A sparse SAR self-focusing imaging method based on undersampling echo

Abstract

The application discloses a kind of based on the sparse SAR self-focusing imaging method of undersampling echo, comprising: based on the echo data of random undersampling acquisition, construct sparse SAR self-focusing imaging model;Through sparse SAR self-focusing imaging model reconstruction observation scene;The azimuth signal of non-sparse solution of observation scene is FrFT, and rotation angle is updated;Calculate Doppler frequency error, update azimuth matching filter operator, and calculate echo simulation value;According to the value of echo simulation, estimate the sparse solution of observation scene;Repeat iteration until Doppler frequency error is less than the threshold value set, and output focused sparse SAR image.The application combines the Doppler frequency estimation algorithm based on FrFT with the sparse SAR imaging algorithm based on complex approximate information transmission, while solving the sparse solution of observation scene and the non-sparse solution of phase preservation, can effectively estimate the Doppler frequency of random undersampling echo data, obtain focused sparse SAR image.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of sparse signal processing and microwave imaging, and particularly relates to a sparse SAR self-focusing imaging method based on under-sampling echo. BACKGROUND

[0002] Synthetic Aperture Radar (SAR) is an active imaging radar, which uses the relative motion between its own real aperture antenna and the target to generate a larger equivalent antenna aperture to obtain high resolution in the azimuth direction, and has the characteristics of all-weather, all-day and strong penetration, and is widely used in civil and military fields.

[0003] The Doppler frequency accuracy in SAR imaging directly affects the quality of the SAR image, and inaccurate Doppler frequency will cause the defocusing of the SAR image. Due to factors such as air flow, the flight trajectory of the airborne SAR platform deviates from the ideal trajectory, and the motion error of the platform will cause the azimuth two-phase error of the echo data. The Doppler frequency estimation method based on echo data is also called self-focusing technology, and the classical self-focusing algorithm includes sub-aperture correlation method (MD), shift correlation method (SAC) and other technologies. The MD algorithm performs cross-correlation operation on two sub-aperture images in the azimuth direction, and estimates the Doppler frequency by using the position of the cross-correlation peak, and is widely used in practical engineering due to its small amount of calculation and easy implementation. As a generalization of Fourier transform, the fractional Fourier transform (FrFT) can accurately estimate the Doppler frequency under low signal-to-noise ratio conditions by using the focusing characteristics of the linear frequency modulation signal (LFM) in the specific fractional Fourier domain.

[0004] Sparse microwave imaging introduces sparse signal processing technology into SAR imaging, and realizes the low sidelobe and high resolution reconstruction of the scene by solving the L q (0<q≤1) regularization problem, and can realize the imaging of under-sampling echo. The traditional sparse self-focusing imaging algorithm is a two-step iterative method, which simultaneously solves the observed scene and the azimuth phase error as an optimization item. Due to the large amount of calculation, it is difficult to be applied in practical engineering. In recent years, sparse SAR fast self-focusing imaging algorithms have been continuously proposed. In each iteration of sparse reconstruction of the observed scene, the Doppler frequency of the simulated echo is estimated by using the MD self-focusing algorithm, and the azimuth matching filter operator is updated until the focused sparse SAR image is output. However, the estimation accuracy of the Doppler frequency is not ideal under the condition of random under-sampling of the echo, which leads to poor image focusing quality and unsatisfactory SAR imaging effect. SUMMARY

[0005] The application aims to overcome the defects in the prior art and provide a sparse SAR self-focusing imaging method based on undersampled echoes, which combines a Doppler frequency estimation algorithm based on FrFT with a sparse SAR imaging algorithm based on complex approximate message passing (CAMP) to effectively estimate the Doppler frequency of random undersampled echo data while solving the sparse solution of the observed scene and the phase-preserving non-sparse solution, and obtain a focused sparse SAR image.

