Inverse scattering imaging method and system based on Bayesian compressed sensing and wavelet tree structure

Abstract

The invention relates to the technical field of signal processing and imaging, in particular to an inverse scattering imaging method and system based on Bayesian compressed sensing and a wavelet tree structure. Comprising the following steps: 1) acquiring original scattered field data, and preprocessing the original scattered field data; 2) constructing a wavelet tree structure based on the preprocessed data, and analyzing the wavelet tree structure to obtain prior information; 3) constructing a Bayesian compressed sensing model based on the extracted prior information and scattered field data, and solving the Bayesian compressed sensing model to obtain an estimated value of a discrete wavelet coefficient; and 4) reconstructing and optimizing the image through inverse discrete wavelet transform. According to the method, the sparsity and complexity challenges in the inverse scattering problem are effectively solved by combining the Bayesian compressed sensing and the wavelet tree structure. Rich prior information provided by a wavelet tree structure is utilized, and the accuracy and robustness of a reconstruction result are improved. Meanwhile, through an iterative optimization method, a real solution is gradually approached, and the solving efficiency is further improved.

Description

Technical Field

[0001] The invention relates to the technical field of signal processing and imaging, and in particular to an inverse scattering imaging method and system based on Bayesian compressed sensing and wavelet tree structure. Background Art

[0002] Inverse scatter imaging is of vital importance in many scientific and engineering fields. In the field of radar detection imaging, it can help identify the shape, position and material characteristics of the target, improve the target detection and identification capabilities of the radar system, and is crucial for military defense, aerospace monitoring and other application scenarios; in medical imaging diagnosis, inverse scatter imaging technologies such as ultrasound imaging and microwave imaging can be used to detect abnormal conditions such as lesions and tumors in human internal organs, assisting doctors in early diagnosis and precise treatment of diseases; in geological structure exploration imaging, it helps geologists understand underground stratigraphic structure, mineral distribution and other information, and provides key basis for resource exploration and geological disaster prediction.

[0003] However, inverse scattering imaging faces many severe challenges. On the one hand, the complexity of the scatterer itself greatly increases the difficulty of imaging. The diversity of its shape, material, and internal structure leads to complex and changeable changes in the scattering field, which is difficult to accurately model and analyze. On the other hand, the measurement data is often interfered by noise, which reduces the quality and reliability of the data. At the same time, the measurement data is usually incomplete, that is, the number of measurements is limited, and it is impossible to fully obtain all the information about the scatterer. When faced with these problems, traditional inverse scattering imaging solution methods find it difficult to find an ideal balance between imaging accuracy and computational efficiency, resulting in unsatisfactory imaging results or excessively high computational costs, which cannot meet the needs of practical applications. Summary of the invention

[0004] The main purpose of the present invention is to propose an inverse scattering imaging method and system based on Bayesian compressed sensing and wavelet tree structure, which effectively improves the accuracy of inverse scattering imaging through innovative algorithm design and technical means, while improving computational efficiency, overcoming the shortcomings of existing technologies in processing complex scatterers and limited measurement data, and providing a more reliable and efficient solution for the wide application of inverse scattering imaging technology in various fields.

[0005] The technical solution adopted by the present invention to achieve the above-mentioned purpose is:

[0006] The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure includes the following steps:

[0007] 1) Obtaining raw scattered field data and preprocessing it;

[0008] 2) Construct a wavelet tree structure based on the preprocessed data and analyze it to obtain prior information;

[0009] 3) Based on the extracted prior information and scattered field data, a Bayesian compressed sensing model is constructed and solved to obtain the estimated value of the discrete wavelet coefficients;

[0010] 4) Reconstruct and optimize the image through inverse discrete wavelet transform.

[0011] The step 1) is specifically as follows:

[0012] The original scattered field data are subjected to denoising and filtering in turn.

[0013] The step 2) is specifically as follows:

[0014] The preprocessed data is subjected to discrete wavelet transform to obtain approximate coefficients and detail coefficients, and a wavelet coefficient tree structure is constructed based on the approximate coefficients and detail coefficients. The distribution law and correlation of the coefficients in the tree structure are analyzed to extract prior information.

