Tikhonov-l in radio tomography p Norm Regularized Sparse Reconstruction Method

Abstract

The present invention relates to the field of radio tomography technology, and particularly relates to a Tikhonov-l p norm regularization sparse reconstruction method. Modeling is performed according to the RSSI attenuation change corresponding to each link in the monitoring area and the attenuation weights of all pixels to obtain a linear equation set for radio tomography. An l2 norm constraint is imposed on the attenuation signal in the linear equation set, a Tikhonov regularization reconstruction model is established and solved. According to the compressive sensing theory, a sparse constraint is imposed on the projection coefficients of the attenuation signal in the transform domain, and an l p norm regularization sparse reconstruction model is established. By fusing the l p norm and the l2 norm constraint terms, a Tikhonov-l p norm regularization sparse reconstruction model is established, which can reduce the algorithm time consumption, improve the operation efficiency and accuracy. Moreover, it can improve the energy aggregation degree of the brightest area of the image, reduce the imaging artifacts, and improve the target positioning error.

Description

Technical Field

[0001] The present invention relates to the technical field of radio tomography, and particularly relates to a Tikhonov-l p norm regularization sparse reconstruction method in radio tomography. Background Art

[0002] With the advent of the 5G era, the Internet of Things and intelligence have put forward higher requirements for location-based services. Solving the "last mile" high-precision positioning from outdoor to indoor is one of the development directions of 5G positioning. Radio tomography (RTI) technology has quickly become one of the main methods of current passive positioning due to its characteristics of non-damage, non-invasion, and strong concealment. The target image reconstruction model is a key physical layer factor affecting the accuracy and real-time performance of target positioning. It is found that in the reconstructed target image, the target position only occupies a very small number of pixel points, and the pixel points corresponding to the target position have the most serious attenuation. Therefore, the target image reconstruction in the RTI system is a signal sparse reconstruction problem.

[0003] The RTI system draws on the idea of CT (Computed Tomography), inversely images through the RSSI measurement values of the wireless network, and obtains the target position by solving the optimization problem corresponding to the linear equations. However, when the number of links in the monitoring area is much smaller than the number of monitoring sub-areas, the least squares method cannot be directly used for solving. The traditional RTI method adds the prior information of the attenuation signal as a constraint term to the solving process, and uses Tikhonov- norm regularization to reconstruct the attenuation image. However, the Tikhonov reconstruction method only considers the correlation between pixels, and the imaging quality is low, which affects the accuracy of target positioning. In terms of signal sparse reconstruction, since norm is a non-deterministic polynomial (NP) problem in mathematics, most studies choose norm to perform sparse constraint on the signal.

[0004] Currently, an (0 < p < 1) norm optimization reconstruction model that can also promote sparsity of the solution has been proven to be superior to norm under low sampling rate conditions, such as ECT image reconstruction and infrared image super-resolution reconstruction. According to the compressive sensing (CS) theory, the (0 < p < 1) norm sparse constraint of the model parameters can be added as prior information to the least squares (LS) model to obtain norm regularization sparse reconstruction model, thereby weakening the interference of the attenuation caused by noise to image reconstruction. However, this model is the same as The norm reconstruction model is similar and is only sensitive to smaller outliers in the attenuation signal. When a large abnormal attenuation occurs in the measured value, the positioning result of the RTI system will deviate from the true position.

[0005] To address the above issues, the relevant algorithms use the model parameters Norm or The norm sparse constraint term is added to the Tikhonov regularized reconstruction model, making the reconstruction model also highly sensitive to large outliers in the attenuation signal. However, since the algorithm directly uses the attenuation signal as the model optimization solution parameter, the introduction of the sparse constraint term will increase the complexity of the weight matrix calculation. Therefore, in the process of reconstructing the attenuated image, too many non-zero values ​​will be involved in the iterative operation, and the algorithm will take a long time. Summary of the invention

[0006] In order to solve the above technical problems, the object of the present invention is to provide a Tikhonov-1 method for radio tomography. p Norm regularized sparse reconstruction method, the technical solutions adopted are as follows:

[0007] A Tikhonov-l in radio tomography p The norm regularized sparse reconstruction method includes the following steps:

[0008] According to the RSSI attenuation change corresponding to each link in the monitoring area and the attenuation weights of all pixels, a linear equation group of wireless tomography is obtained;

[0009] The decaying signal in the linear system is Norm constraint, establish Tikhonov regularized reconstruction model and solve it;

[0010] According to the compressed sensing theory, the projection coefficients of the attenuated signal in the transform domain are sparsely constrained and the Norm regularized sparse reconstruction model;

[0011] Fusion Norm and Norm constraint, establish Tikhonov-l p Norm regularized sparse reconstruction model.

