A structure-coupled variational bayesian through-the-wall radar building layout reconstruction method
By employing a structurally coupled variational Bayesian method, the problem of insufficient structural continuity in the reconstruction of building layouts using through-wall radar was solved, achieving high-precision extraction of walls and corners and improving the effectiveness of building layout reconstruction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING INST OF TECH
- Filing Date
- 2023-12-19
- Publication Date
- 2026-06-09
Smart Images
Figure CN117786799B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar. Background Technology
[0002] Through-wall radar utilizes the ability of low-frequency electromagnetic waves to penetrate walls, allowing it to perceive the internal situation of unknown buildings. Building layout reconstruction, a key application of through-wall radar, can provide technical support for urban warfare, criminal investigation, and disaster relief by mapping the interiors of unknown buildings. It has significant implications in both military and civilian fields and has attracted widespread research.
[0003] Currently, through-wall radar building layout reconstruction methods can be divided into two categories. The first category is image domain methods, which, under the assumption of a point scattering model, obtain a focused radar image by matching and filtering the radar data with the point spread function of the point scatterers. Traditional target detection and image processing methods are then applied to the radar image to extract key structural information within the building. However, this type of method does not consider the differences between different scatterers (walls, corners, etc.) within the building, making it difficult to interpret the imaging results. The second category is frequency domain methods, which analyze the echo characteristics of typical scatterers within the building and directly estimate the position, shape, and orientation of the scatterers in the echo domain to achieve high-precision reconstruction of the building layout. This type of method mainly extracts different scatterers by establishing a dictionary describing them and using sparse recovery techniques. However, existing methods do not consider the structural continuity of different scatterers themselves, resulting in discrete structural extraction. Summary of the Invention
[0004] To address the aforementioned issues, this invention proposes a structurally coupled variational Bayesian method for reconstructing building layouts using through-wall radar. The signal of complex building structures is modeled as the sum of responses from key structures such as planar walls and corners, and scattering characteristic dictionaries are established for each. Considering prior information from construction practice, the azimuth continuity of walls and the two-dimensional extensibility of corners are represented as a hierarchical probability model. Then, a variational expectation-maximization algorithm is used for Bayesian inference to infer the posterior distributions of variables and hyperparameters. Simultaneously, a generalized approximate message-passing algorithm is integrated to approximate the posterior probabilities in Bayesian inference, avoiding matrix inversion to accelerate the algorithm. Finally, complete extraction of walls and corners is achieved, thus obtaining the building layout.
[0005] The beneficial effects of this invention are as follows:
[0006] This invention is applied to the field of building layout reconstruction using through-wall radar. It uses a Bayesian hierarchical model to describe the structural continuity of walls and corners in two-dimensional space, and performs sparse solution through variational expectation maximization and generalized approximate message passing algorithm. While ensuring the sparsity of the solution, it enhances the continuity of the building structure, which is an effective building layout reconstruction method. Attached Figure Description
[0007] Figure 1 This is a flowchart of the signal processing according to an embodiment of the present invention;
[0008] Figure 2 This is a schematic diagram of the structural coupling in step 2 of the present invention;
[0009] Figure 3 This is a schematic diagram of the simulation scene used in this invention;
[0010] Figure 4 These are simulation results of the present invention compared to existing methods; where (a) is the result of the back projection imaging algorithm, (b) is the wall extracted by the two-step orthogonal matching tracking wall corner extraction method, and (c) is the corner extracted by the two-step orthogonal matching tracking wall corner extraction method.
[0011] Figure 5 The above are simulation results of the method proposed in this invention; where (a) is the wall extracted by the proposed method, (b) is the left corner of the wall extracted by the proposed method, and (c) is the right corner of the wall extracted by the proposed method.
[0012] Figure 6 This is a schematic diagram of the actual test scenario used in this invention;
[0013] Figure 7 These are the measured results of the present invention compared to existing methods; where (a) is the result of the back projection imaging algorithm, (b) is the wall extracted by the two-step orthogonal matching tracking wall corner extraction method, and (c) is the corner extracted by the two-step orthogonal matching tracking wall corner extraction method.