[0006] The technical scheme is as follows: to achieve the above-mentioned purpose, the application provides a sparse SAR self-focusing imaging method based on undersampled echoes, which comprises the following steps:

[0007] S1: constructing a sparse SAR self-focusing imaging model based on the collected random undersampled echo data;

[0008] S2: reconstructing the observed scene through the sparse SAR self-focusing imaging model;

[0009] S3: performing FrFT on the azimuth signal of the non-sparse solution of the observed scene and updating the rotation angle;

[0010] S4: calculating the Doppler frequency error, updating the azimuth matching filter operator, and calculating the echo simulation value;

[0011] S5: estimating the sparse solution of the observed scene according to the echo simulation value;

[0012] S6: repeating steps S3-S5 for iteration until the Doppler frequency error is less than a set threshold value, and outputting a focused sparse SAR image.

[0013] Further, the expression of the sparse SAR self-focusing imaging model in step S1 is as follows:

[0014]

[0015] wherein Y represents random undersampled echo data with quadratic phase error; X represents the observed scene; P{·} represents an echo simulation operator, which is the inverse process of the classical matching filter SAR imaging algorithm; E is a range-varying azimuth quadratic phase error matrix; Θ a and Θ r are random undersampling matrices in the azimuth direction and the range direction, respectively; is Hadamard product; and N is Gaussian white noise.

[0016] Further, for the sparse SAR self-focusing imaging model in step S2, the observed scene is reconstructed by solving the following L1 norm regularization problem:

[0017]

[0018] Where λ is the regularization parameter.

[0019] Furthermore, in step S2, the CAMP algorithm is used to solve the L1 norm regularization problem. Unlike the traditional iterative soft thresholding (IST) algorithm, CAMP simultaneously obtains the sparse solution of the observation scene and the phase-preserving non-sparse solution, the latter of which can be used to estimate the Doppler frequency modulation error.

[0020] Furthermore, step S3 specifically includes:

[0021] A1: The non-sparse solution of the observation scene is

[0022]

[0023] Among them, R (n) {·} represents the matched filter imaging operator for the nth iteration, W (n) To simulate echo, For sparse solutions of the observed scene;

[0024] A2: For non-sparse solutions of the scene Range-oriented block processing is performed, and an FrFT with an angle of α is applied to the azimuth signal x(η) containing strong scattering points in each range block data.

[0025] u(k)=F α [x(η)]

[0026] Among them, F α This represents the FrFT operator with a rotation angle of α;

[0027] A3: Using the entropy of the fractional Fourier domain signal u(k) as the objective function, the optimal FrFT rotation angle of x(η) is solved using the gradient descent method. The entropy of u(k) is...

[0028]

[0029] in, The energy of u(k);

[0030] The rotation angle α in the nth iteration (n) (Hereinafter referred to as α) Updated to

[0031]

[0032] Where, γ (n) It is the update step size, the size of which is determined by the Armijo criterion.

[0033] Furthermore, in step A2, the FrFT operator F with a rotation angle of α... α The specific expression is:

[0034] Fα Further denoted as

[0035]

[0036] where H n，σ (x) is the Hermite-Gaussian basis function of order n and variance σ, i.e.

[0037]

[0038] where, is the n-th order Hermite polynomial, and further decompose the operator F α into eigenvalues, denoted as

[0039] F α = VDV H

[0040] where V is the Hermite-Gaussian function matrix, and D is the eigenvalue diagonal matrix, i.e.

[0041] D = diag{e 0 , e -jα , e -j2α ,..., e -j(N-1)α}.

[0042] Further, the rotation angle α update method in step A3 is:

[0043] The first-order partial derivative of I(α) with respect to α is

[0044]

[0045] where p(k) = u * (k)u(k), and the first-order derivative of p with respect to α is

[0046]

[0047] where Q = diag{0, -j1, -j2,..., -j(N-1)}, and the FrFT angle α update is

[0048] The Armijo criterion is as follows:

[0049] Given constants β ∈ (0, 1) and σ ∈ (0, 0.5), let the step factor γ = β m , where m is the smallest non-negative integer satisfying the following inequality

[0050] I(α + β m d) ≤ I(α) + σβ m g T d

[0051] where d is the descent direction of the function at iteration point a; g T denotes the negative direction of the gradient of the objective function.