[0012] Furthermore, the modeling is performed based on the RSSI attenuation change corresponding to each link in the monitoring area and the attenuation weights of all pixels to obtain a linear equation group of wireless tomography, including:

[0013] L sensor nodes are deployed at equal intervals at the edge of the monitoring area, and any two nodes communicate with each other to form M = L (L-1) wireless links; the monitoring area is divided into N sub-areas, each sub-area is a decay of Δxj The RSSI attenuation change of each wireless link is Δy i for:

[0014]

[0015] Where, i = 1, 2, ..., M; j = 1, 2, ..., N; w ij is the attenuation weight of pixel j under the i-th wireless link; n i is the measurement noise of the ith wireless link;

[0016] For M wireless links, the linear equations are:

[0017] y=Wx+n

[0018] Where x is the attenuation signal,

[0019] y=[Δy1,Δy2,...,Δy M ] T ∈R M , W=[w ij ] M×N ∈R M×N

[0020] x=[Δx1,Δx2,...,Δx N ] T ∈R N ,n=[n1,n2,...,n M ] T ∈R

[0021] The calculation formula of the ellipse weight matrix W is:

[0022]

[0023] Among them, d i is the length of the ith wireless link; d ij (1) and d ij (2) are the distances from pixel j to the two foci of the ellipse; λ is the preset parameter for adjusting the size of the minor axis of the ellipse.

[0024] Furthermore, the attenuation signal in the linear equation system is Norm constraints, establish Tikhonov regularized reconstruction model and solve it, including:

[0025] Find the solution of the linear system of equations under the least squares error:

[0026] minf(x)=||Wx-y|| 2

[0027] Based on the prior information of the attenuated signal x, the Tikhonov regularized reconstruction objective function is obtained:

[0028] min f(x)=||Wx-y|| 2 +μ1x T C -1 x

[0029] Among them, μ1 is the Tikhonov regularization parameter; C is the prior covariance matrix of the attenuated signal x;

[0030] Let the gradient of the Tikhonov regularized reconstruction objective function be zero, and obtain the Tikhonov regularized optimal estimate of the attenuated signal x:

[0031] x Tik =(W T W+μ1C -1 ) -1 W T y

[0032] Furthermore, the projection coefficients of the attenuated signal in the transform domain are sparsely constrained according to the compressed sensing theory to establish Norm regularized sparse reconstruction model, including:

[0033] Set the cosine transform matrix:

[0034] x=Ψθ

[0035] Among them, Ψ is the cosine orthogonal transformation matrix, θ is the projection coefficient of the attenuated signal x after transformation;

[0036] Ψ=[Ψ ij ] N×N ∈R N×N

[0037] θ=[θ1,θ2,…,θ N ] T ∈R N

[0038] The projection coefficient θ The norm is added as a loss function to the least squares-based reconstruction model to establish a Norm regularized sparse reconstruction model, the objective function is:

[0039]

[0040] In the formula, μ2 is norm regularization parameter.

[0041] Furthermore, the fusion Norm and Norm constraint, establish Tikhonov- Norm regularized sparse reconstruction model, including:

[0042] Initialize θ 0 =WΨ\y,δ=1,k=1;

[0043] Step (1): Calculate the matrix A:

[0044] A=diag[a1,a2,...,a N ]

[0045] Among them, a j and θ j are the j-th elements in A and θ respectively;

[0046] a j =((θ j k-1 ) 2 +δ) -1+p / 2

[0047] Diagonalize the matrix A to get the matrix Ω k :

[0048] Ω k =diag(1. / A)

[0049] Step (2): Calculate θ according to the following formula: k :

[0050] θ k =Ω k (WΨ) T ((WΨ)Ω k (WΨ) T +μ2I) -1 y

[0051] Where I is the identity matrix;

[0052] Step (3): Determine whether If not, add 1 to the value of k and return to step (1); if satisfied, execute step (4);

