Azimuth multichannel SAR non-uniform sampling reconstruction method and system based on L2 regularization

Abstract

The invention discloses an azimuth multichannel SAR non-uniform sampling reconstruction method and system based on L2 regularization, and the method comprises the steps: carrying out the azimuth fast Fourier transform of echo data of each channel, and converting a signal from a two-dimensional time domain to a distance Doppler domain; calculating a transmission matrix based on the radar parameters, the platform parameters, the antenna parameters and the Doppler center; carrying out SVD (Singular Value Decomposition) on the channel transmission matrix, calculating a signal-to-noise ratio scaling factor phi bf according to the matrix subjected to SVD, and setting a threshold value of the acceptable signal-to-noise ratio scaling factor; a parameter lambda is introduced, a reconstructed filter and a reconstructed signal-to-noise ratio scaling factor are calculated, and the parameter is adjusted until the signal-to-noise ratio scaling factor reaches a threshold value; and calculating a reconstruction filter and reconstructing each Doppler frequency point in the azimuth direction to obtain the reconstructed azimuth direction frequency, and performing SAR imaging according to the reconstructed data. According to the method, the noise amplification problem caused in the matrix inversion process is suppressed.

Description

Technical Field

[0001] The present invention belongs to the technical field of synthetic aperture radar (SAR) signal processing, and particularly relates to a method and system for reconstructing non-uniform sampling of azimuth multi-channel SAR based on L2 regularization. Background Technique

[0002] Constrained by the minimum antenna area limitation, traditional single-channel SAR cannot achieve both high resolution and wide swath imaging simultaneously. Azimuth multi-channel SAR uses a wide-beam antenna to transmit pulse signals at a low pulse repetition frequency (PRF) to ensure a wide swath; at the same time, it uses multiple receiving antennas distributed along the azimuth direction to receive the echo signals reflected by the target simultaneously, supplementing temporal sampling with spatial sampling, so that the equivalent PRF is M (number of receiving channels) times the actual PRF of the system to ensure high azimuth resolution. Therefore, azimuth multi-channel SAR can get rid of the constraint of the minimum antenna area limitation and achieve high-resolution wide-swath imaging. For multi-channel SAR to achieve unambiguous imaging, it must meet the condition of uniform sampling. However, affected by factors such as orbit bending and waveform design, azimuth multi-channel SAR will inevitably have the problem of non-uniform sampling during actual operation, resulting in the generation of azimuth ambiguity. In order to achieve azimuth unambiguous imaging, the azimuth signal spectrum must be accurately reconstructed before spaceborne multi-channel SAR imaging processing.

[0003] Existing methods for reconstructing multi-channel SAR data can be divided into time-domain methods and frequency-domain methods. Time-domain methods cover two techniques: interpolation and interleaving, while frequency-domain methods are divided into two major categories: non-adaptive and adaptive. In non-adaptive frequency-domain methods, common methods include matrix inversion method; while in adaptive frequency-domain methods, there are space-time adaptive processing (STAP), maximum signal-to-noise ratio method, minimum mean square error method (MMSE), etc.

[0004] When discussing the main principle of multi-channel high-resolution wide-swath SAR, an ideal condition is assumed, that is, the azimuth is uniformly sampled. However, in practice, this strict condition is not fully satisfied in most cases because of other timing diagram limitations, such as the need to exclude nadir echoes and avoid interference between transmission and reception events. For uniform sampling, the above-mentioned reconstruction algorithms can all work well and can achieve optimal performance. However, for the case of non-uniform sampling, its imaging performance drops significantly. Although Krieger's DBF algorithm can solve the case of medium non-uniform sampling to a certain extent, when highly non-uniform sampling occurs, its performance will be severely affected because the DBF filter will significantly amplify the noise power. For some PRFs with overlapping spatial sampling points, Krieger's DBF algorithm even fails due to the matrix singularity problem. Summary of the Invention

[0005] The object of the present invention is to provide a method and system for reconstructing non-uniformly sampled azimuth multi-channel SAR based on L2 regularization.