[0014] Figure 8 The figure shows the measured results of the method proposed in this invention; where (a) is the wall extracted by the proposed method, (b) is the left corner of the wall extracted by the proposed method, and (c) is the right corner of the wall extracted by the proposed method. Detailed Implementation
[0015] The purpose of this invention is to overcome the problem of poor continuity in existing building layout reconstruction and to provide a structurally coupled variational Bayesian method for reconstructing building layouts for through-wall radar. Figure 1 This is a signal processing flowchart of an embodiment of the present invention. Figure 1 As shown, the present invention is achieved through the following steps:
[0016] Step 1: Establish a model for the signal received by through-wall radar;
[0017] Modeling the echo, let y(m,n) represent the echo received by the radar antenna at the nth position at the mth frequency, we have
[0018]
[0019] Where P represents the number of scattering units, A p S represents the scattering amplitude of the elementary element. p,m,n This describes the dependence of the scattering primitive on frequency and azimuth, where k is the wavenumber and τ is the azimuth angle. q,n Let υ(m,n) represent the two-way time delay from the nth antenna to the pth scattering element, and let υ(m,n) be complex Gaussian white noise.
[0020] Considering the detection method, there are two main types of scattering elements that play a dominant role within the building: one is the wall parallel to the antenna array, and the other is the dihedral angle formed by two perpendicular walls. Let y w (m,n) represents the wall echo, y c (m,n) represents the echo at the corner, and the formula can be written as follows:
[0021] y(m,n)=y w (m,n)+y c (m,n)+υ(m,n)
[0022] Wall section y w (m,n) is
[0023]
[0024] Where P w G represents the number of walls parallel to the antenna array. p This indicates the number of blocks into which the p-th wall is divided. This represents the amplitude of scattering from the wall block. The signal travels from the nth antenna to the gth wall in the pth wall. p Two-way delay of some walls The dependence of wall scattering on frequency and orientation angle is described as follows:
[0025]
[0026] in This indicates the relationship between the nth antenna and the gth wall in the pth wall. p The direction angle formed by the normals of part of the wall, L w It is the length of each small wall section. This indicates the g-th wall in the p-th wall. p The orientation angle of a portion of the wall is typically 0° for walls parallel to the radar array.
[0027] corner part y c (m,n) can be represented as
[0028]
[0029] Where P c It refers to the number of corners, A p It is the amplitude of the scattering from the corner, τ p,n It is the two-way delay of the signal from the nth antenna to the pth corner, 1 p,n It is an indicator function, and its specific form is as follows:
[0030]
[0031] The dependence of corner scattering on frequency and azimuth is described as follows:
[0032]
[0033] Among them, L c φ represents the length of the corner at that location. p,n This represents the azimuth angle formed by the nth antenna and the pth corner.
[0034] y c (m,n) can be broken down into left and right corners.
[0035] y c (m,n)=y lc (m,n)+y rc (m,n)
[0036] Where y lc (m,n) represents the echo from the left corner of the wall, y rc (m,n) represents the echo from the right corner.
[0037] y(m,n)=y w (m,n)+y lc (m,n)+y rc (m,n)+υ(m,n)
[0038] Stack the signals from the M frequency points received by the antenna at the nth position into an M×1 dimensional vector y. n
[0039]
[0040] The imaging scene is divided into Q = Nx × Nz grids according to the azimuth and range directions. The relationship between the radar echo and the imaging scene can be written as follows:
[0041] y n =W n z+L ns+R n t+υ n
[0042] Among them W n L n and R n All are M×Q dimensional matrices, and the (m,q)th element of each matrix is...
[0043]
[0044]
[0045]
[0046] The Q×1 dimensional vectors z, s, r can be regarded as weighted indicator functions, representing the complex reflection coefficients of the wall, the left corner, and the right corner, respectively.
[0047] Considering all antenna locations, stack all measurement results into an MN×1 dimensional column vector.
