CN108318891B - SAL data side lobe depression method based on improved SVA and CS - Google Patents

SAL data side lobe depression method based on improved SVA and CS Download PDF

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CN108318891B
CN108318891B CN201711214945.3A CN201711214945A CN108318891B CN 108318891 B CN108318891 B CN 108318891B CN 201711214945 A CN201711214945 A CN 201711214945A CN 108318891 B CN108318891 B CN 108318891B
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郭亮
薛心竹
李良超
冯喆珺
韩亮
邢孟道
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Abstract

The invention discloses an SAL data side lobe depression method based on improved SVA and CS, which solves the problems of higher SAL image data side lobe, poor imaging quality and insufficient image resolution. The implementation steps comprise: generating an initial data matrix of synthetic aperture laser radar imaging; constructing an improved SVA algorithm model, and processing the SAL data matrix by applying the model in the distance direction; constructing sparse signals and observation basis matrixes required by the CS; solving a compressed sensing underdetermined equation; generating an SAL image result matrix and carrying out imaging processing; and finishing the depression sidelobe processing of the SAL image data to obtain a high-resolution image. The invention combines the improved SVA algorithm with the CS, can inhibit side lobes, widen the main lobe, reduce the operation amount and the storage amount of SAL image data processing and more effectively reduce the side lobes of the synthetic aperture laser radar data on the premise of keeping the main lobe energy and the image resolution. The method is used for reducing echo noise in synthetic aperture laser radar imaging and improving SAL image resolution and image quality.

Description

SAL data side lobe depression method based on improved SVA and CS
Technical Field
The invention belongs to the technical field of radar data processing, relates to a data side lobe depression technology in a synthetic aperture laser radar, and particularly relates to a synthetic aperture laser radar (SAL) data side lobe depression method based on an improved spatial apodization method (SVA) and a compressed sensing reconstruction method (CS). The method is used for reducing echo noise in synthetic aperture laser radar imaging and improving SAL image resolution and image quality.
Background
The synthetic aperture laser radar (SAL) is a high-resolution imaging laser radar which utilizes an optical synthetic aperture technology and a coherent heterodyne detection technology, and has wide application prospect; in SAL imaging, laser echoes are doped with noise, so that the level of a side lobe is raised, the resolution of an image is affected, and therefore the side lobe depression processing is necessary; in addition, high side lobes of the strong scattering point target annihilate adjacent weak targets, which affects subsequent detection of the SAL image target, so that side lobe depression is also indispensable for improving the detection quality of the SAL target.
Aiming at the problem of higher side lobe of the SAL image, the traditional method realizes the side lobe depression by windowing in a signal frequency domain, but the method can cause the broadening of a main lobe and the reduction of resolution ratio besides realizing the side lobe depression, and influences the image quality of the SAL; in addition, the existing space apodization algorithm (SVA) is only effective for the signal of integral multiple Nyquist sampling, and simultaneously, the energy of the main lobe is lost, and the side lobe effect of suppressing the SAL image is not good; while the compressed sensing technology (CS) can also suppress side lobes and noise, implementing the technology first requires a certain sparsity of the processed signal, which is difficult to be applied in the SAL scene where the target scattering signal is non-sparse.
In the field of synthetic aperture laser radars, a new algorithm capable of suppressing side lobes more effectively on the premise of maintaining main lobe energy and image resolution is objectively needed.
Disclosure of Invention
Aiming at the problem that the imaging effect of SAL image sidelobe depression processing in the prior art is not ideal, the invention provides a synthetic aperture laser radar (SAL) data sidelobe depression method based on an improved spatial apodization method (SVA) and a compressed sensing reconstruction method (CS), which can improve the resolution ratio of an SAL image.
The invention relates to a SAL data sidelobe depression method based on improved SVA and CS, which is characterized by comprising the following steps:
step 1, generating an initial data matrix of synthetic aperture laser radar imaging: inputting actually measured SAL echo complex data to generate an M multiplied by N dimension SAL imaging initial data matrix X;
step 2, constructing an improved SVA algorithm model, and applying the model to process the SAL data matrix in the distance direction: performing distance-up improved SVA processing on the SAL initial data matrix, and performing non-integral multiple Nyquist resampling SVA processing to obtain a first result matrix of the SAL image with M x N dimensions and signal sparsity;
step 3, constructing sparse signals required by CS: performing signal normalization processing on each M-dimensional distance of a first result matrix of the SAL image in the M multiplied by N dimensions, and then performing sparse representation;
step 4, constructing an observation basis matrix required by the CS: setting independent and identically distributed Gaussian random matrixes as an observation base matrix of each M-dimensional signal in a first result matrix of the SAL image, and then compressing each M-dimensional signal by using the observation base matrix to obtain each M-dimensional compression result signal of the SAL image;
step 5, solving a compressed sensing underdetermined equation: solving a CS (circuit switched) underdetermined equation of each M-dimensional compression result signal of the SAL image in a linear programming solving mode to obtain each M-dimensional compression perception estimation vector of the SAL image and reconstruct an original signal of the SAL image;
step 6, generating an SAL image result matrix, and performing imaging processing: and generating a second result matrix of the SAL image in M multiplied by N dimensions according to each M-dimensional compressed sensing estimation vector, and performing imaging processing to obtain an SAL data side lobe depression result image based on the improved SVA and the CS.