[0015] The discrete wavelet transform is specifically:

[0016]

[0017] ε=Φθ+ξ

[0018] in, is the scattered field measurement data of the jth incident source, r and r ′ is a variable, S is the number of data, k0 is the wave number, G(r,r ′ ) is Green's function, J j (r ′ ) is an unknown source of comparison, is the mapping matrix, W -1 is the inverse discrete wavelet transform matrix, the intermediate variable I is the identity matrix, G S and G D is the discrete operator of the Green function, χ is the unknown contrast, θ is the wavelet coefficient, ε=E sca -G S χE inc is the equivalent scattered field, is interference information, E inc is the incident field.

[0019] The step 3) is specifically as follows:

[0020] θ=arg{max[p(θ|ε)]}

[0021]

[0022] θ=ω⊙z

[0023]

[0024] α0~Γ(a0,b0)

[0025] α s ~Γ(c0,d0)

[0026]

[0027] Where p(θ|ε) is the posterior distribution of θ, and ε is modeled as a Gaussian likelihood distribution with precision α0 The spike and slab prior assumption is used for θ, ω represents the state information of the wavelet coefficients, z represents the zero or one indicator of θ, ⊙ represents the Hadamard calculation, represents Bernoulli distribution, Γ represents Gamma distribution, B represents Beta distribution, s represents variable, L represents threshold, and the parameters ω, z, α0, α are estimated by variational inference method. s ,π s ,π s0 ,π s1 , and hyperparameters a0,b0,c0,d0, Finally, an estimate of the discrete wavelet coefficient θ is obtained.

[0028] The step 4) is specifically as follows:

[0029] The optimized wavelet coefficients are applied to the cost function of contrast χ through inverse discrete wavelet transform to obtain the initial contrast χ inverse scattering imaging image. The adaptive contrast enhancement algorithm is used to improve the contrast of the image, and the image smoothing algorithm is used to remove noise artifacts caused by calculation or measurement errors.

[0030] The cost function F(χ) of the contrast χ is specifically:

[0031]

[0032] in, and η s is the normalization coefficient, j represents the number of the incident source, and n represents the number of the optimization iteration.

[0033] The inverse scattering imaging system based on Bayesian compressed sensing and wavelet tree structure includes:

[0034] A scattered field data acquisition module is used to acquire raw scattered field data and pre-process it;

[0035] The wavelet tree structure building module is used to build the wavelet tree structure based on the preprocessed data and analyze it to obtain prior information;

[0036] A Bayesian compressed sensing model building module is used to build a Bayesian compressed sensing model based on the extracted prior information and scattered field data, and solve it to obtain the estimated value of the discrete wavelet coefficient;

[0037] The image reconstruction module is used to reconstruct and optimize the image through inverse discrete wavelet transform.

[0038] The present invention has the following beneficial effects and advantages:

[0039] 1. Significantly improve imaging accuracy: The sparsity constraints introduced by Bayesian compressed sensing theory and the rich prior information provided by the wavelet tree structure can more accurately reconstruct the image details of the scatterer, effectively reduce the errors caused by the complexity of the scatterer and the noise and incompleteness of the measurement data, and make the imaging results closer to the real scatterer structure.

[0040] 2. Significantly improve computational efficiency: The Bayesian compressed sensing method utilizes the sparsity characteristics to effectively reduce the computational complexity in the solution process and avoid large-scale matrix operations. At the same time, the optimization algorithm can converge quickly in the solution process, significantly shortening the calculation time, so that imaging results can be obtained more quickly in practical applications.

[0041] 3. Wide application adaptability: The method and system of the present invention can be flexibly adjusted and optimized according to the needs of different fields (such as radar detection, medical imaging, geological exploration, etc.). By selecting appropriate parameters and algorithms, it can adapt to various types of scatterer imaging tasks and has strong versatility and scalability.

[0042] 4. Enhanced robustness: When faced with varying degrees of noise interference and measurement data uncertainty, the probabilistic framework of Bayesian compressed sensing and the prior information of the wavelet tree structure can provide a certain degree of fault tolerance, keeping the imaging results relatively stable and reliable, and improving the robustness of the system in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A detailed flow chart of an inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure in an embodiment of the present invention;

[0044] Figure 2 Schematic diagram of the tree structure of wavelet coefficients. DETAILED DESCRIPTION

[0045] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0046] An inverse scattering imaging method and system based on Bayesian compressed sensing and wavelet tree structure aims to accurately reconstruct the image of unknown scatterers from the measured scattering field data. It is widely used in many fields such as radar detection imaging, medical imaging diagnosis, geological structure exploration imaging, etc. Figure 1 As shown, the specific steps are:

[0047] 1. Data preprocessing steps

[0048] The measured scattered field data is received using professional measurement equipment, which has specific measurement principles and parameter settings according to different application scenarios (such as radar, medical imaging equipment, geological exploration instruments, etc.).