[0048] y = [y1, y2, ..., y N ] T
[0049] The imaging linear model is obtained.
[0050] y = Wz + Ls + Rt + υ
[0051] Where W, L, and R are all MN×Q dimensional matrices.
[0052]
[0053]
[0054]
[0055] Step 2: Use a hierarchical probability model to describe the continuity of the building structure;
[0056] Assume the noise follows a mean of zero and a variance of β. -1 The complex Gaussian distribution of I, the likelihood function can be written as...
[0057]
[0058] Next, we will consider the priors for walls, corners, and noise.
[0059] a) Wall characteristics
[0060] In real-world architectural scenarios, walls are mostly built parallel or perpendicular to each other. However, due to the specular reflection properties of walls on electromagnetic waves, only walls parallel to the antenna array can be observed. Therefore, we only consider walls parallel to the array. Furthermore, the number of walls in real buildings is very limited, making them sparse relative to the overall scene. Here, we can apply a traditional sparse Bayesian learning model, assigning a complex Gaussian prior to the wall image z, resulting in... However, this prior only considers the sparsity of each pixel itself and does not encourage structured sparsity. In reality, walls often exhibit continuous structure in the orientation direction, so we consider using a structured sparse prior to constrain the wall image. To take advantage of the fact that the wall is continuous in the orientation direction, when assigning a complex Gaussian prior, each pixel z... q Not only due to its own hyperparameter α q Control is also influenced by the hyperparameters of neighboring pixels. Specifically, the structured prior of the wall image can be written as:
[0061]
[0062] in
[0063]
[0064] in Represents the set of pixels adjacent to pixel q, such as Figure 2 As shown in (a). Considering the long continuity of the wall, the definition is... Notice the edge pixels, It will adaptively shrink based on the distance to the edge. When K=0, the structured prior degenerates into a traditional sparse Bayesian learning model. When K>0, each pixel z of the wall image... q Not only due to its own hyperparameter α q Control is also affected by adjacent hyperparameters. The effect of α. q or When any hyperparameter in the equation approaches infinity, the pixel z q It will tend towards zero. That is, when α q As it approaches infinity, it's not just the corresponding pixel z q Driven to zero, the surrounding pixels It will also be driven to zero. Under this structural constraint, only wall components with strong azimuth continuity are preserved, while other structures (such as corners, point targets, etc.) are greatly suppressed. Furthermore, in any pixel group (set), each pixel still has some hyperparameters that are independent of other pixels to control it. This prior adds flexibility to the model, allowing it to adaptively fit structures of arbitrary length through parameter learning.
[0065] b) Corner characteristics
[0066] Compared to walls, corners exhibit greater sparsity, displaying some "point target" characteristics. While traditional sparse Bayesian learning models can still be used for modeling, this clearly doesn't adequately describe the corner characteristics; therefore, a structured prior is considered. Unlike walls, corners possess two-dimensional continuity in the imaging space, meaning they have some continuity in both the range and azimuth directions. Using the same structured description approach as for walls, the corner prior can be written as...
[0067]
[0068]
[0069] in
[0070]
[0071]
[0072] in Represents the set of pixels adjacent to pixel q, such as Figure 2 As shown in (b). Considering the two-dimensional continuity of the corner, we define... N x This represents the number of grid points in the azimuth direction. Note the edge pixels. It will adaptively shrink based on its distance from the edge. When η q (ζ q When any hyperparameter in ) approaches infinity, the pixel s q (t q The value tends towards zero. That is, when λ... q (γ q When the value approaches infinity, it not only corresponds to the pixel s q (t q The pixels around it are driven to zero. It will also be driven to zero. Under this structural constraint, only the corner components with a certain degree of continuity in both the azimuth and distance directions are preserved, while wall structures with continuity only in the distance direction are greatly suppressed.
[0073] Based on the sparse Bayesian learning model, Gamma is assigned as a priori to the hyperparameters α, λ, γ, and β.
[0074]
[0075]
[0076]
[0077] p(β)=Gamma(β|a,b)
[0078] Where a and b are definite constants. The parameter b is assigned a very small value, 1e -8 To further enhance the sparsity of the solution, we can use a larger value for 'a' (e.g., a > 1).