Compared with the prior art, the method has the following advantages:
the invention firstly adopts an improved SVA algorithm, the improved SVA algorithm not only inherits the advantage that the original SVA algorithm can inhibit the side lobe of the image signal, but also can reduce the main lobe of the signal, thus further reducing the energy loss of the image and leading the SAL image to have higher resolution;
the invention improves the SVA algorithm processing of the SAL image, applies the compression perception reconstruction theory, properly utilizes the signal sparsity of the SAL image data matrix after the improved SVA algorithm, further reduces the side lobe of the SAL image signal, restores the useful signal and simultaneously reduces the operation amount and the storage amount of the data.
The invention creatively combines the improved SVA algorithm with the CS, can reduce the operation amount and the storage amount of SAL image data processing on the premise of keeping the main lobe energy and the image resolution, and more effectively reduces the data side lobe of the synthetic aperture laser radar.
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FIG. 1 is a flow chart of the present invention method for improving SAL data sidelobe depression based on SVA and CS;
FIG. 2 is a graph showing a relationship between a weighting function and a difference between a signal sampling point and a peak point;
fig. 3 is a comparison diagram of imaging effect of processing SAL data actually measured by the academy of sciences in china according to the present invention, in which fig. 3(a) is a diagram of direct imaging result of original SAL echo data, fig. 3(b) is a diagram of effect of data processing only by the improved SVA of the present invention, and fig. 3(c) is a diagram of effect of data processing according to the flow of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Example 1
The image generated by signal processing of the synthetic aperture laser radar echo not only contains target information to be detected, but also is doped with background noise, so that the side lobe level of image data is raised, and the image quality is poor, therefore, it is necessary to perform side lobe reduction processing on the affected SAL initial image, and the side lobe effect of the SAL image is poor in the prior art, so that the requirement of the SAL image with high resolution is difficult to meet, therefore, the invention provides a SAL data side lobe reduction method based on improved SVA and CS through innovation, and the method is shown in figure 1, and comprises the following steps:
step 1, generating an initial data matrix of synthetic aperture laser radar imaging: and (3) inputting a converted SAL echo image complex matrix by data conversion aiming at the actually measured SAL echo image to generate an SAL imaging initial data matrix X. To be subjected to the algorithmic processing of the subsequent steps.
Step 2, constructing an improved SVA algorithm model, and applying the improved SVA to process the SAL data matrix in the distance direction: and performing distance-up improved SVA processing on the SAL initial data matrix, and performing non-integral multiple Nyquist resampling SVA processing to obtain a first result matrix of the M × N dimension SAL image with signal sparsity, so as to inhibit side lobes, widen a main lobe and simultaneously sparsify signals.
Step 3, constructing sparse signals required by CS: and performing signal normalization processing on each M-dimensional distance of the first result matrix of the M multiplied by N-dimensional SAL image, and then performing sparse representation to prepare for subsequent CS reconstruction signal calculation. The invention processes each row of signals of a first result matrix of the SAL image in the dimension of M multiplied by N.
Step 4, constructing an observation basis matrix required by the CS: setting independent and identically distributed Gaussian random matrixes as an observation base matrix of each M-dimensional signal in a first result matrix of the M x N-dimensional SAL image, then compressing each M-dimensional signal by using the observation base matrix to obtain each M-dimensional compressed result signal of the SAL image, picking up useful information required by the SAL image, reducing data storage capacity, and preparing for subsequent CS signal reconstruction calculation.
Referring to fig. 1, the observation basis matrix design process in steps 3 and 4 of the present invention may be performed in parallel, or may not be performed in series, and is prepared for each M-dimensional signal compression process of the subsequent M × N dimensional SAL image.
Step 5, solving a compressed sensing underdetermined equation: and solving the CS underdetermined equation of each M-dimensional compression result signal of the SAL image in a linear programming solving mode, reconstructing an original signal of the SAL image, and obtaining each M-dimensional compression perception estimation vector of the SAL image, namely completing the compression perception estimation of N M-dimensional signal vectors.
The compressed sensing technology needs to be based on sparse signals and needs to construct an observation basis matrix, so that steps 3 and 4 of the method are used for laying a cushion for solving CS underdetermined equations and reconstructing original signals of SAL images.
Step 6, generating an SAL image result matrix, and performing imaging processing: and directly generating an M multiplied by N dimensional SAL image second result matrix according to each M dimensional compressed sensing estimation vector, and carrying out imaging processing on the M multiplied by N dimensional SAL image second result matrix to obtain an SAL data side lobe depression result image based on the improved SVA and the improved CS.
In the prior art, SVA is independently adopted for side lobe reduction processing, and CS is independently adopted for side lobe reduction processing.
