizes the phase conjugation principle to calculate phase compensation weights, by extracting the first... m Each transmitting antenna is positioned at a preset virtual focal point. The phase angle of the Green's function of the non-uniform background is inverted, and the amount of compensation for the phase delay accumulated when the electromagnetic wave emitted by the transmitting antenna propagates along the non-uniform background to the virtual focal point is accurately calculated. This enables the phases of each transmitting antenna at the virtual focal point to be superimposed in phase, accurately corrects the phase disturbance of the non-uniform background on the wavefront, and avoids the focus shift and coherent cancellation caused by the change of the refractive index of the medium in traditional hardware focusing under non-uniform background. This provides an accurate phase reference for subsequent amplitude compensation and beamforming.

[0015] As a further preferred embodiment, the amplitude compensation weight is obtained by optimization using the least squares beamforming method, specifically as follows: For a preset virtual focal point, a target field vector is defined where energy is concentrated. The optimization objective is to approximate this target field vector with the weighted composite field of the total field generated by each transmitting antenna under a non-uniform background and the weights. A least-squares objective function with a regularization term is constructed, and the optimal weight vector is obtained by solving it. The optimal weight vector is calculated according to the following formula: , in, W p For each transmitting antenna corresponding to the first p The weight vector of a preset virtual focal point, W p = [ w 1,p , … , w m,p , … , w M,p ]; This represents the field matrix generated by each transmitting antenna at various locations in the imaging region when only a non-uniform background exists. d p The target field vector is where energy is concentrated at the preset virtual focal point. β For regularization parameters, I Let be the identity matrix, (·) H Indicates conjugate transpose; Extract the weight vector W p The absolute values ​​of each element are used as the amplitude compensation weights for the corresponding transmitting antennas. .

[0016] This invention solves for the amplitude compensation weights using the least squares beamforming method, based on the field matrix generated by each transmitting antenna against a non-uniform background. With weight vector W p The weighted composite field approximates the target field vector with energy concentrated at a preset virtual focal point. d p To optimize the objective, a regularization parameter is introduced. β Suppressing the ill-conditioned nature of noise amplification and matrix inversion, the optimal weight vector is obtained by solving the problem. W p The absolute value of each element in the equation represents the amplitude compensation weight for the corresponding transmitting antenna. This optimization process further modulates the radiation amplitude of each transmitting antenna based on the coherent superposition achieved by phase compensation, maximizing the ratio of the peak energy to the sidelobe level of the synthesized field at the focal point. This effectively suppresses the residual field strength in the non-focused region and significantly improves the spatial resolution of the virtual focused field. At the same time, the introduction of the regularization term ensures the numerical stability of the amplitude weight solution under low signal-to-noise ratio conditions.

[0017] Preferably, in steps S3 to S5, the calculation of the synthetic focusing weight and the inversion reconstruction employ an adaptive dynamic compensation mechanism. Specifically, in each iteration, the synthetic focusing weight is updated using the current background contrast, and the virtual focused incident field and virtual focused scattered field are resynthesized. This invention constructs a dynamic compensation mechanism that adaptively adjusts the synthetic focusing weight as the inversion iteration progresses by recalculating the synthetic focusing weight and resynthesizing the virtual focused incident field and virtual focused scattered field using the currently updated background contrast in each iteration. Since the initial non-uniform background Green's function is calculated based on prior background parameters, and the deviation between the real background and the prior background, as well as the presence of the scattering body under test, will affect the actual wavefront propagation characteristics, this dynamic mechanism ensures that the virtual focusing weight is continuously updated as the background contrast is continuously corrected during the iteration process. This ensures that the virtual focused field in each iteration always adapts to the currently updated medium state, thereby effectively suppressing the nonlinear error introduced by the coupling between the unknown background components and the scattering body, and improving the convergence speed and accuracy of the iterative inversion.

[0018] As a further preferred embodiment, the adaptive dynamic compensation mechanism includes the following steps: S31. Initialize contrast distribution: Use the known contrast of the non-uniform background as the initial background contrast, and initialize the contrast of the scattering body to be measured to 0. S32, Iterative Background Update: In each iteration, based on the currently updated background contrast, the non-uniform background Green's function and the virtual focused incident field are recalculated; S33. Adaptive weight update: Based on the updated non-uniform background Green's function, recalculate the synthetic focusing weights of each preset virtual focus point corresponding to each transmitting antenna; and use the updated synthetic focusing weights to resynthesize the virtual focusing incident field and virtual focusing scattered field of the current iteration. S34. Iterative convergence judgment: The contrast increment of the scatterer obtained in this iteration is superimposed on the background contrast to complete the background update, and the next iteration is entered until the upper limit of the number of iterations or the convergence condition is reached, and the final scatterer reconstruction result is output.