[0052] Further, the step S4 specifically comprises:

[0053] B1: Calculate the Doppler frequency error, use the random sampling consensus algorithm (RANSAC) to linearly fit the Doppler frequency estimation value of the range-dependent, and according to the fitted Doppler frequency error, perform secondary phase error compensation on the non-sparse solution, and update the azimuth direction matching filter operator

[0054]

[0055] where PRF is the pulse repetition frequency, Na is the number of azimuth points, is the Doppler frequency estimation value after RANSAC algorithm fitting, f η is the azimuth frequency;

[0056] B2: Estimate the standard deviation of the "noise" matrix

[0057]

[0058] where K is the scene sparsity; denotes the amplitude image , all elements of which are sorted in descending order, and the amplitude value at the K+1th position;

[0059] B3: Calculate the value of the simulated echo

[0060]

[0061] where δ is the downsampling factor; ξ is the iteration parameter; the symbol <·> is the average operator; η R and η I are the real part and the imaginary part of the complex soft threshold function η, respectively.

[0062] Further, the expression of the sparse solution of the observed scene in the step S5 is:

[0063]

[0064] Further, the step S6 comprises: calculating the sparse solution residual, and judging whether it converges,

[0065]

[0066] If Residual is greater than a threshold value e1, or ΔKa is greater than a threshold value e2, return to step S3 to continue iteration until a maximum iteration number, otherwise end iteration and output focused sparse solution and non-sparse solution

[0067] The present application embeds the Doppler frequency estimation algorithm based on FrFT into the sparse SAR imaging algorithm based on CAMP algorithm, estimates and compensates the Doppler frequency error of the non-sparse solution of the scene in each iteration of the scene sparse reconstruction, so as to obtain a focused sparse SAR image.

[0068] Advantages: Compared with the prior art, the present application has the following advantages:

[0069] 1. Compared with the traditional sparse SAR imaging algorithm, the present application embeds the Doppler frequency estimation algorithm into the sparse SAR imaging algorithm based on CAMP, so as to obtain a focused and phase-preserving sparse SAR image.

[0070] 2. Compared with the classical SAR self-focusing imaging algorithm, the present application can obtain a more accurate Doppler frequency estimation value based on the undersampled echo data, so as to improve the image focusing quality and ensure the sparse imaging effect of SAR. BRIEF DESCRIPTION OF DRAWINGS

[0071] Figure 1 is a flowchart of the method of the present application;

[0072] Figure 2 is a comparison chart of imaging results provided in the present embodiment;

[0073] Figure 3 is a root mean square error chart of Doppler frequency estimation of the sparse SAR self-focusing imaging algorithm and the method of the present application under different echo undersampling ratios. DETAILED DESCRIPTION

[0074] The present application will be further illustrated below in combination with the drawings and specific embodiments, and it should be understood that these embodiments are only used to illustrate the present application and not used to limit the scope of the present application, and after reading the present application, various equivalent modifications of the present application by those skilled in the art all fall within the scope defined by the appended claims.

[0075] The present application provides a sparse SAR self-focusing imaging method based on undersampled echo, as shown in Figure 1 which includes the following steps:

[0076] S1: based on the acquired randomly undersampled echo data, constructing a sparse SAR self-focusing imaging model;

[0077] In an ideal case, the sparse SAR imaging model can be expressed as:

[0078] Y = P{X}Θ+N a P{X}Θ r +N

[0079] Where Y is the undersampled echo data; Θ a and Θ r are the azimuth and range random undersampling matrices respectively; P{·} represents the echo simulation operator; N is the Gaussian white noise.