[0079] Thus, the joint distribution of the observed data y and the latent variables θ = {z, s, t, α, λ, γ, β} is obtained.
[0080] p(y,θ)=p(y|z,s,t,β)p(z|α)p(s|λ)
[0081] ×p(t|γ)p(α)p(λ)p(γ)p(β)
[0082] Step 3: Infer the posterior distribution using the variational expectation-maximization algorithm;
[0083] The goal of Bayesian inference is to obtain the posterior distribution p(θ|y) of latent variables given observed data y. However, calculating p(θ|y) is often cumbersome. To address this issue, variational inference is frequently employed. In variational inference, the variational distribution q(θ) is used to approximate the posterior distribution p(θ|y).
[0084]
[0085] in This indicates that, regarding the set θ, excluding θ itself... k The expected value of all elements except those mentioned above. The specific latent variable update criteria are as follows:
[0086] a) Update the posterior distribution of the wall structure lnq(z):
[0087]
[0088] in Clearly, z follows a multidimensional Gaussian distribution, and thus...
[0089]
[0090] in
[0091]
[0092]
[0093] τ will be used later. z To represent the covariance matrix Σ z A vector consisting of the elements along the main diagonal.
[0094] b) Update the posterior distribution lnq(s) of the left corner:
[0095]
[0096] in
[0097]
[0098] in
[0099]
[0100]
[0101] c) Update the posterior distribution lnq(t) of the right corner:
[0102]
[0103] in
[0104]
[0105] in
[0106]
[0107]
[0108] d) Update the posterior distribution lnq(α) of the hyperparameter α
[0109]
[0110] Where μ z,q μ z The q-th element, τ z,q Represents τ z The q-th element. Since the logarithmic term lnδ q The existence of these factors means that the hyperparameters α are coupled together, making it difficult to obtain an analytical solution. Therefore, we choose to use the maximum a posteriori probability. To replace the expectation of the posterior probability This is so that iterations can continue.
[0111] Setting the derivative of the logarithmic function to zero, for any hyperparameter α... q ,have
[0112]
[0113] in
[0114]
[0115]
[0116] All of them with The relevant quantities are placed on the left side of the equation, and we have
[0117]
[0118] Suppose that in updating α q At that time, with α q Adjacent hyperparameters Sharing the same weight, that is have
[0119]
[0120] Finally obtained
[0121]
[0122] Where τ z,i Represents matrix Σ z The i-th element on the diagonal.
[0123] e) Update the posterior distribution lnq(λ) of the hyperparameter λ.
[0124]
[0125] Where μ s,q μ s The q-th element, τ s,q Represents τ s The q-th element. Similar to (d), the hyperparameter λ q The update formula is
[0126]
[0127] f) Update the posterior distribution lnq(γ) of the hyperparameter γ
[0128]
[0129] Where μ t,q μ t The q-th element, τ z,q Represents τ z The q-th element. Similar to (d), the hyperparameter γ q The update formula is
[0130]
[0131] g) Update the hyperparameter β and the posterior distribution lnq(β)
[0132]
[0133] Clearly, β follows a Gamma distribution, and thus...
[0134]
[0135] in
[0136]
[0137]
[0138] Finally, there is
[0139]
[0140] Step 4: Accelerate computation using a generalized approximate message passing algorithm;
[0141] Each iteration μ () and Σ () This involves a large number of matrix inversion operations, which brings a huge amount of computation, especially for building layout reconstruction, where the imaging scene is often very large, and a large number of matrix inversions is unacceptable.