[0006] The technical solution for realizing the present invention is: A method for reconstructing non-uniformly sampled azimuth multi-channel SAR based on L2 regularization, comprising the following steps:

[0007] Step 1: Reorganize the SAR echo data according to the channel number, perform fast Fourier transform in the azimuth direction on the echo data of each channel, and transform the signal from the two-dimensional time domain to the range-Doppler domain;

[0008] Step 2: Calculate the transmission matrix based on radar parameters, platform parameters, antenna parameters, Doppler center f dc and so on.

[0009] Step 3: Perform SVD decomposition on the channel transmission matrix, and calculate the signal-to-noise ratio scaling factor Φ bf according to the matrix after SVD decomposition, and set the threshold of the acceptable signal-to-noise ratio scaling factor;

[0010] Step 4: Introduce the parameter λ, calculate the reconstruction filter and the signal-to-noise ratio scaling factor after reconstruction, and adjust the parameter until the signal-to-noise ratio scaling factor reaches the threshold.

[0011] Step 5: Calculate the reconstruction filter and perform reconstruction on each Doppler frequency point in the azimuth direction to obtain the reconstructed azimuth frequency, and perform SAR imaging based on the reconstructed data.

[0012] Assume that the signal of the m-th channel at f b has a frequency of S m (f b ), then

[0013] S(f b ) = W r (f b )S c (f b )

[0014] where S c (f b ) = [S1(f b ), S2(f b ), …, S M (f b )] T , S(f b ) = [S(f b + i min f p ), …, S(f b + ifp ),..., S(f b +i max f p )] T represents the values of the non-ambiguous echo signal in different aliasing intervals;

[0015] For each Doppler frequency point f b ∈[-f p / 2, f p / 2], reconstruction is performed to recover the spectrum.

[0016] Furthermore, step 2: Based on radar parameters, platform parameters, antenna parameters, and Doppler center f dc , etc., calculate the transmission matrix A(f b ), specifically:

[0017]

[0018] where a i (f b ) is the steering vector of the Doppler frequency shift at f b +if p , f b is the instantaneous frequency of the radar in the azimuth direction, and f b is the pulse repetition frequency of the radar.

[0019] a i (f b ) = [H1(f b +if p )H2(f b +if p )…H M (f b +if p )] T

[0020] H m (f b +i·f p ) = exp[j2π(f b +i·f p )x m / v]

[0021] Assume that the number of azimuth channels of the multi-channel SAR is M. When M is odd, f b ∈[-f p / 2, f p / 2], and the value range of i is {-(M - 1) / 2,..., (M - 1) / 2}. If M is even, f b ∈[0, fp , the value range of i is {-M / 2, ……, M / 2 - 1}, x m is the position of each channel relative to the reference channel, where the reference channel is selected as the first channel, and v is the speed of the satellite traveling.

[0022] Furthermore, in step 3, perform SVD decomposition on the channel transmission matrix and calculate the signal-to-noise ratio scaling factor Φ according to the matrix after SVD decomposition bf , and set the threshold of the acceptable signal-to-noise ratio scaling factor, specifically:

[0023] Decompose the transmission matrix A(f b ) into a diagonal matrix D(f b ) that varies with f b and a Vandermonde matrix A that is independent of f b :

[0024]

[0025] Assume the SVD decomposition of A is A = U∑V H , both U and V are unitary matrices, and ∑ is a diagonal matrix containing the singular values of the A matrix. Combining with A(f b ) gives A(f b ) = D(f b )A = D(f b )U∑V H , since D(f b )U is also a unitary matrix, the SVD decomposition of A(f b ) is expressed as:

[0026] A(f b ) = D(f b )U∑V H = U(f b )∑V H

[0027] Define the original signal-to-noise ratio scaling factor Φ bf as the ratio of the input signal-to-noise ratio SNR in before reconstruction and the output signal-to-noise ratio SNR out after reconstruction, and its formula is:

[0028]

[0029] where 1 / σ i is the i-th singular value of the original channel transmission matrix reconstruction filter A -1 (f b ), σ i is the i-th singular value of the matrix A(f b ), which is equal to the value of the i-th diagonal of the ∑ matrix.