[0080] However, the non-ideal motion of the SAR platform and other factors will introduce azimuth phase errors in the echo data, resulting in defocusing and distortion of the sparse SAR imaging results based on the above model. Among the types of phase errors caused by motion errors, the quadratic phase error is relatively typical. The present application only considers the quadratic phase error in the azimuth direction, and the expression of the sparse SAR autofocusing imaging model is:

[0081]

[0082] Where Y represents the random undersampled echo data with quadratic phase error; X represents the observed scene; P{·} represents the echo simulation operator, which is the inverse process of the classical matched filter SAR imaging algorithm; E is the azimuth quadratic phase error matrix which is range-varying; Θ a and Θ r are the azimuth and range random undersampling matrices respectively; is the Hadamard product; N is the Gaussian white noise.

[0083] S2: reconstructing the observed scene through the sparse SAR autofocusing imaging model;

[0084] For the above sparse SAR autofocusing imaging model, the observed scene is reconstructed by solving the following L1 norm regularization problem:

[0085]

[0086] Where λ is the regularization parameter, is the Hadamard product;

[0087] In the present application, the CAMP algorithm is used to solve the L1 norm regularization problem. Unlike the traditional iterative soft thresholding (IST) algorithm, CAMP simultaneously obtains the sparse solution of the observed scene and the phase-preserving non-sparse solution, which can be used for the estimation of the Doppler frequency error.

[0088] S3: performing FrFT on the azimuth signal of the non-sparse solution of the observed scene to update the rotation angle α, which specifically includes:

[0089] A1: the non-sparse solution of the observed scene is

[0090]

[0091] where R (n) {·} is the matched filter imaging operator of the nth iteration, W (n) is the simulated echo, is the sparse solution of the observed scene;

[0092] A2: The non-sparse solution of the scene is processed in the distance direction, and the azimuth signal x(η) containing strong scattering points in each distance block data is FrFTed at an angle of a, i.e.

[0093] u(k) = F α [x(η)]

[0094] where F α represents the FrFT operator with a rotation angle of a; F α is further represented as

[0095]

[0096] where H n，σ (x) is the Hermite-Gaussian basis function with order n and variance σ, i.e.

[0097]

[0098] where, is the n-order Hermite polynomial, and the operator F α is further decomposed into eigenvalues, represented as

[0099] F α = VDV H

[0100] where V is the Hermite-Gaussian function matrix, and D is the eigenvalue diagonal matrix, i.e.

[0101] D = diag{e 0 , e -jα , e -j2α ,..., e -j(N-1)α}.

[0102] A3: Taking the entropy of the fractional Fourier domain signal u(k) as the objective function, the optimal FrFT rotation angle of x(η) is solved by the gradient descent method, and the entropy of u(k) is

[0103]

[0104] where, is the energy of u(k);

[0105] the rotation angle of the n th iteration (n) is updated to

[0106]

[0107] where γ (n) is the update step size, which is determined by the Armijo rule;

[0108] The rotation angle α update method is:

[0109] The first-order partial derivative of I(α) with respect to α is

[0110]

[0111] where p(k)=u * (k)u(k), and the first-order derivative of p with respect to α is

[0112]

[0113] where Q=diag{0,-j1,-j2,...,-j(N-1)}, and the FrFT angle α is updated as

[0114] The Armijo rule is as follows:

[0115] Given a constant β∈(0,1) and σ∈(0,0.5), let the step factor γ=β m , where m is the smallest non-negative integer satisfying the following inequality

[0116]

[0117] where d is the descent direction of the function at the iteration point α; g T represents the negative direction of the gradient of the objective function.

[0118] S4: Calculate the Doppler frequency error, update the azimuth matching filter operator, and calculate the value of the echo simulation;

[0119] Specifically, it includes:

[0120] B1: Calculate the Doppler frequency error, use the random sampling consensus algorithm (RANSAC) to linearly fit the Doppler frequency error of the distance-varying Doppler frequency estimation value, perform secondary phase error compensation on the non-sparse solution according to the fitted Doppler frequency error, and update the azimuth matching filter operator:

[0121] Calculate the Doppler frequency error, and the corresponding relationship formula of the Doppler frequency K of the LFM signal and the FrFT rotation angle α is

[0122] K = cot (a / 2)

[0123] In actual engineering calculation, the dimensionless processing of discrete signals needs to be considered to obtain correct frequency estimation value. The discrete dimensionless normalization method is adopted in the application, and the Doppler frequency error estimation value is

[0124]

[0125] Wherein, Na is the number of echo azimuth points, and PRF is the transmission pulse repetition frequency.