[0049] The acquired raw scattered field data is subjected to comprehensive preprocessing operations. First, advanced denoising algorithms are used to remove noise components in the data, such as threshold denoising methods based on wavelet transform, which effectively suppress noise by thresholding the wavelet coefficients while retaining the key features of the data. Secondly, filtering techniques are used to further optimize the data quality, such as using appropriate low-pass, high-pass or band-pass filters to remove unnecessary frequency components according to the frequency characteristics of the scattered field data and highlight information related to scatterer imaging.

[0050] 2. Bayesian Compressed Sensing Modeling Stage

[0051] Based on the Bayesian compressed sensing theory, the mathematical model of inverse scattering imaging is carefully constructed. The imaging characteristics of the scatterer (such as reflectivity, dielectric constant distribution, etc.) are taken as unknown variables, and the complex relationship between the measured data and the unknown variables is fully considered.

[0052] By cleverly introducing sparsity constraints and assuming that the scatterer has sparsity in a certain transform domain (such as wavelet domain) based on prior knowledge of its characteristics, the posterior probability distribution model of the unknown variables is established by using the measured data and combining the Bayesian inference framework, thus providing a solid theoretical basis for finding the optimal solution to the unknown variables.

[0053] 3. Wavelet tree structure sparse coding process

[0054] like Figure 2 As shown in the figure, the discrete wavelet transform (DWT) is used to efficiently decompose the unknown variables and convert them into approximate coefficients and detail coefficients. In the decomposition process, the appropriate wavelet basis function (such as Daubechies wavelet basis, Haar wavelet basis, etc.) is selected, and the appropriate decomposition level is determined according to the characteristics and requirements of scatterer imaging to retain as much detail information as possible, which is crucial for accurately describing the fine structure of the scatterer.

[0055] The tree structure of wavelet coefficients is constructed, and the intrinsic connection of wavelet coefficients at different scales and spatial positions is utilized to form a rich prior information network by establishing parent-child relationship, brother relationship, etc. For example, in the tree structure, the coefficients of the higher layers can be regarded as the parent nodes of the coefficients of the lower layers. This hierarchical relationship reflects the correlation of data at different scales, providing more constraints and guidance for subsequent imaging solutions.

[0056] 4. Solution and reconstruction

[0057] Based on the carefully constructed Bayesian compressed sensing model and wavelet tree structure sparse coding, advanced optimization algorithms are used to solve the optimal solution of unknown variables. For example, conjugate gradient method and variational inference algorithm can be used. These algorithms can effectively search for the optimal solution under complex probability models and constraints.

[0058] After obtaining the optimal wavelet coefficients, the inverse discrete wavelet transform (IDWT) is used to accurately restore them to the imaging characteristics of the scatterer, completing the solution process of inverse scattering imaging. In the inverse transformation process, the accurate mapping of the wavelet coefficients to the original imaging space is ensured, so as to obtain high-quality and accurate scatterer images.

[0059] The system architecture of the present invention is:

[0060] 1. Data preprocessing module

[0061] Equipped with a data interface compatible with the measurement equipment, it can accurately receive scattered field data in different formats and sources.

[0062] It has built-in multiple denoising and filtering algorithms, which can automatically select or manually adjust algorithm parameters according to the characteristics of the data and user needs, perform real-time preprocessing of data, and output high-quality preprocessed data.

[0063] 2. Modeling module

[0064] The mathematical model and algorithm library related to Bayesian compressed sensing theory is stored, and the mathematical model of inverse scattering imaging is automatically constructed according to the input measurement data and system preset parameters.

[0065] It has model verification and optimization functions, can check the rationality of the constructed model, and fine-tune the model according to actual data to ensure the accuracy and applicability of the model.

[0066] 3. Sparse Coding Module

[0067] It integrates multiple wavelet transform algorithms, supports the selection of different wavelet basis functions and decomposition levels, and efficiently performs discrete wavelet transform operations based on the input unknown variable data to generate accurate approximate coefficients and detail coefficients.

[0068] It has the function of building and managing the tree structure of wavelet coefficients. It can automatically generate the tree structure according to the relationship between the coefficients, and update and maintain the structural information in real time, providing reliable prior information for subsequent calculations.