Example 2
Similar to embodiment 1, the process of obtaining the first result matrix of the SAL image in M × N dimensions in step 2 includes:
2a) improvement of SVA algorithm:
performing distance-direction improved SVA algorithm processing on an M multiplied by N dimension data matrix X of an initial SAL image, performing same improved SVA algorithm processing on a real part and an imaginary part of each line of data respectively, taking the real part as an example, recording the real part of each line of data as an M dimension signal vector I, taking M as a positive integer, and performing non-integral multiple Nyquist resampling on the signal vector I to obtain an output signal vector I0：
I0(n)＝I(n)+α(n)*(I(n-1/Ns)+I(n+1/Ns))
Wherein, I (N) represents the nth sampling point data of the signal vector I, N is the serial number of X line number, N is more than or equal to 1 and less than or equal to M, N is a positive integer, 1/NsIs a non-integral multiple of the Nyquist sampling rate, 0 < NsAlpha (n) is a weighting function of the sum of the data items of the sample points equally spaced before and after n, I0And (n) is the output value of the nth sampling point data I (n) in the signal vector I after non-integral multiple Nyquist resampling. For corresponding output values where n is in the interval 1 to M, the whole constitutes an output signal vector.
The invention improves the mode of resampling by utilizing integral multiple Nyquist sampling rate in the original SVA algorithm, resamples by adopting non-integral multiple Nyquist sampling rate to obtain an output signal vector, narrows the main lobe while suppressing the side lobe of the signal, and reduces the energy loss of the main lobe.
2b) In order to minimize the signal output sidelobe energy, the real part energy and the imaginary part energy of the signal need to be simultaneously minimized, and taking the real part as an example, the weighting function α (n) of the sum of n front and back equally spaced data items should satisfy the calculation formula:
Figure BDA0001485338090000061
where d represents the derivative operation, | I0(n)2Is the energy of the real part of the signal.
Obtaining a solving expression of the weighting function α (n):
α(n)＝-I(n)/(I(n-1/Ns)+I(n+1/Ns)) (2)
when n is equal to0As the signal peak point, the expression of the amplitude value at the signal sampling point is considered:
I(n)＝sinc[Ns(n-n0)]substituting the expression into an expression (2) to obtain a deformed solving expression of alpha (n):
Figure BDA0001485338090000062
the expression contains information that the value of the non-integer multiple Nyquist resampling weighting function changes with the distance between the sampling point and the peak point, when | n-n0When | < 1, the sampling point is in the range of the main lobe, the data of the sampling point should be kept, and at this time, alpha (n) < 0; when | n-n0When | ≧ 1, the sampling point is in the side lobe area, the sampling point data should be discarded, at this time, α (n) is not less than 0 and not more than 0.5, which is equivalent to the analysis conclusion of the original SVA algorithm resampling by integer multiple Nyquist.
2c) Constructing an improved SVA algorithm model:
in order to further reduce side lobes and inhibit main lobe broadening, an improved SVA algorithm for resampling at a non-integer Nyquist sampling rate optimizes the value taking conditions of a weighting function of signal output, and according to the difference of the values of the weighting function alpha (n), any sampling point data I (n) in a signal vector I is obtained, and different output values I (n) are obtained after the data I (n) is processed by the non-integer Nyquist resampling improved SVA algorithm0m(n)：
Figure BDA0001485338090000071
Referring to fig. 2, fig. 2 is a graph showing a relationship between a weighting coefficient and a difference between a signal sampling point and a peak point, wherein γ is used to reduce a width of a main lobe and improve a resolution of an imageminLess than zero, which makes the distance between the sampling point and the peak point less than 1/Ns(ii) a In order to effectively recover the weak target main lobe from the side lobes of a plurality of strong targets and restore the real SAL scene, gamma is usedmaxGreater than 1/2.
And performing same non-integral multiple Nyquist resampling improvement SVA algorithm processing on imaginary parts of N columns of signal vectors of an M multiplied by N dimension data matrix X of the initial SAL image, and generating an M multiplied by N dimension SAL image first result matrix, wherein M represents the row number of the M multiplied by N dimension SAL image first result matrix, and N represents the column number of the M multiplied by N dimension SAL image first result matrix.
The improved SVA algorithm model constructed by the invention comprehensively reflects the requirement of image resolution to be improved in SAL scene, and describes a novel nonlinear inhibition method of SAL image data side lobe.
The improved SVA algorithm used by the invention not only inherits the advantage that the original SVA algorithm can inhibit the signal side lobe, but also can reduce the signal main lobe, further reduce the energy loss, enable the SAL image to have better resolution, and enable the SAL image data to have signal sparsity, thereby creating conditions for the next compressed sensing processing.
Example 3
The same as the embodiment 1-2, the process of constructing the sparse signal required by CS in step 3 includes:
3a) performing the same normalization processing on all M-dimensional signal vectors of the first result matrix of the M × N-dimensional SAL image, recording one M-dimensional signal vector of all M-dimensional signals as I ', and performing normalization processing on the signal vector I' to obtain an expression:
I”＝-orth(I')
wherein orth represents a normalization operation on a vector, I ″ represents an M-dimensional signal vector after normalization processing on a signal vector I', and I | ═ 1;
3b) thinning the signal representation, setting an M multiplied by M dimension sparse basis matrix psi as an M multiplied by M dimension identity matrix,
the M-dimensional signal vector I "is expressed as:
I”＝ψ*s
here, ψ denotes a sparse basis matrix of an M-dimensional signal vector I ", s denotes a sparse coefficient of I" on ψ, and is an M × 1-dimensional vector, and in the present embodiment, s ═ I ".