[0126] The estimated distance-varying Doppler frequency is linearly fitted by using a random sampling consensus (RANSAC) algorithm, and the azimuth matching filter operator is updated as

[0127]

[0128] Wherein, PRF is the pulse repetition frequency, and f η represents the azimuth frequency, is the Doppler frequency fitted by the RANSAC algorithm.

[0129] B2: Estimate the standard deviation of the "noise" matrix

[0130]

[0131] Wherein, K is the scene sparsity; represents the amplitude image of all elements from large to small after sorting, and the amplitude value at the K+1th position;

[0132] B3: Calculate the value of the simulated echo

[0133]

[0134] Wherein, δ is the downsampling factor; ξ is the iteration parameter; the symbol <·> is the average operator; η R and η I are the real part and the imaginary part of the complex soft threshold function η, respectively; and represent the partial derivative with respect to the input element real part and imaginary part, respectively.

[0135] S5: Estimate the sparse solution of the observed scene according to the value of the echo simulation, and the expression of the sparse solution of the observed scene is:

[0136]

[0137] S6: Repeat steps S3-S5 for iteration until the Doppler frequency error is less than the set threshold value, and output the focused sparse SAR image.

[0138] Step S6 specifically comprises: calculating sparse solution residual, and judging whether it converges or not,

[0139]

[0140] If Residual is greater than threshold value e1, or ΔKa is greater than threshold value e2, return to step S3 to continue iteration until maximum iteration number, otherwise end iteration, and output focused sparse solution and non-sparse solution

[0141] In order to verify the effectiveness and effect of the method of the application, experimental verification is carried out in this embodiment, which is specifically as follows:

[0142] This embodiment verifies the method of the application by C-band Radarsat-1 satellite measured data, and the specific parameters are shown in Table 1:

[0143] Table 1 SAR system parameters

[0144]

[0145] The experimental results in this embodiment are shown in Figure 2 , wherein, Figure 2 (a) in (a) is the result of classical matching filter imaging on echo data with quadratic phase error; Figure 2 (b), (c), (d) in (b), (c), (d) are respectively the imaging results of the method for estimating SAR Doppler frequency based on undersampled echo and sparse imaging proposed by the application on full-sampling, 70% random undersampling, and 50% random undersampling echo data with quadratic phase error, based on full-sampling and random undersampling echo data, the method of the application can obtain focused sparse SAR image.

[0146] In order to further verify the effectiveness of the method of the application, the root mean square error (RMSE) of Doppler frequency estimation of the sparse SAR self-focusing imaging algorithm solved by IST and the method of the application under different echo undersampling ratios is compared through 100 Monte Carlo experiments, and the results are shown in Figure 3 . The experimental results show that for echo data with quadratic phase error, the method of the application can accurately estimate the Doppler frequency while obtaining the phase-preserving sparse SAR image, and can realize accurate estimation of the Doppler frequency and focusing of the sparse SAR image under the condition of echo undersampling.

Claims

1. A method for sparse SAR autofocusing based on undersampled echoes, characterized in that, The method comprises the following steps: S1: constructing a sparse SAR self-focusing imaging model based on the collected random undersampled echo data; S2: reconstructing an observed scene through the sparse SAR self-focusing imaging model; S3: performing FrFT on the non-sparse solution of the observed scene in the azimuth direction and updating the rotation angle; S4: calculating the Doppler frequency error, updating the azimuth matching filter operator, and calculating the value of the echo simulation; S5: estimating the sparse solution of the observed scene according to the value of the echo simulation; S6: repeating steps S3-S5 for iteration until the Doppler frequency error is less than a set threshold, and outputting a focused sparse SAR image.

