A sparsity estimation compressed sensing reconstruction method

Abstract

The application discloses a sparsity estimation compressed sensing reconstruction method, which finds a linear relationship between the sum of pixel values of each column of an image and a real sparsity through statistical analysis, fits a sparsity estimation function through least square, and obtains an initial sparsity estimation value; and the optimal sparsity estimation value is further obtained by using a local search method. The application can complete fast sparsity estimation operation, solve the problem that unknown sparsity seriously influences the accuracy of a greedy reconstruction algorithm, provide guarantee for accurate compressed sensing signal reconstruction, and has the advantages of low calculation complexity, good robustness and strong generalization ability.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of sparsity estimation compressed sensing reconstruction method of least square and local search combination, belong to sub-sampling signal recovery technical field. BACKGROUND

[0002] Inverse synthetic aperture radar is widely used in air moving target imaging research, but radar system bandwidth cannot be increased unlimitedly, which limits the imaging resolution. Compressed sensing technology has the advantages of reducing bandwidth and data storage space, and is the key to solve the problem of high sampling rate. Compressed sensing theory mainly includes: signal sparse representation, measurement matrix construction and reconstruction algorithm design. Among them, reconstruction algorithm design is the key and difficulty of compressed sensing theory. In actual reconstruction process, the unknown image sparsity leads to the problem of oversampling and undersampling. Accurate estimation of the sparsity of the image is very important for the development of compressed sensing reconstruction algorithm. SUMMARY

[0003] The present application aims to provide a kind of sparsity estimation compressed sensing reconstruction method of least square and local search combination, solve the problem of unknown sparsity in compressed sensing reconstruction, reduce reconstruction accuracy, and provide protection for final high-quality signal reconstruction.

[0004] In order to achieve the above purpose, the reconstruction method of the present application comprises the following steps: the method is used in space-based high-speed moving target inverse synthetic aperture radar imaging, the linear relationship between the sum of the pixel values of each column of the image and the true sparsity is found by statistical analysis, the sparsity estimation function is fitted by least square, and the initial sparsity estimation value is obtained;The sparsity estimation value meeting the set requirement is obtained by using local search method, and finally the original signal is recovered according to the sparsity estimation value meeting the set requirement.

[0005] Further, the linear relationship between the sum of the pixel values of each column of the image and the true sparsity found by statistical analysis is as follows:

[0006] An error function is established, as shown in formula (1):

[0007]

[0008] Wherein, x is the sum of the pixel values of the image, y is the true sparsity, n is the total number of columns of the image, and i is the current column number;The error function coefficients θ0, θ1 are determined by derivation of error function.

[0009] Further, the sparsity estimation function is fitted by least square, and the initial sparsity estimation value is obtained, which is: the sum of the column element values of the sparse signal to be reconstructed is calculated in turn, ε is the pixel value of each point of the image to be reconstructed, i is the current column number, j is the current row number, and m is the total row number of the image to be reconstructed; the preliminary estimated signal sparsity of is substituted into the following formula:

[0010] Further, the local search method is used to obtain the sparsity estimation value meeting the set requirement, and finally the original signal is recovered according to the sparsity estimation value meeting the set requirement, specifically as follows:

[0011] The local search is performed in the vicinity of the initial sparsity estimation value to obtain the optimal sparsity estimation value: the large step length changes the current sparsity estimation value to find the sparsity interval with continuously reduced reconstruction error; the small step length changes the sparsity estimation value with the minimum greedy reconstruction error as the current optimal sparsity estimation value

[0012] The loop approximates the local optimal value to obtain the optimal sparsity estimation value, that is: wherein, represents the sparsity estimation value with the minimum ROMP reconstruction error, and i is the current column number of the image to be reconstructed.

[0013] The measurement matrix, the sub-sampling signal and the optimal sparsity estimation value are taken as the input of the regularized orthogonal matching pursuit algorithm to obtain the sparse coefficient The optimal solution of the compressed sensing underdetermined equation is found based on the minimum norm method to recover the original signal.

[0014] Beneficial effects

[0015] The sparsity estimation and reconstruction of the compressed measurement signal can be completed through the above steps, which provides guarantee for the completion quality of the sparse signal compressed sensing technology. BRIEF DESCRIPTION OF DRAWINGS

[0016] The application will be further described in detail below with reference to the accompanying drawings and specific embodiments

[0017] Figure 1 which is an algorithm flowchart;

[0018] Figure 2 which is a statistical chart of the sum of pixel values of each column of the image;

[0019] Figure 3 which is a statistical chart of the real sparsity of each column of the image;

[0020] Figure 4 which is a chart of the correlation coefficient between the sum of pixel values of each column of the image and the real sparsity. DETAILED DESCRIPTION

[0021] The application will be further described in detail below with reference to the accompanying drawings and specific embodiments