In the invention, the real part and the imaginary part of SAL image data are sparsely represented by columns, so that the data processing is convenient, and after the signal vector I 'is normalized, an M multiplied by M dimensional unit matrix psi is set as a sparse basis matrix of a sparse signal vector I'.
Example 4
The method for reducing the side lobe of SAL data based on improved SVA and CS is the same as that in embodiments 1-3, and the process of constructing the observation basis matrix required for CS for each M-dimensional signal vector I ″ of the first result matrix of the M × N-dimensional SAL image described in step 4 is the same, and includes:
4a) determining a reasonable dimension of the observation basis matrix:
let us note that the observation basis matrix is an a × B dimensional matrix phi, a denotes the number of rows of phi, B denotes the number of columns of phi, B should be equal to the dimension M of the signal vector I ″, and a should satisfy the computational expression:
A＝fix(K*ln(M/K)*β)
where K denotes the number of nonzero elements contained in the M-dimensional signal vector I ″, ln denotes the natural logarithm of the solution, fix denotes the tail-end rounding operation, β is an observation coefficient, and β should be a value such that K < a < M, where β is 1 in this embodiment. For the M-dimensional signal vector I ', the row number A of the observation basis matrix phi is fixedly valued as a result value obtained by substituting the K mean value of N M-dimensional signal vectors I' into the formula.
4b) Designing an observation basis matrix of the M-dimensional signal vector I':
the observation base matrix of the M-dimensional signal vector I 'is designed by making the observation base matrix phi irrelevant to the sparse base matrix psi and making a matrix formed by any A column vectors in the observation base matrix phi nonsingular, setting the observation base matrix as an A multiplied by B independent and identically distributed Gaussian random matrix, wherein the expression of the observation base matrix of the M-dimensional signal vector I' is as follows:
φ＝randn(A,B)+i*randn(A,B)
here, randn (a, B) represents an a × B-dimensional random matrix in which the mean is 0 and the variance is 1 in a normal distribution, and i represents an imaginary unit.
4c) Compression processing of an M-dimensional signal vector I ":
compressing the M-dimensional signal vector I' signal by using the observation basis matrix, wherein the compression processing expression is as follows:
Y＝φ*I”
wherein, Y represents the M-dimensional compression result vector after the compression processing of the M-dimensional signal vector I'.
The method determines the reasonable dimension of the observation basis matrix required by the CS, sets the independent and identically distributed Gaussian random matrix as the observation basis matrix of each M-dimensional signal in the first result matrix of the M x N-dimensional SAL image, and meets the design requirement of the observation basis matrix in the compressed sensing theory.
Example 5
The method for suppressing the side lobe of SAL data based on the improved SVA and CS is the same as the embodiments 1 to 4, and the process for solving the compressed sensing underdetermined equation in the step 5 includes:
5a) the mathematical expression of the compressed sensing underdetermined equation is as follows:
y＝φ*x
wherein x represents a sparse signal, phi represents an observation basis matrix, and y represents a compression result vector;
theoretically reconstructing the original signal by0Solving the signal reconstruction optimization problem under the norm, wherein the reconstruction expression is as follows:
Figure BDA0001485338090000101
where α denotes a sparse coefficient of x on ψ, and x ═ ψ α, the meaning of the reconstruction expression is to find an optimum estimated value α' when the number of non-zero elements in the vector α is minimized under the constraint of y ═ Φ ψ α.
5b) Reconstructing the SAL image original signal:
substituting an M-dimensional signal vector I ', a sparse coefficient s of the I' on a sparse basis matrix psi and an M-dimensional compression result vector Y into a compressed sensing underdetermined equation and a reconstructed expression;
converting the optimization problem of signal reconstruction in theory into a linear programming solving problem, wherein the expression is as follows:
Figure BDA0001485338090000102
thereby obtaining an estimate s' of the sparse coefficient s;
the compressed perceptual evaluation value expression of any M-dimensional signal vector I' of the first result matrix of the M × N-dimensional SAL image is as follows:
I”'＝ψ*s'
wherein ψ represents a sparse basis matrix, I '"represents a compressed perceptual estimation value of the original signal I", and I' "is an M-dimensional vector.
In the step of reconstructing the original signal by carrying out compressed sensing processing on the first result matrix of the SAL image in the dimension of M multiplied by N, the linear programming mode is adopted to solve the underdetermined equation, and the method is a reasonable transformation method for the optimization problem of signal reconstruction.
A more detailed example is given below, which is taken in conjunction with the accompanying drawings to further illustrate the present invention.
Example 6
The method for suppressing the side lobe of the SAL data based on the improved SVA and CS is the same as the embodiment 1-5, and fig. 1 is a flow chart of the method for suppressing the side lobe of the SAL data based on the improved SVA and CS of the present invention; the SAL data sidelobe depression method based on the improved SVA and CS comprises the following steps:
step 1, generating an initial data matrix of synthetic aperture laser radar imaging: inputting an actually measured SAL echo complex matrix, generating an SAL imaging initial data matrix X, and carrying out algorithm processing on the SAL imaging initial data matrix X to implement subsequent steps.