2. The method of claim 1, wherein, The expression of the sparse SAR self-focusing imaging model in step S1 is: ； where Y denotes the random undersampling echo data with quadratic phase error; X denotes the observed scene; represents the echo simulation operator, which is the inverse process of the classical matched filter SAR imaging algorithm; is the range-dependent azimuth quadratic phase error matrix; and are the random undersampling matrices in azimuth and range respectively; is the Hadamard product; N is the Gaussian white noise.

3. The method of claim 2, wherein, The step S2 is to reconstruct the observed scene by solving the following norm-regularized problem for the sparse SAR autofocusing imaging model: norm-regularized problem for the sparse SAR autofocusing imaging model: ； wherein is a regularization parameter.

4. The method of claim 3, wherein, The step S2 adopts the CAMP algorithm for solving Unlike the traditional iterative soft thresholding algorithm, the CAMP simultaneously obtains a sparse solution and a phase-preserved non-sparse solution of the observed scene.

5. The method of claim 4, wherein, Step S3 specifically comprises: A1: the non-sparse solution of the observed scene is ； wherein, is the matched filter imaging operator for the nth iteration, is the simulated echo, is the sparse solution of the observed scene; A2: Non-sparse solution to the scene Distance direction block processing is performed, and the azimuth direction signal containing strong scattering points in each distance block data is processed FrFT with an angle of , that is ； wherein, represents a FrFT operator with a rotation angle of ; A3: Entropy of fractional Fourier domain signal is taken as the objective function, the optimal FrFT rotation angle is solved by gradient descent method, the entropy of ； wherein, the energy of the light source; Rotation angle for the n-th iteration updated to ； wherein, is an update step size, the size of which is determined by the Armijo rule.

6. The method of claim 5, wherein, The rotation angle in the step A2 is The specific expression of the FrFT operator is: Further represented as ； where is the Hermite-Gaussian basis function of order n and variance σ, i.e. ； where are the n-th order Hermite polynomials, and further decomposing the operator into eigenvalues ； wherein V is a Hermite-Gaussian function matrix, and D is an eigenvalue diagonal matrix, that is, 。 7. The method of claim 5, wherein the method is based on undersampled echo. The rotation angle in step A3 The updating method is: For the first order partial derivative of ； wherein , p is the first derivative of with respect to ； wherein , FrFT angle updated to ; The Armijo criterion is as follows: Given constant , Let step factor where m is the smallest non-negative integer satisfying the inequality ； where d is the descent direction of the function at the iteration point ; denotes the negative direction of the gradient of the objective function.

8. The method of claim 5, wherein, Step S4 specifically comprises: B1: calculating the Doppler frequency error, performing linear fitting on the Doppler frequency estimation value of the range space variation by using a random sampling consensus algorithm, performing secondary phase error compensation on the non-sparse solution according to the fitted Doppler frequency error, and updating the azimuth matching filter operator ； ； where PRF is the pulse repetition frequency, Na is the number of azimuth points, is the Doppler frequency estimate after RANSAC algorithm fitting, is the azimuth frequency; B2: estimating the standard deviation of the noise matrix ； wherein, is a scene sparsity; denotes a magnitude image sorted in descending order, the magnitude value at the th position; B3: calculating the value of the simulated echo ； wherein is a downsampling factor; is an iteration parameter; symbol is an averaging operator; and are the real and imaginary parts of the complex soft threshold function respectively.

9. The method of claim 8, wherein, The expression of the sparse solution of the observed scene in step S5 is: 。 10. The method of claim 8, wherein, Step S6 comprises: calculating the sparse solution residual, and judging whether convergence is achieved, ； If Residual is greater than a threshold or greater than a threshold then return to step S3 for continued iterative execution until a maximum number of iterations, otherwise end the iteration and output the focused sparse solution and non-sparse solution .

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