[0030] Furthermore, step 4: Introduce the parameter λ, calculate the reconstruction filter and the SNR scaling factor after reconstruction, and adjust the parameter until the SNR scaling factor reaches the threshold, specifically:

[0031] Write the reconstruction filter as:

[0032] W r (f b )=(A(f b ) H A(f b )+λI) -1 A(f b ) H

[0033] Substitute A(f b ) into W r (f b ) to get:

[0034] w r (f b )=V(∑ 2 +λI) -1 ∑U H D(f b ) H

[0035] The formula for the SNR scaling factor after reconstruction is:

[0036]

[0037] Set the initial value of λ to 0, compare the magnitudes of Φ r and the threshold K of the acceptable SNR scaling factor. If Φ r >K, then increase λ until Φ r ≤K.

[0038] Furthermore, step 5: Calculate the reconstruction filter and perform reconstruction for each Doppler frequency point in the azimuth direction to obtain the reconstructed azimuth frequency, and perform SAR imaging based on the reconstructed data, specifically:

[0039] Assume that the signal of the m-th channel at the frequency f b is S m (f b ). There is

[0040] S(f b )=W r (f b )S c (f b )

[0041] where Sc (f b ) = [S1(f b ), S2(f b ), …, S M (f b )] T , S(f b ) = [S(f b + i min f p ), …, S(f b + if p ), …, S(f b + i max f p )] T is a value representing the non-ambiguous echo signal in different aliasing intervals;

[0042] For each Doppler frequency point of f b ∈ [-f p / 2, f p / 2], reconstruction is performed, that is, the spectrum of is restored.

[0043] An azimuth multi-channel SAR non-uniform sampling reconstruction system based on L2 regularization, implementing the azimuth multi-channel SAR non-uniform sampling reconstruction method based on L2 regularization, to achieve azimuth multi-channel SAR non-uniform sampling reconstruction based on L2 regularization, and five modules are respectively used to execute steps 1 to 5.

[0044] A computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the azimuth multi-channel SAR non-uniform sampling reconstruction method based on L2 regularization is implemented to achieve azimuth multi-channel SAR non-uniform sampling reconstruction based on L2 regularization.

[0045] A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the azimuth multi-channel SAR non-uniform sampling reconstruction method based on L2 regularization is implemented to achieve azimuth multi-channel SAR non-uniform sampling reconstruction based on L2 regularization.

[0046] Compared with the prior art, the significant advantage of the present invention is that: based on the Krieger reconstruction matrix, L2 regularization constraint is used, and the Lagrange multiplier method is used to re-derive the reconstruction matrix of the multi-channel SAR transmission matrix, successfully suppressing the noise amplification problem caused during the matrix inversion process. Description of the Drawings

[0047] Figure 1This is the flowchart of the azimuth multi-channel SAR non-uniform sampling reconstruction method based on L2 regularization of the present invention.

[0048] Figure 2 This is the imaging comparison diagram between the method of the present invention and the matrix inversion method, where (a) is the direct imaging result, (b) is the matrix inversion result, and (c) is the result of the method of the present invention. Detailed implementation manners

[0049] In order to make the objectives, technical solutions and advantages of the present application clearer, the following further describes the present application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0050] As Figure 1 shown, a kind of azimuth multi-channel SAR non-uniform sampling reconstruction method based on L2 regularization of the present invention has the following specific implementation steps:

[0051] Step 1: Reorganize the SAR echo data according to the channel number, perform fast Fourier transform in the azimuth direction on the echo data of each channel, and transform the signal from the two-dimensional time domain to the range-Doppler domain;

[0052] Step 2: Calculate the transfer matrix A(f dc ) based on radar parameters, platform parameters, antenna parameters, Doppler center f b and so on;

[0053]

[0054] where a i (f b ) is the steering vector of the Doppler frequency shift at f b +if p , f b is the instantaneous frequency of the radar in the azimuth direction, and f p is the pulse repetition frequency of the radar.