Specifically, the initial SAL image data matrix X is generated as follows: the method comprises the steps of intercepting an M multiplied by N dimensional complex matrix corresponding to an interested region from an actual measurement SAL echo complex matrix of Chinese academy of sciences, recording the M multiplied by N dimensional complex matrix as an initial SAL image data matrix X, wherein M represents the row number of the initial SAL image data matrix X, N represents the column number of the initial SAL image data matrix X, and M and N are positive integers respectively.
Referring to fig. 3(a), it is a diagram of the initial SAL image data matrix X direct imaging result.
Step 2, processing the SAL data matrix by applying the improved SVA in the distance direction: and performing distance-up improved SVA processing on the SAL initial data matrix, and performing non-integral multiple Nyquist resampling SVA processing to obtain a first result matrix of the M × N dimension SAL image with signal sparsity, so as to inhibit side lobes, widen a main lobe and simultaneously sparsify signals.
2a) The method includes the steps of performing distance direction zero filling operation on an initial SAL image data matrix X to obtain an M '× N' dimension statistical matrix X 'after initial SAL image zero filling, wherein the longitudinal direction is the distance direction, the transverse direction is the azimuth direction, M' represents the row number of the M '× N' dimension statistical matrix X 'after initial SAL image zero filling, N' represents the column number of the M '× N' dimension statistical matrix X 'after initial SAL image zero filling, M' ═ M + L, N '═ N,1 < L < M, L is the number of row zero filling of the M' × N 'dimension statistical matrix X' after initial SAL image zero filling, and L, M 'and N' are positive integers respectively.
Performing distance-direction improved SVA algorithm processing on an M multiplied by N dimension data matrix X of an initial SAL image, performing same improved SVA algorithm processing on a real part and an imaginary part of each line of data respectively, taking the real part as an example, recording the real part of each line of data as an M dimension signal vector I, taking M as a positive integer, and performing non-integral multiple Nyquist resampling on the signal vector I to obtain an output signal vector I0：
I0(n)＝I(n)+α(n)*(I(n-1/Ns)+I(n+1/Ns))
Wherein, I (N) represents the nth sampling point data of the signal vector I, N is the serial number of X line number, N is more than or equal to 1 and less than or equal to M, N is a positive integer, 1/NsIs a non-integral multiple of the Nyquist sampling rate, 0 < Ns< 1, in this example, take N s1/L, alpha (n) is a weighting function of the sum of the data items of the sampling points at equal intervals before and after n, I0(n) is letterAnd (3) the nth sampling point data I (n) in the number vector I is the output value after non-integral multiple Nyquist resampling. For corresponding output values where n is in the interval 1 to M, the whole constitutes an output signal vector.
2b) In order to minimize the signal output sidelobe energy, the real part energy and the imaginary part energy of the signal need to be simultaneously minimized, and taking the real part as an example, the weighting function α (n) of the sum of n front and back equally spaced data items should satisfy the calculation formula:
Figure BDA0001485338090000121
where d represents the derivative operation, | I0(n)|2Is the energy of the real part of the signal.
Obtaining a solving expression of the weighting function α (n):
α(n)＝-I(n)/(I(n-1/Ns)+I(n+1/Ns)) (2)
when n is equal to0As the signal peak point, the expression of the amplitude value at the signal sampling point is considered: i (N) sinc [ N ]s(n-n0)]Substituting the expression into an expression (2) to obtain a deformed solving expression of alpha (n):
Figure BDA0001485338090000131
2c) constructing an improved SVA algorithm model:
in order to further reduce side lobes and inhibit main lobe broadening, an improved SVA algorithm for resampling at a non-integer Nyquist sampling rate optimizes the value taking conditions of a weighting function of signal output, and according to the difference of the values of the weighting function alpha (n), any sampling point data I (n) in a signal vector I is obtained, and different output values I (n) are obtained after the data I (n) is processed by the non-integer Nyquist resampling improved SVA algorithm0m(n)：
Figure BDA0001485338090000132
Referring to FIG. 2, FIG. 2 shows weighting coefficients and signal samplesThe relation curve diagram of the difference between the points and the peak value points is that in order to reduce the width of the main lobe and improve the image resolution, the gamma is setminLess than zero, which makes the distance between the sampling point and the peak point less than 1/Ns(ii) a In order to effectively recover the weak target main lobe from the side lobes of a plurality of strong targets and restore the real SAL scene, gamma is usedmaxGreater than 1/2. In this embodiment, let γmax＝-γmin＝0.89。
And performing same non-integral multiple Nyquist resampling improvement SVA algorithm processing on imaginary parts of N columns of signal vectors of an M multiplied by N dimension data matrix X of the initial SAL image, and generating an M multiplied by N dimension SAL image first result matrix, wherein M represents the row number of the M multiplied by N dimension SAL image first result matrix, and N represents the column number of the M multiplied by N dimension SAL image first result matrix.
Referring to fig. 3(b), it is a diagram of the effect of the SAL image data processing by the improved SVA algorithm of the present invention.