[0053] Step (4): Reduce the value of δ by ten times, increase the value of k by 1, and then determine whether δ≤10 is satisfied. -5 Or k ≥ 20, if it is not satisfied, return to step (1), if it is satisfied, stop the iteration and convert the obtained θ k As the final solution;

[0054] Step (5): Inverse transform the coefficients to obtain the attenuated signal x Norm regularization estimate:

[0055] x p =Ψθ k

[0056] Step (6): Calculate the Tikhonov regularized estimate of the attenuated signal x according to the following formula:

[0057] x Tik =(W T W+μ1C -1 ) -1 W T y

[0058] Step (7): Reconstruct signal normalization:

[0059] x p =x p / max(max(x p ))

[0060] x Tik =x Tik / max(max(x Tik ))

[0061] Step (8): Pass The norm calculates the imaging error of the two regularized estimates:

[0062] Error_p=norm(x p )

[0063] Error_Tik=norm(x Tik )

[0064] Step (9): Weighted fusion x according to the following algorithm p With x Tik Get the final solution:

[0065] If Error_p<Error_Tik, then x opt =0.7x p +0.3x Tik , otherwise x opt =0.3x p +0.7x Tik .

[0066] The present invention provides a method for Tikhonov- The norm regularized sparse reconstruction method can reduce the algorithm time consumption, improve the computational efficiency and accuracy, and also increase the energy concentration in the brightest area of ​​the image, reduce imaging artifacts, and improve target positioning errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0068] Figure 1 The present invention provides a Tikhonov-1 radio tomography method. p Schematic diagram of the process of norm regularized sparse reconstruction method;

[0069] Figure 2 This is a schematic diagram of RTI sensor node deployment;

[0070] Figure 3 It is a schematic diagram of the imaging results of three target positions using three different reconstruction methods;

[0071] Figure 4 is the imaging error curve at different target positions;

[0072] Figure 5 It is the algorithm time consumption curve diagram of different target positions;

[0073] Figure 6 It is the positioning error curve of different target positions. DETAILED DESCRIPTION

[0074] The following specifically describes a Tikhonov-1 radio tomography method provided by the present invention in conjunction with the accompanying drawings. p Specific scheme of norm regularized sparse reconstruction method.

[0075] See also Figure 1 , which shows a Tikhonov-1 in radio tomography provided by the present invention p A flowchart of the steps of the norm regularized sparse reconstruction method, the method comprising the following steps:

[0076] Step 1: Model the RSSI attenuation change corresponding to each link in the monitoring area and the attenuation weights of all pixels to obtain the linear equations of wireless tomography:

[0077] like Figure 2 As shown, L sensor nodes are deployed at equal intervals at the edge of the monitoring area. Any two nodes communicate with each other to form M = L (L-1) wireless links. It should be understood that the specific value of L is set according to actual needs. The monitoring area is divided into N sub-areas. It should be understood that the specific value of N is set according to actual needs. Each sub-area is a decay of Δx jThe RSSI attenuation change of each wireless link is Δy i for:

[0078]

[0079] Where, i = 1, 2, ..., M; j = 1, 2, ..., N; w ij is the attenuation weight of pixel j under the i-th wireless link; n i is the measurement noise of the ith wireless link, which is usually assumed to be a univariate Gaussian random variable.

[0080] For M wireless links, the linear equations can be obtained according to the above formula:

[0081] y=Wx+n

[0082] Where x is the attenuation signal,

[0083] y=[Δy1,Δy2,...,Δy M ] T ∈R M , W=[w ij ] M×N ∈R M×N

[0084] x=[Δx1,Δx2,...,Δx N ] T ∈R N ,n=[n1,n2,...,n M ] T ∈R

[0085] The calculation formula of the ellipse weight matrix W is:

[0086]

[0087] Among them, d i is the length of the ith wireless link; d ij (1) and d ij (2) are the distances from pixel j to the two foci of the ellipse; λ is a preset parameter for adjusting the size of the minor axis of the ellipse, which is usually an empirical value.

[0088] Step 2: Perform the attenuation signal in the linear equation system Norm constraint, establish Tikhonov regularized reconstruction model and solve:

[0089] The established Tikhonov regularized reconstruction model is able to constrain larger outliers in the attenuated signal x.