[0069] 4. Solving and Reconstruction Module

[0070] It integrates a variety of advanced optimization algorithms, and can automatically select or allow the user to specify the optimization algorithm according to the characteristics of the model and the data scale to solve the Bayesian compressed sensing model and obtain the optimal wavelet coefficients.

[0071] The inverse discrete wavelet transform algorithm is used to accurately convert the solved wavelet coefficients into the imaging characteristics of the scatterer, generate high-quality scatterer images, and provide image post-processing functions such as contrast adjustment and image smoothing to meet the needs of different application scenarios.

[0072] Example

[0073] 1. Data collection and preparation

[0074] According to specific application requirements (such as target detection in radar imaging, organ detection in medical ultrasound imaging, stratum exploration in geological radar imaging, etc.), select appropriate measurement equipment and collect scattered field data according to the equipment's operating procedures. Ensure that the parameter settings during the acquisition process (such as emission frequency, sampling rate, measurement angle, etc.) meet the imaging requirements and obtain high-quality original scattered field data. Transfer the collected data to the data preprocessing module for format conversion and preliminary inspection to ensure the integrity and accuracy of the data.

[0075] 2. Wavelet tree structure construction and analysis

[0076] In the wavelet tree structure construction step, appropriate wavelet basis functions and decomposition levels are selected according to the expected resolution and detail requirements of scatterer imaging. For example, for medical imaging applications that require high-resolution imaging, a wavelet basis with a higher vanishing moment (such as the Daubechies wavelet basis) and more decomposition levels may be selected; while for larger-scale structural imaging in geological exploration, a relatively simple wavelet basis (such as the Haar wavelet basis) and an appropriate decomposition level may be selected. The preprocessed data is subjected to a discrete wavelet transform to obtain approximate coefficients and detail coefficients, and a wavelet coefficient tree structure is constructed. The distribution law and correlation of the coefficients in the tree structure are analyzed, and prior information is extracted, such as the energy distribution of the coefficients, the dependency between levels, etc., to provide a basis for subsequent Bayesian compressed sensing modeling. The technical route is to transform the data equation of the inverse scattering problem, r∈S, is redefined using the wavelet basis as:

[0077] ε=Φθ+ξ(1)

[0078] Used to solve the wavelet coefficient θ of the contrast source. In the above formula, is the scattering field measurement data of the jth incident source, k0 is the wave number, G(r,r ′ ) is Green's function, J j (r ′ ) is an unknown source of comparison, is the mapping matrix, W -1 is the inverse discrete wavelet transform matrix, I is the identity matrix, G S and G S is the discrete operator of the Green function, χ is the unknown contrast, ε=E sca -G S χE inc is the equivalent scattered field, is interference information, E inc is the incident field.

[0079] 3. Bayesian Compressed Sensing Modeling and Solution

[0080] Based on the extracted prior information and measurement data, the prior probability distribution model of the unknown variables is determined in the Bayesian compressed sensing modeling stage. For example, assuming that the wavelet coefficients obey Gaussian distribution or Laplace distribution with different parameters at different scales, the distribution parameters are reasonably estimated based on the data characteristics and prior knowledge. Using the Bayesian formula, combined with the likelihood function of the measured data and the prior distribution of the unknown variables, a posterior probability distribution model is constructed. A suitable optimization algorithm (such as the variational inference algorithm) is used to solve the maximum or expected value of the posterior distribution to obtain the estimated value of the unknown variable, that is, the optimized wavelet coefficient. The mathematical expression of the model established based on the Bayesian compressed sensing method is as follows:

[0081] θ=arg{max[p(θ|ε)]}(2)

[0082]

[0083] θ=ω⊙z

[0084]

[0085] α0~Γ(a0,b0)

[0086] α s ~Γ(c0,d0)

[0087]

[0088] where p(θ|ε) is the posterior distribution of θ and ζ is modeled as a Gaussian likelihood distribution with precision α0 In order to make full use of the wavelet tree structure, the “spike and slab” prior assumption is used for θ, ω represents the state information of the wavelet coefficient, z represents the zero or one indicator of θ, ⊙ represents the Hadamard calculation, represents Bernoulli distribution, Γ represents Gamma distribution, and B represents Beta distribution. By using the variational inference method, the parameters ω, z, α0, α in formula (3) are estimated. s ,π s ,π s0 ,π s1 , and hyperparameters a0,b0,c0,d0, Finally, an estimate of the discrete wavelet coefficient θ is obtained.