Step 3, constructing sparse signals required by CS: performing signal normalization processing on each M-dimensional distance of a first result matrix of the SAL image in the M multiplied by N dimensions, and then performing sparse representation to prepare for subsequent CS reconstruction signal calculation;
3a) for convenience of data processing, all M-dimensional signal vectors of the first result matrix of the M × N-dimensional SAL image are subjected to the same normalization processing, one M-dimensional signal vector of all M-dimensional signals is recorded as I ', and an expression after normalization processing on the signal vector I' is as follows:
I”＝-orth(I')
wherein orth represents a normalization operation on a vector, I ″ represents an M-dimensional signal vector after normalization processing on a signal vector I', and I | ═ 1;
3b) the reason why the signal representation is thinned is that any M-dimensional signal vector of the first result matrix of the M × N-dimensional SAL image obtained after the initial SAL image data matrix X is processed by the distance-wise improved SVA algorithm in this embodiment is a sparse signal vector, and the M-dimensional signal vector I ″ is sparsely expressed as:
I”＝ψ*s
here, ψ denotes a sparse basis matrix of an M-dimensional signal vector I ", s denotes a sparse coefficient of I" on ψ, and is an M × 1-dimensional vector, and in the present embodiment, s ═ I ".
Step 4, constructing an observation basis matrix required by the CS: setting independent and identically distributed Gaussian random matrixes as an observation base matrix of each M-dimensional signal in a first result matrix of the M x N-dimensional SAL image, then compressing each M-dimensional signal by using the observation base matrix to obtain each M-dimensional compressed result signal of the SAL image, picking up useful information required by the SAL image, reducing data storage capacity, and preparing for subsequent CS signal reconstruction calculation.
4a) Determining a rational dimension of the observation basis matrix;
specifically, let us note that the observation base matrix is a matrix Φ of dimension a × B, a represents the number of rows of Φ, B represents the number of columns of Φ, B should be equal to dimension M of the signal vector I ″, and a should satisfy the computational expression:
A＝fix(K*ln(M/K)*β)
wherein, K represents the number of nonzero elements contained in the M-dimensional signal vector I ', ln represents the natural logarithm is obtained, fix represents the tail-cutting and integer-taking operation, beta is an observation coefficient, the value of beta is to ensure that K < A < M, and for the M-dimensional signal vector I ', the row number A of the observation base matrix phi is fixedly taken as a result value obtained by substituting the K mean value of N M-dimensional signal vectors I ' into the formula;
in this embodiment, β is 1.43, so the calculation expression may also be:
A＝fix(K*ln(M/K)*1.43)
4b) designing an observation basis matrix of the M-dimensional signal vector I':
the design method of the observation base matrix of the M-dimensional signal vector I 'is characterized in that in order to ensure equivalent distance, the observation base matrix phi is not related to the sparse base matrix psi, and a matrix formed by any A column vectors in the observation base matrix phi is nonsingular, in the embodiment, the observation base matrix is set to be an A multiplied by B independent and identically distributed Gaussian random matrix, and the observation base matrix expression of the M-dimensional signal vector I' is as follows:
φ＝randn(A,B)+i*randn(A,B)
here, randn (a, B) represents an a × B-dimensional random matrix in which the mean is 0 and the variance is 1 in a normal distribution, and i represents an imaginary unit.
4c) Compression processing of an M-dimensional signal vector I ":
compressing the M-dimensional signal vector I' signal by using the observation basis matrix, wherein the compression processing expression is as follows:
Y＝φ*I”
wherein, Y represents the M-dimensional compression result vector after the compression processing of the M-dimensional signal vector I'.
Step 5, solving a compressed sensing underdetermined equation: solving the CS underdetermined equation of each M-dimensional compression result signal of the SAL image in a linear programming solving mode, reconstructing an original signal of the SAL image, and obtaining each M-dimensional compression perception estimation vector of the SAL image, wherein the compression perception technology needs to take sparse signals as the basis and needs to construct an observation basis matrix, so that steps 3 and 4 of the method are used for laying a cushion for solving the CS underdetermined equation and reconstructing the original signal of the SAL image.
5a) The mathematical expression of the compressed sensing underdetermined equation is as follows:
y＝φ*x
wherein x represents a sparse signal, phi represents an observation basis matrix, and y represents a compression result vector;
theoretically reconstructing the original signal by0Solving the signal reconstruction optimization problem under the norm, wherein the reconstruction expression is as follows:
Figure BDA0001485338090000161
where α denotes a sparse coefficient of x on ψ, and x ═ ψ α, the meaning of the reconstruction expression is to find an optimum estimated value α' when the number of non-zero elements in the vector α is minimized under the constraint of y ═ Φ ψ α.
5b) Reconstructing the SAL image original signal:
in this embodiment, let x be I ═ s, Y be Y, and the sparse coefficients s of the M-dimensional signal vectors I ", I" on the sparse basis matrix ψ and the M-dimensional compression result vector Y are substituted into the compressed sensing underdetermined equation and the reconstruction expression, and the SAL image original signal reconstruction process is:
implementing a convex optimization algorithm, said convex optimization algorithm having the significance of0Norm minimization requires relaxation to l with equivalence thereto1Norm minimization is required, so that the theoretical optimization problem of signal reconstruction is converted into a linear programming solution problem, and the expression is as follows:
Figure BDA0001485338090000171
thus, an estimation s 'of the sparse coefficient s is obtained, and the expression of the compressed sensing estimation value of the original signal I' is as follows:
I”'＝ψ*s'
where ψ denotes a sparse basis matrix, I '"denotes a compressed perceptual estimation value of the original signal I", and in the present embodiment, I' "is s ', and I'" is an M-dimensional vector.