[0019] This invention embeds an adaptive dynamic compensation mechanism into a nonlinear iterative inversion framework. By initializing the non-uniform background contrast and setting the contrast of the scattering object to zero, in each iteration, the non-uniform background Green's function under background contrast update is recalculated with the virtual focusing incident field, the composite focusing weight is recalculated, and the virtual focusing incident field and virtual focusing scattering field are recombined. Finally, the scattering object contrast increment is superimposed on the background contrast to complete the background update. This process enables the gradual correction of the background medium and the dynamic adjustment of the virtual focusing weight to form a synergistic evolution relationship. Each update of the background contrast is immediately reflected in the virtual focusing field of the next iteration. The improvement of the virtual focusing field quality enhances the inversion accuracy of the scattering object contrast increment. The two alternately advance until convergence, thereby achieving deep coupling between physical focusing and iterative inversion in a non-uniform background. This effectively overcomes the defect of traditional methods where a fixed incident field cannot adapt to changes in background parameters, and significantly improves the reconstruction stability and imaging quality under strong scattering conditions.

[0020] Preferably, in step S2, each sub-region is a gridded region of equal size, and each virtual focal point is set at the geometric center of its respective sub-region. This ensures uniform coverage of the imaging area by the virtual focal field, allowing all scatterers within each sub-region to receive focused illumination of equal intensity. This avoids insufficient or excessive focusing in some areas due to uneven focal point distribution. Simultaneously, the selection of the geometric center minimizes the average propagation distance between the focal point and each location within the sub-region, which helps reduce wavefront distortion and energy attenuation at the edges of the sub-region. This provides spatially balanced incident field conditions for local inversion of each sub-region, thereby ensuring the uniformity and consistency of the reconstruction results across the entire imaging area.

[0021] Preferably, the inversion reconstruction in S5 employs an iterative optimization algorithm. This invention uses an iterative optimization algorithm as the inversion reconstruction framework, taking virtual focused scattering field data and virtual focused incident field as algorithm inputs. Utilizing the characteristics of suppressed multiple scattering effects and reduced nonlinearity in the focused data, the iterative optimization algorithm can search for the optimal solution in a more favorable solution space. This avoids the problem of traditional iterative algorithms under plane wave illumination getting trapped in local extrema due to severe nonlinearity, thus achieving higher reconstruction accuracy with the same number of iterations, or requiring fewer iterations to achieve the same reconstruction accuracy. This effectively improves the computational efficiency and reconstruction quality of quantitative inverse scattering imaging against non-uniform backgrounds.

[0022] Preferably, the non-uniform background Green's function is a known Green's function obtained through pre-measurement or numerical calculation. This invention uses a known non-uniform background Green's function obtained through pre-measurement or numerical calculation as the physical basis for the forward propagation model in virtual focus weight calculation and iterative inversion. The electromagnetic parameter information of the background medium is explicitly introduced into the imaging algorithm in the form of a Green's function, ensuring that subsequent virtual focus weight calculation and inversion reconstruction are based on an accurate background propagation model. This avoids wavefront calculation errors caused by using free-space Green's functions or simplified background models. Furthermore, the pre-obtained method eliminates the need to repeatedly calculate the background Green's function during online imaging; correction calculations are only required during iterations based on background contrast updates, effectively controlling the amount of online computation and balancing imaging accuracy and computational efficiency.

[0023] Compared with the prior art, the present invention has the following advantages: (1) This invention calculates beamforming weights through numerical post-processing and synthesizes equivalent virtual focused incident field and virtual focused scattered field in a purely numerical manner, which can accurately correct wavefront distortion caused when electromagnetic waves penetrate non-uniform backgrounds. It does not require expensive hardware such as complex phased array antennas, superlenses or reflecting lenses. Virtual focusing can be achieved based on conventional transmitting and receiving antennas, which significantly reduces the hardware complexity and imaging cost of the system.

[0024] (2) Furthermore, this invention proposes a dual calibration mechanism that combines phase compensation weights and amplitude compensation weights for beamforming. The phase compensation weights are solved using the Green's function of the non-uniform background based on the principle of phase conjugation, accurately correcting wavefront phase distortion in complex non-uniform backgrounds and ensuring coherent superposition of signals from each transmitting antenna at a preset virtual focal point. The amplitude compensation weights are solved using a least-squares beamforming optimization method, effectively suppressing the energy diffusion of sidelobe levels. The synergistic effect of phase compensation and amplitude compensation achieves high-quality synthesis of the virtual focal field.