[0089] 4. Image reconstruction and post-processing

[0090] The optimized wavelet coefficients are applied to the cost function of contrast χ through inverse discrete wavelet transform, that is,

[0091]

[0092] The initial contrast χ inverse scattering imaging image is obtained by optimization method, where and η s is the normalization coefficient, j represents the number of the incident source, and n represents the number of the optimization iteration. Image processing technology is used, such as the adaptive contrast enhancement algorithm to improve the contrast of the image, so that the scatterer structure in the imaging result is clearer and more discernible; the image smoothing algorithm is used to remove noise artifacts caused by calculation or measurement errors to improve image quality. According to specific application requirements, further processing such as image segmentation and feature extraction can also be performed to provide richer information for subsequent analysis and decision-making.

Claims

1. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure is characterized by: The following steps are involved: 1) Obtaining raw scattered field data and preprocessing it; 2) Construct a wavelet tree structure based on the preprocessed data and analyze it to obtain prior information; 3) Based on the extracted prior information and scattered field data, a Bayesian compressed sensing model is constructed and solved to obtain the estimated value of the discrete wavelet coefficients; 4) Reconstruct and optimize the image through inverse discrete wavelet transform.

2. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure according to claim 1 is characterized in that: The step 1) is specifically as follows: The original scattered field data are subjected to denoising and filtering processes in turn.

3. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure according to claim 1, characterized in that: The step 2) is specifically as follows: The preprocessed data is subjected to discrete wavelet transform to obtain approximate coefficients and detail coefficients, and a wavelet coefficient tree structure is constructed based on the approximate coefficients and detail coefficients. The distribution law and correlation of the coefficients in the tree structure are analyzed to extract prior information.

4. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure according to claim 3 is characterized in that: The discrete wavelet transform is specifically: in, is the scattered field measurement data of the jth incident source, r and r ′ is a variable, S is the number of data, k0 is the wave number, G(r,r ′ ) is the Green function, J j (r ′ ) is an unknown source of comparison, is the mapping matrix, W -1 is the inverse discrete wavelet transform matrix, the intermediate variable I is the identity matrix, G S and G D is the discrete operator of the Green function, χ is the unknown contrast, θ is the wavelet coefficient, ε=E sca -G S χE inc is the equivalent scattered field, is interference information, E inc is the incident field.

5. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure according to claim 1, characterized in that: The step 3) is specifically as follows: Where p(θ|ε) is the posterior distribution of θ, and ε is modeled as a Gaussian likelihood distribution with precision α0 The spike and slab prior assumption is used for θ, ω represents the state information of the wavelet coefficients, z represents the zero or one indicator of θ, ⊙ represents the Hadamard calculation, represents Bernoulli distribution, Γ represents Gamma distribution, B represents Beta distribution, s represents variable, L represents threshold, and the parameters ω, z, α0, α are estimated by variational inference method. s ,π s ,π s0 ,π s1 , and hyperparameters Finally, an estimate of the discrete wavelet coefficient θ is obtained.

6. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure according to claim 1, characterized in that: The step 4) is specifically as follows: The optimized wavelet coefficients are applied to the cost function of contrast χ through inverse discrete wavelet transform to obtain the initial contrast χ inverse scattering imaging image. The adaptive contrast enhancement algorithm is used to improve the contrast of the image, and the image smoothing algorithm is used to remove noise artifacts caused by calculation or measurement errors.

7. The inverse scattering imaging method based on Bayesian compressed sensing and wavelet tree structure according to claim 6, characterized in that: The cost function F(χ) of the contrast χ is specifically: in, and η s is the normalization coefficient, j represents the number of the incident source, and n represents the number of the optimization iteration.

8. The inverse scattering imaging system based on Bayesian compressed sensing and wavelet tree structure is characterized by: include: A scattered field data acquisition module is used to acquire raw scattered field data and pre-process it; The wavelet tree structure building module is used to build the wavelet tree structure based on the preprocessed data and analyze it to obtain prior information; A Bayesian compressed sensing model building module is used to build a Bayesian compressed sensing model based on the extracted prior information and scattered field data, and solve it to obtain the estimated value of the discrete wavelet coefficient; The image reconstruction module is used to reconstruct and optimize the image through inverse discrete wavelet transform.

Images