Step 6, generating an SAL image result matrix, and performing imaging processing: and generating a second result matrix of the SAL image in M multiplied by N dimensions according to each M-dimensional compressed sensing estimation vector, and performing imaging processing to obtain an SAL data side lobe depression result image based on the improved SVA and the CS.
Referring to fig. 3(c), on the basis of the synthetic aperture lidar result map obtained in step 2, the effect map obtained by performing data processing on the SAL image by using the CS algorithm is obtained after the SAL image is processed, which is also the effect map obtained by performing data processing based on the improved SVA and CS on the initial SAL image according to the flow of the present invention.
The design idea of the invention is as follows: firstly, generating an initial SAL image data matrix to be subjected to algorithm processing so as to implement subsequent steps; then, performing improved SVA (singular value analysis) processing on synthetic aperture laser radar imaging matrix distance direction data to inhibit side lobes and widen a main lobe, so that signals are thinned, and a first result matrix of an MXN-dimensional image is obtained; thus, the depression sidelobe and the thinning processing of the original image data by utilizing SVA are realized; then, performing sparse representation on any M-dimensional signal vector of the first result matrix of the M × N-dimensional image; then constructing an observation base matrix of any M-dimensional signal vector of the first result matrix of the M multiplied by N-dimensional image to compress signals and pick up useful information so as to reduce the data storage capacity; then solving a compressed sensing underdetermined equation and reconstructing an original signal; so far, the recovery of the sparse SAL image by using the CS is realized; finally, generating a second result matrix of the MxN dimensional image according to each row of compressed sensing estimation values, and performing imaging processing to obtain a synthetic aperture laser radar data side lobe depression result image; and finishing the depression sidelobe processing of the SAL image data to obtain a high-resolution image.
In short, the invention discloses a synthetic aperture laser radar (SAL) data side lobe depression method based on an improved spatial apodization method (SVA) and a compressed sensing reconstruction method (CS), which solves the problems of higher SAL image data side lobe, poor imaging quality and insufficient image resolution. The implementation steps comprise: generating an initial data matrix of synthetic aperture laser radar imaging; constructing an improved SVA algorithm model, and processing the SAL data matrix by applying the model in the distance direction; constructing sparse signals and observation basis matrixes required by the CS; solving a compressed sensing underdetermined equation; generating an SAL image result matrix and carrying out imaging processing; and finishing the depression sidelobe processing of the SAL image data to obtain a high-resolution image. The invention combines the improved SVA algorithm with the CS, can inhibit side lobes, widen the main lobe, reduce the operation amount and the storage amount of SAL image data processing and more effectively reduce the side lobes of the synthetic aperture laser radar data on the premise of keeping the main lobe energy and the image resolution. The method is used for reducing echo noise in synthetic aperture laser radar imaging and improving SAL image resolution and image quality.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (5)

1. A method for suppressing side lobe of SAL data based on improved SVA and CS is characterized by comprising the following steps:
step 1, generating an initial data matrix of synthetic aperture laser radar imaging: inputting actually measured SAL echo complex data to generate an M multiplied by N dimension SAL imaging initial data matrix X;
step 2, constructing an improved SVA algorithm model, and applying the model to process the SAL data matrix in the distance direction: performing distance-up improved SVA processing on the SAL initial data matrix, and performing non-integral multiple Nyquist resampling SVA processing to obtain a first result matrix of the SAL image with M x N dimensions and signal sparsity;
step 3, constructing sparse signals required by CS: performing signal normalization processing on each M-dimensional distance of a first result matrix of the SAL image in the M multiplied by N dimensions, and then performing sparse representation;
step 4, constructing an observation basis matrix required by the CS: setting independent and identically distributed Gaussian random matrixes as an observation base matrix of each M-dimensional signal in a first result matrix of the SAL image, and then compressing each M-dimensional distance direction signal after normalization processing by using the observation base matrix to obtain each M-dimensional compression result signal of the SAL image;
step 5, solving a compressed sensing underdetermined equation: solving a CS (circuit switched) underdetermined equation of each M-dimensional compression result signal of the SAL image in a linear programming solving mode to obtain each M-dimensional compression perception estimation vector of the SAL image and reconstruct an original signal of the SAL image;
step 6, generating an SAL image result matrix, and performing imaging processing: and generating a second result matrix of the SAL image in M multiplied by N dimensions according to each M-dimensional compressed sensing estimation vector, and performing imaging processing to obtain an SAL data side lobe depression result image based on the improved SVA and the CS.