[0142] Use Generalized Approximate Message Passing (GAMP) to approximate μ (·) and τ (·) This avoids numerous matrix inversion operations, significantly reducing computation time. Given a priori p(z,s,t) and a likelihood function p(y|z,s,t), GAMP utilizes second-order approximation and Taylor series expansion to obtain approximate MAP or MMSE estimates of z,s,t. Taking the wall image z as an example, for notation convenience, we define... Represent the relevant latent variables and hyperparameters, and define intermediate variables r and τ. r Let z represent the noisy variable and its variance, respectively, and define the noiseless variable. Intermediate variables p and τ p Given the noisy variables and their variances for k, then the input function g... in (p,τ p ,θ z ) and output function g out (r,τ r ,θ z )have
[0143]
[0144]
[0145] Where mn∈MN represents the element of the mn-th input function, and q∈Q represents the element of the q-th output function. Output function g out (r,τ r ,θ zThe simplified update rules can be obtained.
[0146] g out (r,τ r ,θ z )=r. / (1+δ.τ r )
[0147] g′ out (r,τ r ,θ z )=1. / (1+δ.τ r )
[0148] Where ab represents element-wise multiplication of vectors, and a. / b represents element-wise division of vectors. Input function g in (p,τ p ,θ z Update rules
[0149] g in (p,τ p ,θ z )=[pβp-βτ p ·(y-Ls-Rt)]· / (β+τ p )
[0150] g′ in (p,τ p ,θ z )=β· / (β+τ p )
[0151] It can be seen that the y-Ls-Rt term indicates that the influence of the left and right corners is eliminated when estimating the wall composition z. Similarly, there are corresponding operations when estimating the left and right corners s and t.
[0152] To slow down C z and μ z To improve update speed and convergence, a damping coefficient ρ is introduced. c ,ρ z ∈(0,1). When ρ c =ρ z When the value is 1, the damped GAMP degenerates into the original GAMP. Algorithm 1 illustrates the specific process of GAMP.
[0153]
[0154]
[0155] Finally, μ is obtained z and τ z Approximate estimate and
[0156] For the corner images s and t, we can obtain corresponding approximate estimates by analogy with the wall image z.
[0157] Finally, the Structural Coupled Variational Bayesian (SC-VB-GAMP) building layout reconstruction method was obtained, and the specific steps of the algorithm are shown in Algorithm 2.
[0158]
[0159]
[0160] The algorithm first initializes the latent variables θ = {z, s, t, α, λ, γ, β} to be determined, assigning α, λ, and γ very large initial values (1e7), and letting the initial estimates... These two operations assume no prior information about the entire scene, allowing the algorithm to run from a zero state. The initial estimate of variance is obtained from the hyperparameters α, λ, and γ defined in the model. The image difference between two iterations is negligible and considered to indicate that the algorithm has converged.
[0161] Thus, a structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar has been completed.
[0162] Example
[0163] To verify the structurally coupled variational Bayesian method for reconstructing building layouts for through-wall radar proposed in this invention, experiments were conducted using electromagnetic simulation data and real data from actual test environments to verify the effectiveness of various algorithms, including the back projection imaging (BP) algorithm, the two-step orthogonal matching tracking wall corner extraction method (Two-step OMP), and the structurally coupled variational Bayesian method for reconstructing building layouts for through-wall radar proposed in this invention (SC-VB-GAMP).
[0164] Simulation data was generated using the software gprMax based on the Finite-Difference Time-Domain (FDTD) method. The entire building measures 5.0 x 5.0 m, with walls made of 0.12 m thick concrete. The concrete has a relative permittivity of 6.0 and a conductivity of 0.001 S / m. The building comprises three walls parallel to the antenna array, three walls perpendicular to the antenna array, three left corners, and three right corners. It includes a T-shaped structure formed by the left and right corners. Figure 3 As shown. The antenna transmits stepped-frequency signals with a bandwidth of 1-3 GHz and a frequency step of 10 MHz, totaling 201 frequency points. Noise υ follows complex Gaussian white noise and is added to the echo data y, with a signal-to-noise ratio (SNR) set to -5 dB. Because electromagnetic wave echoes at long distances are severely attenuated when observing large scenes, amplitude compensation is performed on the radar echoes. In the time domain, according to (c0t / 2)... 0.7The compensation factor compensates for the amplitude of the radar echo, where c0 represents the speed of light.