[0090] When estimating the attenuated signal x from the RSSI measurements, it is necessary to find a solution to the linear equations under the least squares (LS) error. Therefore, find the solution to the linear equations under the least squares error:

[0091] minf(x)=||Wx-y|| 2

[0092] Based on the prior information of the attenuated signal x, the prior information of the attenuated signal x is added to the above formula to obtain the Tikhonov regularized reconstruction objective function:

[0093] minf(x)=||Wx-y|| 2 +μ1x T C -1 x

[0094] Wherein, μ1 is the Tikhonov regularization parameter; C is the prior covariance matrix of the attenuated signal x, and the covariance matrix is ​​calculated by conventional technical means. In this embodiment, the exponential decay function is used for approximate calculation. Let the element of the i-th row and j-th column of the prior covariance matrix C be C ij ,but:

[0095]

[0096] Among them, d ij represents the distance between the i-th pixel and the j-th pixel (it should be understood that the element C in the prior covariance matrix C ij The i and j in here have different meanings from those in the above text), δ is a parameter related to the space constant and is a known value.

[0097] Let the gradient of the Tikhonov regularized reconstruction objective function be zero, and obtain the Tikhonov regularized optimal estimate of the attenuated signal x:

[0098] x Tik =(W T W+μ1C -1 ) -1 W T y

[0099] Step 3: According to the compressed sensing theory, the projection coefficients of the attenuated signal in the transform domain are sparsely constrained to establish Norm regularized sparse reconstruction model:

[0100] According to the compressed sensing theory, the projection coefficients of the attenuated signal in the transform domain are sparsely constrained and the Norm regularization sparse reconstruction model, by increasing The norm sparsity constraint reduces the interference of small outliers in the attenuation signal x on image reconstruction.

[0101] In the RTI system, the cosine transform matrix is ​​selected to perform sparse transform processing on the attenuated signal x to improve the quality of sparse reconstruction. Set the cosine transform matrix:

[0102] x=Ψθ

[0103] Among them, Ψ is the cosine orthogonal transformation matrix, and θ is the projection coefficient of the attenuated signal x after transformation.

[0104] Ψ=[Ψ ij ] N×N ∈R N×N

[0105] θ=[θ1,θ2,…,θ N ] T ∈R N

[0106] Based on the projection coefficient θ, we establish Norm regularized sparse reconstruction model, in this embodiment, the projection coefficient θ The norm is added as a loss function to the least squares-based reconstruction model to establish a Norm regularized sparse reconstruction model, the objective function is:

[0107]

[0108] In the formula, μ2 is norm regularization parameter.

[0109] Step 4: Fusion Norm and Norm constraint, establish Tikhonov- Norm regularized sparse reconstruction model:

[0110] Established by Tikhonov- The norm regularized sparse reconstruction model can have a certain constraint ability on both large and small outliers in the attenuated signal x.

[0111] In this step, the iterative reweighted least squares method is used to solve the new objective function, and the attenuation signal is obtained by sparse inverse transformation. p Then x p With x Tik The final target attenuated reconstructed image is obtained by weighted fusion, and the target position is estimated from the reconstructed image.

[0112] Initialize θ 0 =WΨ\y,δ=1,k=1.

[0113] Step (1): Calculate the matrix A:

[0114] A=diag[a1,a2,...,a N ]

[0115] Among them, a j and θ j are the j-th elements in A and θ respectively, where:

[0116] a j =((θ j k-1 ) 2 +δ) -1+p / 2

[0117] Diagonalize the matrix A to get the matrix Ω k :

[0118] Ω k =diag(1. / A)

[0119] Step (2): Calculate θ according to the following formula: k :

[0120] θ k =Ω k (WΨ) T ((WΨ)Ω k (WΨ) T +μ2I) -1 y

[0121] Where I is the identity matrix.

[0122] Step (3): Determine whether If not, increase the value of k by 1 and return to step (1); if satisfied, execute step (4).

[0123] Step (4): Reduce the value of δ by ten times, increase the value of k by 1, and then determine whether δ≤10 is satisfied. -5 Or k ≥ 20, if it is not satisfied, return to step (1), if it is satisfied, stop the iteration and convert the obtained θ k As the final solution.