[0055] a i (f b ) = [h1(f b +if p )H2(f b +if p )…H M (f b +if p )] T

[0056] H m (f b +i·f p ) = exp[j2π(f b+i·f p )x m / v]

[0057] Assume that the number of azimuth channels of the multi-channel SAR is M. When M is an odd number, f p ∈[-f p / 2,f p / 2], the value range of i is {-(M - 1) / 2, ……, (M - 1) / 2}. If M is an even number, f p ∈[0,f p , the value range of i is {-M / 2, ……, M / 2 - 1}, x m is the position of each channel relative to the reference channel, where the reference channel is selected as the first channel, and v is the speed of the satellite.

[0058] Step 3, perform SVD decomposition on the channel transmission matrix, and calculate the signal-to-noise ratio scaling factor Φ bf , and set the threshold of the acceptable signal-to-noise ratio scaling factor;

[0059] The transmission matrix A(f b ) can be decomposed into a diagonal matrix D(f b ) that varies with f b and a Vandermonde matrix A that is independent of f b :

[0060]

[0061] Assume that the SVD decomposition of A is A = U∑V H , where both U and V are unitary matrices, and ∑ is a diagonal matrix containing the singular values of the A matrix. Combining with A(f b ) can obtain A(f b ) = D(f b )A = D(f b )U∑V H . Since D(f b )U is also a unitary matrix, the SVD decomposition of A(f b ) can be expressed as:

[0062] A(f b ) = D(f b )U∑V H = D(f b )∑V H

[0063] The original signal-to-noise ratio scaling factor Φ bf is defined as the ratio of the input signal-to-noise ratio SNR in before reconstruction and the output signal-to-noise ratio SNR out after reconstruction, and its formula is:

[0064]

[0065] where 1 / σ i is the i-th singular value of the original channel transmission matrix reconstruction filter A -1 (f b ), σ i is the i-th singular value of matrix A(f b ), equal to the value of the i-th diagonal of the ∑ matrix. Set the threshold of the signal-to-noise ratio scaling factor Φ bf to be K.

[0066] Step 4: Introduce the parameter λ, calculate the reconstruction filter and the reconstructed signal-to-noise ratio scaling factor, and adjust the parameter until the signal-to-noise ratio scaling factor reaches the threshold.

[0067] The reconstruction filter can be written as:

[0068] W r (f b ) = (A(f b ) H A(f b ) + λI) -1 A(f b ) H

[0069] Substitute A(f b ) into W r (f b ) to get:

[0070] W r (f b ) = V(∑ 2 + λI) -1 ∑U H D(f b ) H

[0071] The formula for the reconstructed signal-to-noise ratio scaling factor is:

[0072]

[0073] Set the initial value of λ to 0, compare the magnitudes of Φ r and the threshold K. If Φ r > K, then increase λ until Φ r ≤ K.

[0074] Step 5: Calculate the reconstruction filter and perform reconstruction for each Doppler frequency point in the azimuth direction to obtain the reconstructed azimuth frequency, and perform SAR imaging based on the reconstructed data.

[0075] Assume that the signal of the m-th channel has a frequency of S at f b which is S m (f b ). There is

[0076] S(f b ) = W r (f b )S c (f b )

[0077] where S c (f b ) = [S1(f b ), S2(f b ), …, S M (f b )] T , and S(f b ) = [S(f b + i min f p ), …, S(f b + if p ), …, S(f b + i max f p )] T which represents the values of the unambiguous echo signal in different aliasing intervals;

[0078] For each Doppler frequency point of f b ∈[-f p / 2, f p / 2], reconstruction is performed, and then the spectrum of can be recovered.