[0025] (3) Furthermore, this invention embeds the virtual focusing strategy into the nonlinear iterative inversion framework, constructing an adaptive dynamic compensation mechanism. In each iteration, the synthesized focusing weights are dynamically corrected based on the updated background contrast, and the virtual focused incident field and virtual focused scattered field are resynthesized, ensuring that the virtual focused field in each iteration always adapts to the currently updated medium state. This completely solves the problem of wavefront distortion and energy diffusion that easily occur in the focused field in a non-uniform background, and significantly improves the iterative convergence stability and noise robustness of strong scatterer imaging in low signal-to-noise ratio environments. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of a typical system configuration for the inverse scattering problem under a non-uniform background, as shown in the embodiment. Figure 2This is a schematic diagram illustrating the principle of synthesizing a virtual focused incident field based on plane waves against a non-uniform background in the embodiment. Figure 3 This is a schematic diagram comparing the reconstruction results of the method of the present invention with those of the traditional plane wave inversion method; Figure 4 This is a comparison of the root mean square error iterative convergence curves of the embodiment and the traditional plane wave inversion method during the reconstruction process. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0028] The method of this invention employs a microwave imaging system, which includes multiple transmitting antennas and multiple receiving antennas, all uniformly distributed around the imaging region. The antennas operate in single-frequency mode; the transmitting antennas emit plane waves, and the receiving antennas acquire the scattered field data. A typical system configuration diagram for inverse scattering under non-uniform backgrounds is shown in the embodiment. Figure 1 As shown, the imaging region 5 includes a non-uniform background 3 and a scattering object 4 embedded therein, which are uniformly arranged on the outer observation boundary. M One transmitting antenna and N There are 36 receiving antennas 2. In this embodiment, there are 36 transmitting antennas 1 and 36 receiving antennas 2, and the imaging area 5 is divided into multiple equally sized gridded sub-regions 6.

[0029] Based on the microwave imaging system described above, this embodiment provides a virtual focusing-based inverse scattering imaging method, which includes the following steps.

[0030] S1. Multiple transmitting antennas and multiple receiving antennas are arranged outside the imaging region. The imaging region includes a non-uniform background and a scattering object to be measured placed within it. M Each transmitting antenna sequentially emits plane waves into the imaging region. The electromagnetic waves interact with the non-uniform background and the scattering object under test within the imaging region to form a scattered field. N Each receiving antenna receives the scattered field signal and acquires the scattered field data.

[0031] S2. Divide the imaging area into multiple equally sized gridded sub-regions, and preset the geometric center of each sub-region as a virtual focal point to ensure uniform coverage of the imaging area by the virtual focal field, so that the scattering objects under test in each sub-region can obtain balanced focused illumination. The number and size of the sub-regions are set according to the imaging resolution requirements and the effective focal area size of the focused incident field.

[0032] S3. For each virtual focal point, use the non-uniform background Green's function of the imaging region to calculate the synthetic focusing weight required for each transmitting antenna to focus on the virtual focal point.

[0033] The schematic diagram of the principle of synthesizing a virtual focused incident field based on plane waves against a non-uniform background in the embodiment is shown below. Figure 2 As shown, this invention synthesizes an equivalent virtual focused incident field numerically by applying beamforming weights to conventional plane wave measurement data during the data post-processing stage. Unlike traditional methods that rely on hardware phase shifters for physical focusing, the virtual focusing of this invention is entirely performed at the algorithm level: the synthetic focusing weights of each transmitting antenna are calculated using a non-uniform background Green's function, and the scattered field data under the original plane wave illumination is weighted. Mathematically, the plane wave incident field is equivalently converted into a virtual focused incident field corresponding to each virtual focal point, while the corresponding scattered field data is converted into virtual focused scattered field data. Through beamforming weighting, the plane wave illumination data, originally scattered throughout space, is equivalently converted into focused field data constrained within a local sub-region, thus achieving spatial focusing of the incident field without any hardware modifications.

[0034] The composite focusing weight is in complex form and is generated by combining the phase compensation weight and the amplitude compensation weight. Its complex form is expressed as follows: , in, Indicates the first m The transmitting antenna corresponds to the first... p The composite focus weights in complex form of a preset virtual focus point, This indicates the corresponding magnitude compensation weight. This indicates the corresponding phase compensation weight. m =1,…, M , M This represents the total number of transmitting antennas.