[0124] Step (5): Inverse transform the coefficients to obtain the attenuated signal x Norm regularization estimate:

[0125] x p =Ψθ k

[0126] Step (6): Calculate the Tikhonov regularized estimate of the attenuated signal x according to the following formula:

[0127] x Tik =(W T W+μ1C-1 ) -1 W T y

[0128] Step (7): Reconstruct signal normalization:

[0129] x p =x p / max(max(x p ))

[0130] x Tik =x Tik / max(max(x Tik ))

[0131] Step (8): Pass The norm calculates the imaging error of the two regularized estimates:

[0132] Error_p=norm(x p )

[0133] Error_Tik=norm(x Tik )

[0134] Step (9): Weighted fusion x according to the following algorithm p With x Tik Get the final solution:

[0135] If Error_p<Error_Tik, then x opt =0.7x p +0.3x Tik , otherwise x opt =0.3x p +0.7x Tik .

[0136] Then, x p With x Tik The final target attenuated reconstructed image is obtained by weighted fusion, and the target position is estimated from the reconstructed image.

[0137] The following is a description of the Tikhonov-1 method in radio tomography provided in this embodiment. p The verification process of the norm regularized sparse reconstruction method. This embodiment selects the proposed algorithm (i.e., the Tikhonov-1 in radio tomography provided in this embodiment) in a relatively complex indoor environment. pThe effectiveness of the proposed algorithm (hereinafter referred to as the proposed algorithm) is verified by a single target positioning experiment. The experimental environment is as follows: the WSN node is placed on a bracket 1m above the ground. At the same time, in order to suppress the reflected signals from the walls and stone pillars on both sides, a planar directional antenna with horizontal and vertical beam widths of 110° and 30° is used. The node supports the IEEE 802.15.4 protocol with a maximum transmission power of 4.5dBm and adopts a token ring mechanism. Each node is assigned a unique ID to determine the transmission order. Table 1 lists the relevant experimental deployment parameters.

[0138] Table 1

[0139] Node spacing Pixel size Number of nodes N λ 1.5m 0.1m×0.1m 12 45×45 0.05

[0140] In the experiment, five target positions are randomly selected with coordinates of (1.2m, 1.2m), (3.0m, 1.5m), (0.9m, 3.6m), (1.5m, 3.0m) and (3.0m, 3.0m), and they are recorded in order as positions [1]-[5]. Table 2 shows the Tikhonov regularized reconstruction model, Tikhonov- Norm regularized reconstruction model and Tikhonov- Norm regularization parameters of the sparse reconstruction model.

[0141] Table 2

[0142]

[0143]

[0144] Figure 3 The imaging results of different reconstruction methods at the target positions [1]-[3] are given, where the point with the maximum gray value is taken as the target position. Figure 3 In: ac represents the algorithm proposed in this embodiment (Tikhonov- ) is the imaging result (i.e., image reconstruction result); df is the imaging result of the Tikhonov algorithm; gi is the Tikhonov- Imaging results of the algorithm.

[0145] Figure 4 , Figure 5 and Figure 6 The imaging error curves, algorithm time consumption and positioning error of different target positions are given respectively. Table 3 gives the RMSE, mean error, median error and average algorithm time consumption of the imaging and positioning results.

[0146] Table 3

[0147]

[0148] like Figure 3 As shown, the Tikhonov- Regularized reconstruction algorithm can provide better imaging effect, and there is almost no background noise in the reconstructed image, but the algorithm takes a long time (such as Figure 4 and Table 3), which cannot meet the requirements of real-time positioning. Compared with the traditional Tikhonov regularized reconstruction model, the algorithm proposed in this embodiment can also improve the energy concentration of the brightest area of ​​the image and reduce imaging artifacts by sparsely constraining the projection coefficients of the attenuated signal in the transform domain. The target positioning errors of the proposed algorithm in this embodiment are improved by 16.49% and 6.07% respectively, and compared with the Tikhonov- The regularized reconstruction model reduces the time consumption of the algorithm proposed in this embodiment by 3 / 4.