[0079] In summary, based on the Krieger reconstruction matrix, the present invention uses L2 regularization constraints and re-derives the reconstruction matrix of the multi-channel SAR transmission matrix using the Lagrange multiplier method, successfully suppressing the noise amplification problem caused during the matrix inversion process.

[0080] Embodiment

[0081] To verify the effectiveness of the solution of the present invention, the parameters of the GF-3 SAR satellite and the actual acquired data are used for verification.

[0082] In this embodiment, a multi-channel SAR signal with one transmit and five receives is simulated through the parameters of the GF-3 SAR satellite. The imaging result of non-uniform sampling is as shown in Figure 2 (a). Using the existing matrix inversion method and then performing subsequent multi-channel imaging processing operations, the obtained imaging result is as shown in Figure 2(b); The imaging result obtained after reconstruction using the L2 reconstruction filter of the present invention is as shown in Figure 2 (c). The azimuth ambiguity signals obtained by the existing matrix inversion method and the method used in the present invention are shown in Table 1. It can be seen that the present invention has good effects on noise suppression and reduction of azimuth ambiguity signals in the case of a high degree of non-uniform sampling, indicating the effectiveness of the method for non-uniform sampling noise suppression in azimuth multi-channel SAR.

[0083] Table 1 Results of azimuth ambiguity signal ratio

[0084] Method Azimuth Ambiguity Signal Ratio Matrix Inversion -29.84dB The method of the present invention -35.37dB

[0085] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0086] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for reconstructing non-uniformly sampled azimuth multi-channel SAR based on L2 regularization, characterized in that, It includes the following steps: Step 1: Reorganize the SAR echo data according to the channel number, perform azimuth fast Fourier transform on the echo data of each channel, and transform the signal from the two-dimensional time domain to the range-Doppler domain; Step 2: Calculate the transmission matrix based on radar parameters, platform parameters, antenna parameters, Doppler center f dc and so on Step 3: Perform SVD decomposition on the channel transmission matrix and calculate the signal-to-noise ratio scaling factor Φ based on the matrix after SVD decomposition bf , and set the threshold of the acceptable signal-to-noise ratio scaling factor Step 4: Introduce the parameter λ, calculate the reconstruction filter and the signal-to-noise ratio scaling factor after reconstruction, and adjust the parameter until the signal-to-noise ratio scaling factor reaches the threshold; Step 5: Calculate the reconstruction filter and perform reconstruction on each Doppler frequency point in the azimuth direction to obtain the reconstructed azimuth frequency, and perform SAR imaging based on the reconstructed data.

2. The azimuth multi-channel SAR non-uniform sampling reconstruction method based on L2 regularization according to claim 1, wherein Step 2: Based on radar parameters, platform parameters, antenna parameters, Doppler center f dc etc., calculate the transmission matrix A(f b ), specifically: where a i (f b ) is the steering vector of the Doppler shift at f b +if p , f b is the instantaneous frequency of the radar in the azimuth direction, and f b is the pulse repetition frequency of the radar. a i (f b ) = [H1(f b + if p )H2(f b + if p )…H M (f b + if p )] T H m (f b +i·f p )=exp[j2π(f b +i·f p )x m / v] Assume that the number of azimuth channels of a multi-channel SAR is M. When M is odd, f b ∈[-f p / 2,f p / 2], and the range of i is {-(M - 1) / 2, ……, (M - 1) / 2}. If M is even, f b ∈[0,f p , and the range of i is {-M / 2, ……, M / 2 - 1}. x m is the position of each channel relative to the reference channel, where the reference channel is selected as the first channel, and v is the velocity of the satellite's movement.