[0035] The phase compensation weight is calculated based on the phase conjugation principle, and the calculation formula is as follows: , Where ∠(·) represents the phase extraction operator, Indicates the first m Each transmitting antenna at the virtual focal point The corresponding non-uniform background Green's function at that location, Represents the position vector of the virtual focal point. Indicates the first m The position vector of each transmitting antenna jThe unit is the imaginary number. By extracting and inverting the phase angle of the non-uniform background Green's function at the virtual focal point of the transmitting antenna, the compensation amount for the phase delay accumulated when the electromagnetic wave transmitted by the transmitting antenna propagates along the non-uniform background to the virtual focal point is accurately calculated, so that the phases of each transmitting antenna at the virtual focal point are superimposed in phase, thus correcting the phase disturbance of the wavefront caused by the non-uniform background.

[0036] The amplitude compensation weights are optimized using the least squares beamforming method. Specifically, for a preset virtual focal point, a target field vector with energy concentrated at that focal point is defined. The optimization objective is to approximate the target field vector with the weighted composite field of the total field generated by each transmitting antenna under a non-uniform background and the weights. A least squares objective function with a regularization term is constructed, and the optimal weight vector is obtained by solving this function. In this embodiment, the target field vector... d p Let the vector be a column vector that is 1 only at the preset virtual focal point and 0 at all other positions. The optimal weight vector is calculated according to the following formula: , in, W p For each transmitting antenna corresponding to the first p The weight vector of a preset virtual focal point, W p = [ w 1,p , … , w m,p , … , w M,p ]; This represents the field matrix generated by each transmitting antenna at various locations in the imaging region when only a non-uniform background exists. d p The target field vector is where energy is concentrated at the preset virtual focal point. β For regularization parameters, I Let be the identity matrix, (·) H This represents the conjugate transpose. Extract the weight vector. W p The absolute values ​​of each element are used as the amplitude compensation weights for the corresponding transmitting antennas. This optimization process further modulates the radiation amplitude of each transmitting antenna based on the coherent superposition achieved by phase compensation, so as to maximize the ratio of the peak energy of the composite field to the sidelobe level at the focal point, effectively suppressing the residual field strength in the non-focused region.

[0037] S4. Use the composite focusing weight to perform beamforming weighting on the scattered field data to obtain virtual focused scattered field data corresponding to each virtual focus point, and synthesize the virtual focused incident field corresponding to each virtual focus point.

[0038] By applying synthetic focusing weights to the original scattered field data matrix, the plane wave incident field is mathematically equivalently transformed into a focused incident field, and the corresponding scattered field data is transformed into virtual focused scattered field data. Through beamforming weighting, the plane wave illumination data, which was originally scattered throughout space, is equivalently transformed into focused field data constrained within a local sub-region.

[0039] S5. Based on the virtual focused scattering field data and the virtual focused incident field, perform inversion reconstruction to obtain the dielectric constant distribution of the scattering body under test.

[0040] The inversion reconstruction uses an iterative optimization algorithm (such as the distortion Born iterative method), taking the virtual focused scattering field data and the virtual focused incident field as algorithm inputs. Taking advantage of the characteristics that the multiple scattering effect of the focused data is suppressed and the degree of nonlinearity is reduced, the dielectric constant distribution of the scattering body under test is iteratively reconstructed.

[0041] In steps S3 to S5, the calculation and inversion reconstruction of the synthetic focusing weights employ an adaptive dynamic compensation mechanism. This invention embeds a virtual focusing strategy into a nonlinear iterative inversion framework, constructing an adaptive dynamic compensation mechanism. Specifically, in each iteration, the synthetic focusing weights are updated using the current background contrast, and the virtual focusing incident field and virtual focusing scattered field are resynthesized.

[0042] The adaptive dynamic compensation mechanism includes the following steps: S31. Initialize contrast distribution: Use the known contrast of the non-uniform background as the initial background contrast, and initialize the contrast of the scattering body to be measured to 0. S32, Iterative Background Update: In each iteration, based on the currently updated background contrast, the non-uniform background Green's function and the virtual focused incident field are recalculated; S33. Adaptive weight update: Based on the updated non-uniform background Green's function, recalculate the synthetic focusing weights of each preset virtual focus point corresponding to each transmitting antenna; and use the updated synthetic focusing weights to resynthesize the virtual focusing incident field and virtual focusing scattered field of the current iteration. S34. Iterative convergence judgment: The contrast increment of the scatterer obtained in this iteration is superimposed on the background contrast to complete the background update, and the next iteration is entered until the upper limit of the number of iterations or the convergence condition is reached, and the final scatterer reconstruction result is output.