[0022] The algorithm flow is shown in Figure 1 The optimal sparse degree estimation value is determined based on least square and local search, and the signal is reconstructed by combining the regularized orthogonal matching pursuit algorithm. The specific method is as follows:

[0023] The method of the embodiment is used in the imaging of space-based high-speed moving target inverse synthetic aperture radar, and the Yake-42 scene image is restored and processed. Through statistical analysis, the linear relationship between the sum of the pixel values of each column of the image and the true sparse degree is found. The sparse degree estimation function is fitted by least square, and the initial sparse degree estimation value is obtained. Then, the sparse degree estimation value meeting the set requirement is obtained by using the local search method, and finally the original signal is restored according to the sparse degree estimation value meeting the set requirement. The specific process is as follows:

[0024] The sum of the pixel values of each column of the Yake-42 scene image and the true sparse degree are counted respectively, as shown in Figure 2 and Figure 3 The linear correlation coefficient between the sum of the pixel values of each column of the scene image and the true sparse degree is calculated, as shown in Figure 4 Any two correlation coefficients are greater than 0.9, indicating that the two are strongly positively correlated.

[0025] The Yake-42 image is taken as the prior image, and the sparse degree estimation function coefficient is determined based on the least square method. The error function is established, as shown in equation (1).

[0026]

[0027] Wherein, x is the sum of the column pixel values of the sub-sampled scene image, y is the true sparse degree of the scene image column, θ0, θ1 are the error function coefficients. The value of θ0, θ1 is determined by derivation of the error function, as shown in equations (2) to (3).

[0028]

[0029]

[0030] Wherein, n is the total number of columns of the Yake-42 image, i is the current column number, x and y values of the Yake-42 image are substituted, and θ0, θ1 are obtained, as shown in equations (4-5).

[0031]

[0032]

[0033] The sum of the column element values of the sparse signal to be reconstructed is calculated in turn, Substituting equation (6) can preliminarily estimate the signal sparse degree Kpre ε is the pixel value of each point of the image to be reconstructed, i is the current column number, j is the current row number, and m is the total row number of the image to be reconstructed.

[0034]

[0035] The local search is performed near the initial sparsity estimation value The specific method is as follows: the current sparsity estimation value is changed by a large step size The sparsity interval with continuously reduced reconstruction error is searched; the current sparsity estimation value is changed by a small step size The sparsity estimation value with the minimum greedy reconstruction error is taken as the current optimal sparsity estimation value The specific method is as follows: the current sparsity estimation value is changed by a large step size The loop is approximated to the local optimal value to obtain the optimal sparsity estimation value. That is: Wherein, The sparsity estimation value with the minimum ROMP reconstruction error is taken as the current optimal sparsity estimation value, and i is the current column number.

[0036] The measurement matrix, the sub-sampled signal, and the optimal sparsity estimation value are taken as the input of the regularized orthogonal matching pursuit algorithm to obtain the sparse coefficient The optimal solution of the compressed sensing underdetermined equation is searched based on the minimum norm method, and the original signal can be accurately recovered.

[0037] The above is only the preferred embodiment of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and adjustments can be made, and these improvements and adjustments should be considered as the protection scope of the present application.

Claims

1. A sparsity estimation compressive sensing reconstruction method, characterized in that, The method is used in space-based high-speed moving target inverse synthetic aperture radar imaging, and a linear relationship between the sum of pixel values of each column of the image and the real sparsity is found through statistical analysis, specifically: An error function is established, as shown in equation (1): Wherein, x is the sum of pixel values of the image, y is the real sparsity, n is the total number of columns of the image, and i is the current column number; the error function coefficients θ0 and θ1 are determined by derivation of the error function; The initial sparsity estimation value is obtained by least square fitting the sparsity estimation function, specifically, the sum of the element values of each column of the sparse signal to be reconstructed is calculated in sequence, ε is the pixel value of each point of the image to be reconstructed, i is the current column number, j is the current row number, and m is the total number of rows of the image to be reconstructed; the initial sparsity estimation value is obtained by substituting the following formula for calculation: Then, a local search method is used to obtain the sparsity estimation value meeting the set requirement, and finally, the original signal is recovered according to the sparsity estimation value meeting the set requirement, specifically: Local search around the initial sparsity estimate to get the best sparsity estimate: large step changes the current sparsity estimate Find the sparsity interval where the reconstruction error is successively reduced; small step changes The greedy reconstruction error minimum as the current best sparsity estimate The cycle approximation local optimum value, get the best sparsity estimate value, namely: wherein, denotes the sparsity estimate of the minimum ROMP reconstruction error, i is the current column number of the image to be reconstructed. The measurement matrix, the subsampling signal and the optimal sparsity estimation value are taken as inputs of a regularized orthogonal matching pursuit algorithm to obtain sparse coefficients An optimal solution of the compressed sensing underdetermined equation is found based on a minimum norm method to restore the original signal.

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