3. The method for reconstructing azimuth multi-channel SAR non-uniform sampling based on L2 regularization according to claim 1, characterized in that Step 3: Perform SVD decomposition on the channel transmission matrix and calculate the signal-to-noise ratio scaling factor Φ based on the matrix after SVD decomposition bf , set the threshold of the acceptable signal-to-noise ratio scaling factor, specifically: The transmission matrix A(f b ) decomposes into a random f b The changing diagonal matrix D(f b ) and one with f b The independent Vandermonde matrix A: Suppose the SVD decomposition of A is A = U∑V H , where U and V are both unitary matrices, and ∑ is a diagonal matrix containing the singular values of matrix A. Combining with A(f b ) gives A(f b ) = D(f b )A = D(f b )U∑V H . Since D(f b )U is also a unitary matrix, the SVD decomposition of A(f b ) is expressed as: A(f b ) = D(f b )U∑V H = U(f b )∑V H Scale the original signal-to-noise ratio factor Φ bf and define it as the ratio of the input signal-to-noise ratio SNR in before reconstruction to the output signal-to-noise ratio SNR out after reconstruction. The formula is as follows: where 1 / σ i is the original channel transfer matrix reconstruction filter A -1 (f b )'s ith singular value, σ i is the ith singular value of matrix A(f b ), equal to the value of the ith diagonal of the ∑ matrix.

4. The method for reconstructing non-uniform sampling of azimuth multi-channel SAR based on L2 regularization according to claim 1, wherein Step 4: Introduce the parameter λ, calculate the reconstruction filter and the signal-to-noise ratio scaling factor after reconstruction, and adjust the parameter until the signal-to-noise ratio scaling factor reaches the threshold, specifically: Write the reconstruction filter as: W r (f b )=(A(f b ) H A(f b )+λI) -1 A(f b ) H Substitute A(f b ) into W r (f b ) to obtain: W r (f b )=V(∑ 2 +λI) -1 ∑U H D(f b ) H The formula for the signal-to-noise ratio scaling factor after reconstruction is: Set the initial value of λ to 0 and compare it with Φ r and the threshold K of the acceptable signal-to-noise ratio scaling factor. If Φ r > K, then increase λ until Φ r ≤ K.

5. The method for reconstructing azimuth multi-channel SAR non-uniform sampling based on L2 regularization according to claim 1, wherein Step 5: Calculate the reconstruction filter and perform reconstruction on each Doppler frequency point in the azimuth direction to obtain the reconstructed azimuth frequency, and perform SAR imaging based on the reconstructed data, specifically: Assume that the signal of the m-th channel has a frequency of S b at f m (f b ), and there is S(f b ) = W r (f b )S c (f b ) Where S c (f b ) = [S1(f b ), S2(f b ), …, S M (f b )] T , S(f b ) = [S(f b + i min f p ), …, S(f b + if p ),..., S(f b + i max f p )] T is a value representing the unfuzzy echo signal in different aliasing intervals; For each Doppler frequency point f b ∈[-f p / 2, f p / 2], reconstruction is performed, that is, the spectrum of is restored.

6. A system for reconstructing non-uniform sampling of azimuth multi-channel SAR based on L2 regularization, which implements the method for reconstructing non-uniform sampling of azimuth multi-channel SAR based on L2 regularization according to any one of claims 1-5, and realizes the reconstruction of non-uniform sampling of azimuth multi-channel SAR based on L2 regularization, and executes steps 1-5 in five modules respectively.

7. A computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the method for reconstructing non-uniform sampling of azimuth multi-channel SAR based on L2 regularization according to any one of claims 1-5, and realizes the reconstruction of non-uniform sampling of azimuth multi-channel SAR based on L2 regularization.

8. A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the method for reconstructing non-uniform sampling of azimuth multi-channel SAR based on L2 regularization according to any one of claims 1-5, and realizes the reconstruction of non-uniform sampling of azimuth multi-channel SAR based on L2 regularization.

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