[0043] This process enables the gradual correction of the background medium and the dynamic adjustment of the virtual focusing weight to form a synergistic evolution relationship. Each update of the background contrast is reflected in the virtual focusing field of the next iteration. The improvement of the quality of the virtual focusing field enhances the inversion accuracy of the contrast increment of the scatterer. The two alternately advance until convergence.

[0044] The non-uniform background Green's function is a known Green's function obtained through pre-measurement or numerical calculation. Using the pre-obtained non-uniform background Green's function as the physical basis for the forward propagation model in virtual focus weight calculation and iterative inversion ensures that subsequent virtual focus weight calculation and inversion reconstruction are based on an accurate background propagation model. This pre-obtaining method eliminates the need for repeated calculation of the background Green's function during online imaging; correction calculations are only required during iterations based on background contrast updates, effectively controlling the amount of online computation.

[0045] In this embodiment, the imaging area is divided into equally sized gridded sub-regions, and each virtual focal point is set at the geometric center of each sub-region. In this embodiment, the size of a single sub-region matches the effective focusing area size of the focusing incident field, and the number of virtual focal points is determined according to the imaging area size and the desired resolution.

[0046] To verify the effectiveness of the method of this invention, an imaging comparison was performed between the method of this invention and the traditional plane wave inversion method. A schematic diagram comparing the reconstruction results of the method of this invention and the traditional plane wave inversion method is shown below. Figure 3 As shown. Figure 3 The sub-image 'a' in the figure represents the true pattern of the scattering object under test and the non-uniform background. Figure 3 The b-sub-image in the image represents the true pattern when only a non-uniform background exists, and is used to verify the cleanliness of the inverted background region. Figure 3 The c-subgraph in the figure represents the reconstruction result obtained by the traditional plane wave inversion method; Figure 3 The d-sub-image in the figure is the reconstruction result obtained by the virtual focusing dynamic inversion method of this invention. Calculations show that it is comparable to the real pattern ( Figure 3 Compared to the sub-image (a) in the traditional plane wave inversion method, the inversion pattern obtained by the traditional plane wave inversion method (a) Figure 3 The root mean square error (RMSE) of the c-sub-image in the traditional method is as high as 1.521. Under strong scattering and non-uniform background interference, the outline of the scattering object reconstructed by the traditional method is blurred and severely distorted, failing to accurately reflect the true distribution characteristics of the object. In contrast, the inversion pattern obtained by the method of this invention ( Figure 3 The root mean square error of the d-subplot is 0.936. Combined with... Figure 3 As can be seen, the method of this invention not only clearly and accurately reconstructs the position and geometry of the scattering object under test, but also produces a clean background area, effectively suppressing artifact interference caused by complex environments. Furthermore, Figure 4The root mean square error iterative convergence curves for the two methods in the reconstruction process are presented. Figure 4 The horizontal axis represents the number of iterations, and the vertical axis represents the root mean square error. The results show that the error curve of plane wave inversion decreases slowly and is prone to getting trapped in local optima, resulting in a high final error; while the error curve of dynamic focusing inversion using the method of this invention decreases rapidly, not only with fast convergence speed but also achieving an extremely low error level.

[0047] As can be seen from the above embodiments and comparative results, the virtual focusing-based inverse scattering imaging method proposed in this invention effectively reduces the nonlinearity and ill-conditioned nature of the inverse scattering problem by combining numerical post-processing synthetic focusing weight calculation with an adaptive dynamic iteration mechanism, thus significantly improving imaging accuracy against non-uniform backgrounds. This method does not rely on complex hardware such as phased array antennas or specially designed reflective lenses; it only requires conventional transmitting and receiving antennas to achieve equivalent virtual focusing. It boasts outstanding technical advantages such as low hardware cost, low system complexity, low calibration difficulty, and strong convergence stability.