[0165] The echo data was processed using three different distribution methods, and the results are as follows: Figure 4 and Figure 5 As shown. Figure 4 (a) shows the BP imaging results. Due to the high signal-to-noise ratio, the BP image clearly shows all walls and corners. However, the entire image still exhibits a large amount of noise, affecting image quality. Furthermore, at the T-shaped structure, the BP image only shows a single high-intensity bright spot, making it impossible to determine the building structure at that location. Because the traditional BP method treats all structures as standard point scatterers, the identification of walls and corners still requires manual judgment or other subsequent processing steps, and the quality of these subsequent processing steps heavily depends on the quality of the BP image.
[0166] Figure 4 (b)(c) show the results of building structure reconstruction using the two-step orthogonal matching tracking wall corner extraction method. Figure 4 (b) shows the results of the first step of the wall inspection. Figure 4 (c) shows the results of the second step, corner detection within the measured wall. In the first step, because this method requires manually setting a fixed length for the wall detection blocks, it is prone to producing wall blocks that are too long or too short at the wall edges, and also to the phenomenon of missing sections of the wall within the wall. The second step, corner detection, performs corner detection near the wall detected in the first step. Although this reduces the computational load, the results of corner detection are directly affected by the wall detection results, and the algorithm cannot handle T-shaped structures. Furthermore, this method uses OMP (Optical Methods for Multiplication) and requires manual setting of the number of iterations.
[0167] Next, we will use the proposed method to refactor the layout. Figure 5 This represents the convergence result of the proposed method. Figure 5 (a) The wall structure reconstructed by the proposed method. Clearly, the proposed method fully reconstructs all walls parallel to the observation line. Observing the walls in the image, it can be found that under the wall structure coupling constraint, all scatterers in the image are walls with a certain length only in the azimuth direction, while scatterers with shorter azimuth projections, such as those at wall corners, are suppressed. Moreover, because the structural coupling mode used by the proposed method has greater flexibility, it is compatible with… Figure 4 (b) In contrast, the proposed method can automatically adapt to the wall boundary while improving the continuity of the wall interior.
[0168] Figure 5 (b) and (c) show the left and right corners reconstructed by the proposed method, respectively. Clearly, the proposed method reconstructs all corners, including the two adjacent corners of the T-shaped structure. Furthermore, the corner structure constraints further enhance the two-dimensional point scattering characteristics of the corners, and... Figure 4 (c) In comparison, the proposed method can reconstruct all wall corners more accurately. Since the reconstruction of the left and right wall corners is independent, the proposed method can infer the walls perpendicular to the observation array from the positions of the left and right wall corners, including building exterior walls and internal structures such as T-shaped structures.
[0169] An observation was conducted on a two-story room within a real building. The room measures 6m x 4m, and the walls have two thicknesses: 12cm and 23cm. The 23cm thick wall consists of two layers of hollow bricks, as shown below. Figure 6 As shown, a single-transmit, single-receive, ultra-wideband stepped-frequency through-wall radar system was mounted on a cart for easy movement. It performed a single-view scan of the scene along one side of the room, with a 5cm interval between observations. Both the transmitting and receiving antennas were Vivaldi antennas with 3dB beamwidths of 40° and 60° in the vertical and horizontal directions, respectively. The radar transmit signal was generated using a vector network analyzer, with a bandwidth of 1-3 GHz, a frequency step of 10 MHz, and 201 frequency points. Similar to the simulation data, the measured data also underwent amplitude compensation.
[0170] Figure 7 (a) shows an image obtained directly from radar data using BP. In the image, although the walls and corners inside the building are relatively clear after amplitude compensation, the background clutter in the image is also significantly enhanced, making it difficult to accurately determine the layout from the BP image alone.
[0171] Figure 7 (b)(c) show the results of the two-step orthogonal matching tracking method for wall corner extraction. Figure 7 In (b), thanks to the sparse prior penalty of compressed sensing, background clutter is suppressed, resulting in a relatively clean wall. However, due to the use of a fixed-length wall dictionary, the resulting wall exhibits a strong blocky distribution and poor continuity. Figure 7 In (c), the method only found the corners of the first two walls that are closer to the radar, and the corners are scattered and cannot be understood intuitively, so further processing is needed.