2. The method of claim 1, wherein the step 2 of obtaining the first result matrix of the SAL image in M x N dimension comprises:
2a) performing distance-direction improved SVA algorithm processing on an M multiplied by N dimension data matrix X of an initial SAL image, performing same improved SVA algorithm processing on a real part and an imaginary part of each line of data respectively, taking the real part as an example, recording the real part of each line of data as an M dimension signal vector I, taking M as a positive integer, and performing non-integral multiple Nyquist resampling on the signal vector I to obtain an output signal vector I0：
I0(n)＝I(n)+α(n)*(I(n-1/Ns)+I(n+1/Ns))
Wherein, I (N) represents the nth sampling point data of the signal vector I, N is the serial number of X line number, N is more than or equal to 1 and less than or equal to M, N is a positive integer, 1/NsIs a non-integral multiple of the Nyquist sampling rate, 0 < Ns< 1, α (n) is a weighting function of the sum of n front and rear equally spaced data items, I0(n) is the output value of the nth sampling point data I (n) in the signal vector I after non-integral multiple Nyquist resampling;
2b) calculating a weighting function:
the solving expression of the weighting function α (n) is:
α(n)＝-I(n)/(I(n-1/Ns)+I(n+1/Ns))
2c) constructing an improved SVA algorithm model:
according to the difference of the values of the weighting function alpha (n), acquiring data I (n) of any sampling point in the signal vector I, and obtaining different output values I after non-integral multiple Nyquist resampling improvement SVA algorithm processing0m(n)：
Figure FDA0003151271500000021
Wherein, γminIs a real number less than zero, γmaxReal numbers greater than 1/2;
and performing the same processing on imaginary parts of N columns of signal vectors of an M multiplied by N dimension data matrix X of the initial SAL image, and generating an M multiplied by N dimension SAL image first result matrix, wherein M represents the row number of the M multiplied by N dimension SAL image first result matrix, and N represents the column number of the M multiplied by N dimension SAL image first result matrix.
3. The method as claimed in claim 1, wherein the step 3 of constructing the sparse signal required for CS comprises:
3a) performing the same normalization processing on all M-dimensional signal vectors of the first result matrix of the M × N-dimensional SAL image, recording one M-dimensional signal vector of all M-dimensional signals as I ', and performing normalization processing on the signal vector I' by using an expression:
I”＝-orth(I')
wherein orth represents a normalization operation on a vector, I ″ represents an M-dimensional signal vector after normalization processing on a signal vector I', and I | ═ 1;
3b) signal representation sparsification, expressing an M-dimensional signal vector I ″ as:
I”＝ψ*s
where ψ denotes a sparse basis matrix of an M-dimensional signal vector I ", and s denotes a sparse coefficient of I" on ψ, which is an M × 1-dimensional vector.
4. The method of claim 1, wherein the step 4 of constructing the observation basis matrix required by the CS comprises:
4a) determining a reasonable dimension of the observation basis matrix:
let us note that the observation basis matrix is an a × B dimensional matrix phi, a denotes the number of rows of phi, B denotes the number of columns of phi, B should be equal to the dimension M of the signal vector I ″, and a should satisfy the computational expression:
A＝fix(K*ln(M/K)*β)
wherein K represents the number of nonzero elements contained in the M-dimensional signal vector I', ln represents the natural logarithm calculation, fix represents the tail-cutting and rounding operation, and beta is an observation coefficient;
4b) designing an observation basis matrix of the M-dimensional signal vector I':
the observation base matrix of the M-dimensional signal vector I 'is designed by making the observation base matrix phi irrelevant to the sparse base matrix psi and making a matrix formed by any A column vectors in the observation base matrix phi nonsingular, setting the observation base matrix as an A multiplied by B independent and identically distributed Gaussian random matrix, wherein the expression of the observation base matrix of the M-dimensional signal vector I' is as follows:
φ＝randn(A,B)+i*randn(A,B)
wherein randn (A, B) represents obtaining an A multiplied by B dimension random matrix with a mean value of 0 and a variance of 1 normal distribution, and i represents an imaginary number unit;
4c) compression processing of an M-dimensional signal vector I ":
compressing the M-dimensional signal vector I' by using the observation basis matrix, wherein the compression processing expression is as follows:
Y＝φ*I”
wherein, Y represents the M-dimensional compression result vector after the compression processing of the M-dimensional signal vector I'.
5. The method of claim 1, wherein the step of solving the compressed sensing underdetermined equation in step 5 comprises:
5a) the mathematical expression of the compressed sensing underdetermined equation is as follows:
y＝φ*x
wherein x represents a sparse signal, phi represents an observation basis matrix, and y represents a compression result vector;
theoretically reconstructing the original signal by0Solving the signal reconstruction optimization problem under the norm, wherein the reconstruction expression is as follows:
Figure FDA0003151271500000041
wherein α represents a sparse coefficient of x on ψ, and x ═ ψ α, and the meaning of the reconstruction expression is to find an optimized estimated value α' when the number of non-zero elements in the vector α is minimized under the constraint of y ═ Φ ψ α;
5b) reconstructing the SAL image original signal:
substituting an M-dimensional signal vector I ', a sparse coefficient s of the I' on a sparse basis matrix psi and an M-dimensional compression result vector Y into a compressed sensing underdetermined equation and a reconstructed expression;
converting the optimization problem of signal reconstruction in theory into a linear programming solving problem, wherein the expression is as follows:
Figure FDA0003151271500000051
thereby obtaining an estimate s' of the sparse coefficient s;
the compressed perceptual evaluation value expression of any M-dimensional signal vector I' of the first result matrix of the M × N-dimensional SAL image is as follows:
I”'＝ψ*s'
where ψ denotes a sparse basis matrix, I '"denotes a compressed perceptual estimation value of the original signal I", I' "is s ', and I'" is an M-dimensional vector.
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