[0149] It should be noted that the sequence of the embodiments of the present invention described above is for description only and does not represent the advantages and disadvantages of the embodiments. The above describes specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0150] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0151] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A Tikhonov-l in radio tomography p The norm regularized sparse reconstruction method is characterized by: The following steps are involved: According to the RSSI attenuation change corresponding to each link in the monitoring area and the attenuation weight of all pixels, a linear equation group of wireless tomography is obtained. Specifically, it includes: deploying L sensor nodes at equal intervals at the edge of the monitoring area, and any two nodes communicate with each other to form a total of M = L (L-1) wireless links; dividing the monitoring area into N sub-areas, each sub-area is a region with an attenuation of Δx j The RSSI attenuation change of each wireless link is Δy i for: Where, i = 1, 2, ..., M; j = 1, 2, ..., N; w ij is the attenuation weight of pixel j under the i-th wireless link; n i is the measurement noise of the ith wireless link; For M wireless links, the linear equations are: y=Wx+n Where x is the attenuation signal, y=[Δy1,Δy2,...,Δy M ] T ∈R M ,W=[w ij ] M×N ∈R M×N x=[Δx1,Δx2,...,Δx N ] T ∈R N ,n=[n1,n2,...,n M ] T ∈R The calculation formula of the ellipse weight matrix W is: Among them, d i is the length of the ith wireless link; d ij (1) and d ij (2) are the distances from pixel j to the two foci of the ellipse; λ is the preset parameter for adjusting the size of the minor axis of the ellipse; The attenuation signal in the linear equations is constrained by l2 norm, and a Tikhonov regularized reconstruction model is established and solved. Specifically, the solution of the linear equations is found under the least squares error: minf(x)=||Wx-y|| 2 Based on the prior information of the attenuated signal x, the Tikhonov regularized reconstruction objective function is obtained: minf(x)=||Wx-y|| 2 +μ1x T C -1 x Among them, μ1 is the Tikhonov regularization parameter; C is the prior covariance matrix of the attenuated signal x; Let the gradient of the Tikhonov regularized reconstruction objective function be zero, and obtain the Tikhonov regularized optimal estimate of the attenuated signal x: x Tik =(W T W+μ1C -1 ) -1 W T y; According to the compressed sensing theory, the projection coefficients of the attenuated signal in the transform domain are sparsely constrained and l p Norm regularized sparse reconstruction model, specifically, including: setting the cosine transform matrix: x=Ψθ Among them, Ψ is the cosine orthogonal transformation matrix, θ is the projection coefficient of the attenuated signal x after transformation; Ψ=[Ψ ij ] N×N ∈R N×N θ=[θ1,θ2,…,θ N ] T ∈R N The projection coefficient θ is l p The norm is added as a loss function to the least squares-based reconstruction model to establish a l p Norm regularized sparse reconstruction model, the objective function is: In the formula, μ2 is l p norm regularization parameter; y is the linear equation system of the wireless link; Fusion p norm and l2 norm constraints, establish Tikhonov-l p Norm regularized sparse reconstruction model, specifically, including: Initialize θ 0 =WΨ\y,δ=1,k=1; Step (1): Calculate the matrix A: <h2 style=";text-align:left;direction:ltr">A = diag[a1,a2,...,a<h2 style=";text-align:left;direction:ltr"> N <h2 style=";text-align:left;direction:ltr"> ] Among them, a j and θ j are the j-th elements in A and θ respectively; a j =((θ j k-1 ) 2 +d) -1+p / 2 Diagonalize the matrix A to get the matrix Ω k : Oh k =diag(1. / A) Step (2): Calculate θ according to the following formula: k : i k =Oh k (WΨ) T ((WΨ)Ω k (WΨ) T +μ2I) -1 y Where I is the identity matrix; Step (3): Determine whether If not, add 1 to the value of k and return to step (1); if satisfied, execute step (4); Step (4): Reduce the value of δ by ten times, increase the value of k by 1, and then determine whether δ≤10 is satisfied. -5 Or k ≥ 20, if it is not satisfied, return to step (1), if it is satisfied, stop the iteration and convert the obtained θ k As the final solution; Step (5): Inverse transform the coefficients to obtain the l of the attenuated signal x p Norm regularization estimate: x p =Ψθ k Step (6): Calculate the Tikhonov regularized estimate of the attenuated signal x according to the following formula: x Tik =(W T W+μ1C -1 ) -1 W T y Step (7): Reconstruct signal normalization: x p =x p / max(max(x p )) x Tik =x Tik / max(max(x Tik )) Step (8): Calculate the imaging errors of the two regularized estimates using the l2 norm: Error_p=norm(x p ) Error_Tik=norm(x Tik ) Step (9): Weighted fusion x according to the following algorithm p With x Tik Get the final solution: If Error_p<Error_Tik, then X opt =0.7X p +0.3X Tik , otherwise X opt =0.3X p +0.7X Tik , where x opt is the weighted fusion X p With X Tik The final solution obtained.

Images