[0172] Figure 8 The reconstruction results of the proposed method are shown. Figure 8 In (a), it is clear that the proposed method reconstructs all the walls parallel to the array, while ensuring the continuity of the walls. Figure 8 (b) and (c) demonstrate the reconstruction results of the left and right corners. Compared with existing methods, the proposed method extracts all corners and ensures clustering in two-dimensional space. Simulation and field tests both prove that the present invention can effectively enhance the two-dimensional spatial continuity of walls and corners in building layout reconstruction.
[0173] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A structure-coupled variational Bayesian through-the-wall radar building layout reconstruction method, characterized by The steps of this method include: Step 1: Establish a model for the signal received by through-wall radar; Step 2: Use a hierarchical probability model to describe the continuity of the building structure; Step 3: Infer the posterior distribution using the variational expectation-maximization algorithm; Step 4: Accelerate computation using a generalized approximate message-passing algorithm; The method models the echo in step 1, letting Indicates wall echo, Radar echoes are represented by corner echoes. ； Wall section for ； in This represents the number of walls parallel to the antenna array. Indicates the first The number of blocks the wall is divided into. This represents the amplitude of scattering from the wall block. The signal comes from the first The antenna to the first The first in the wall Two-way delay of some walls The dependence of wall scattering on frequency and orientation angle is described as follows: ； in Indicates the first The antenna and the first The first in the wall The direction angle formed by part of the wall normal. It is the length of each small wall section. Indicates the first The first in the wall The orientation angle of a portion of the wall is generally 0° for walls parallel to the radar array. corner Represented as ； in It refers to the number of corners. It is the amplitude of light scattering from the corner of the wall. The signal comes from the first The antenna to the first Two-way delay at the corner of the wall, It is an indicator function, and its specific form is as follows: ； The dependence of corner scattering on frequency and azimuth is described as follows: ； in, This indicates the length of the corner. Indicates the first The antenna and the first The directional angle formed by the corner of the wall; Will Disassembled into left and right corners ； in The echo representing the left corner of the wall. The echo representing the right corner; ultimately ； The first The antenna at each location received Signals at various frequencies are stacked together dimensional vector , ； The imaging scene is divided into two parts according to the azimuth and range directions: The relationship between the radar echo and the imaging scene is given by a grid. ； in , and All A matrix of dimension , the first dimension of each matrix The elements are ； dimensional vector Considered as a weighted indicator function, it represents the complex reflection coefficients of the wall, the left corner, and the right corner, respectively; Considering all antenna locations, stack all measurement results into one. dimensional column vector ； The imaging linear model is obtained. ； in All 3D matrix 。 2. The structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar according to claim 1, characterized in that, In step 2, it is assumed that the noise follows a mean of zero and a variance of... The complex Gaussian distribution, the likelihood function is written as 。 3. The structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar according to claim 1, characterized in that, The structured prior of the wall image in step 2 is written as follows: ； in ； in Represents pixels The set of adjacent pixels; Considering the long continuity of the wall, define .
4. The structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar according to claim 1, characterized in that, In step 2, the corner is first verified as... ； ； in ； ； in Represents pixels The set of adjacent pixels; considering the two-dimensional continuity of the corner, define , This represents the number of grid points divided in the azimuth direction.
5. The structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar according to claim 1, characterized in that, Hyperparameters in step 3 The update formula is ； in Representation matrix The diagonal One element; Hyperparameters The update formula is ； Hyperparameters The update formula is 。 6. The structurally coupled variational Bayesian method for reconstructing the building layout of through-wall radar according to claim 1, characterized in that, Step 4, the structurally coupled variational Bayesian building layout reconstruction method, has the following specific steps: Input: Radar echo ,dictionary Error tolerance , ； initialization: , , , ； cycle: ； ； ； ； ； ； ； ； until ; Output: Wall left corner Right corner .