[0048] The above embodiments are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A backscattering imaging method based on virtual focusing, characterized in that, Includes the following steps: S1. Multiple transmitting antennas and multiple receiving antennas are arranged outside the imaging area. The imaging area includes a non-uniform background and a scattering object to be measured disposed therein. Plane waves are transmitted into the imaging area through the multiple transmitting antennas, and scattered field data are collected through the multiple receiving antennas. S2. Divide the imaging area into several sub-regions, and preset virtual focus points in each sub-region; S3. For each virtual focal point, the composite focusing weight required for each transmitting antenna to focus on the virtual focal point is calculated using the non-uniform background Green's function of the imaging region. S4. The scattered field data is subjected to beamforming weighting processing using the synthetic focusing weight to obtain virtual focused scattered field data corresponding to each virtual focus point, and virtual focused incident field corresponding to each virtual focus point is synthesized. S5. Based on the virtual focused scattering field data and the virtual focused incident field, perform inversion reconstruction to obtain the dielectric constant distribution of the scattering body under test.

2. The inverse scattering imaging method based on virtual focusing according to claim 1, characterized in that, In step S3, the synthesized focusing weight is in complex form and is generated by combining the phase compensation weight and the amplitude compensation weight. Its complex form is expressed as follows: ， in, Indicates the first m The transmitting antenna corresponds to the first... p The composite focus weights in complex form of a preset virtual focus point, This indicates the corresponding magnitude compensation weight. This indicates the corresponding phase compensation weight. m =1,…, M , M This represents the total number of transmitting antennas.

3. The inverse scattering imaging method based on virtual focusing according to claim 2, characterized in that, The phase compensation weight is calculated based on the phase conjugation principle, and the calculation formula is as follows: ， Where ∠(·) represents the phase extraction operator, Indicates the first m Each transmitting antenna at the virtual focal point The corresponding non-uniform background Green's function at that location, Represents the position vector of the virtual focal point. Indicates the first m The position vector of each transmitting antenna j It is the imaginary unit.

4. The inverse scattering imaging method based on virtual focusing according to claim 2, characterized in that, The amplitude compensation weights are obtained by optimization using the least squares beamforming method, specifically: For a preset virtual focal point, a target field vector is defined where energy is concentrated. The optimization objective is to approximate this target field vector with the weighted composite field of the total field generated by each transmitting antenna under a non-uniform background and the weights. A least-squares objective function with a regularization term is constructed, and the optimal weight vector is obtained by solving it. The optimal weight vector is calculated according to the following formula: ， in, W p For each transmitting antenna corresponding to the first p The weight vector of a preset virtual focal point, W p = [ w 1,p , … , w m,p , … , w M,p ]; This represents the field matrix generated by each transmitting antenna at various locations in the imaging region when only a non-uniform background exists. d p The target field vector is where energy is concentrated at the preset virtual focal point. β For regularization parameters, I Let be the identity matrix, (·) H Indicates conjugate transpose; Extract the weight vector W p The absolute values ​​of each element are used as the amplitude compensation weights for the corresponding transmitting antennas. .

5. The inverse scattering imaging method based on virtual focusing according to claim 1, characterized in that, In steps S3 to S5, the calculation of the synthetic focusing weight and the inversion reconstruction adopt an adaptive dynamic compensation mechanism. Specifically, in each iteration, the synthetic focusing weight is updated using the current background contrast, and the virtual focusing incident field and virtual focusing scattering field are resynthesized.

6. The inverse scattering imaging method based on virtual focusing according to claim 5, characterized in that, The adaptive dynamic compensation mechanism includes the following steps: S31. Initialize contrast distribution: Use the known contrast of the non-uniform background as the initial background contrast, and initialize the contrast of the scattering body to be measured to 0. S32, Iterative Background Update: In each iteration, based on the currently updated background contrast, the non-uniform background Green's function and the virtual focused incident field are recalculated; S33. Adaptive weight update: Based on the updated non-uniform background Green's function, recalculate the synthetic focusing weights of each preset virtual focus point corresponding to each transmitting antenna; and use the updated synthetic focusing weights to resynthesize the virtual focusing incident field and virtual focusing scattered field of the current iteration. S34. Iterative convergence judgment: The contrast increment of the scatterer obtained in this iteration is superimposed on the background contrast to complete the background update, and the next iteration is entered until the upper limit of the number of iterations or the convergence condition is reached, and the final scatterer reconstruction result is output.

7. The inverse scattering imaging method based on virtual focusing according to claim 1, characterized in that, In S2, each sub-region is a gridded region of equal size, and each virtual focal point is set at the geometric center of each sub-region.

8. The inverse scattering imaging method based on virtual focusing according to claim 1, characterized in that, The inversion reconstruction in S5 employs an iterative optimization algorithm.

9. The inverse scattering imaging method based on virtual focusing according to claim 1, characterized in that, The non-uniform background Green's function is a known Green's function obtained through pre-measurement or numerical calculation.

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