CN111562578A - A distributed array SAR sparse representation 3D imaging algorithm considering the real-value constraints of the scene amplitude - Google Patents

Abstract

The invention provides a distributed array SAR sparse representation three-dimensional imaging algorithm considering the real-value constraints of the scene amplitude. The algorithm adopts the sparse representation theory, expresses the complex scene as a combination of amplitude and phase, and uses the three-dimensional scene sparsity and the scene amplitude as Two kinds of prior information of real numbers are added to the regularized reconstruction model by adding the real-valued constraint term of the scene amplitude, and the quasi-Newton algorithm is used to estimate the scene amplitude and phase respectively, so as to complete the three-dimensional reconstruction that is more in line with the actual situation; this method is regularized reconstruction. Amplitude real-value constraints are added to the model to make the measurement model more reasonable and in line with the actual situation, which can achieve higher super-resolution and stronger high-resolution 3D imaging.

Description

Distributed Array SAR Sparse Representation 3D Imaging Considering Real-valued Constraints of Scene Amplitude algorithm

technical field

The invention relates to a distributed array SAR sparse representation three-dimensional imaging algorithm taking into account the real-value constraints of scene amplitude, and belongs to the field of application based on three-dimensional imaging design.

Background technique

Array SAR technology sparsely arranges array antennas with separate transceivers in the cross-course direction, and adopts the method of nadir observation to realize the azimuth direction and elevation direction of the observation object (equivalent to the distance of traditional SAR system) through synthetic aperture, pulse compression and beamforming technology respectively. direction) and three-dimensional resolution across headings, greatly improving the radar's regional information perception. This technology can realize the three-dimensional reconstruction of the observation area through a single straight-line navigation down-looking imaging method, which effectively solves the problems of the bottom blind area, shadow, geometric distortion and left and right blur of the traditional SAR technology; Baseline tomographic SAR, circular track SAR, etc.) technology has many problems such as multiple flights and difficult control of motion trajectories.

In foreign countries, the German Aerospace Center (DLR), the German Institute of Applied Sciences (FGAN), the Georgia Tech University, the Sandia Laboratory, and the French Defense Research Projects Agency have all carried out research on array SAR technology, but the results of 3D imaging have not been See announcement. In China, the research on array SAR technology has just started. In terms of 3D imaging algorithms, it is mainly divided into three categories. The first type is to use traditional SAR imaging technology to first complete the azimuth-elevation two-dimensional compression, and then perform cross-course compression. This type of algorithm introduces more approximations to the echo distance history, and the imaging accuracy is low; the second type is direct. For 3D reconstruction of 3D echo data, this type of algorithm does not approximate the distance history, and the imaging accuracy is high, but the timeliness is not strong. Imaging, this kind of algorithm is complex, and the imaging accuracy and timeliness need to be further verified. However, limited by the influence of cross-course resolution, the third category of methods to achieve high-resolution 3D imaging through sparse sampling will be the future development direction.

The sparse representation theory can achieve accurate signal recovery with sparse signals much lower than the Nyquist sampling frequency. However, the traditional sparse representation method is to take the real part and imaginary part of the complex scene and process them separately, ignoring the sparseness of the amplitude of the scene and the constraints that the amplitude should be a real number. The present invention uses the prior information whose scene amplitude is a real value to study the sparse representation imaging algorithm of the array SAR, which is of great significance for the array SAR system to further reduce the number of array elements, system cost and physical implementation.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a distributed array SAR sparse representation three-dimensional imaging algorithm that takes into account the real-value constraints of the scene amplitude. The magnitude is two pieces of prior information, and the real-valued constraint term of the scene magnitude is added to the regularization reconstruction model, and the quasi-Newton algorithm is used to estimate the magnitude and phase of the scene respectively, so as to complete the 3D reconstruction that is more in line with the actual situation.

A distributed array SAR sparse representation 3D imaging algorithm considering the real-value constraints of the scene amplitude mainly includes the following steps:

Step R1, construct a sparse array SAR complex signal linear measurement model:

Step R2, sparse three-dimensional reconstruction is performed by means of a quasi-Newton algorithm.

A distributed array SAR sparse representation three-dimensional imaging algorithm considering the real-value constraints of the scene amplitude as described above, in the step R1, based on the full array linear array, the echo data of the i-th receiving array element of the array SAR passes through. Range compression, range migration correction and azimuth compression can be expressed as

where t is the range fast time, n is the azimuth slow time, N is the number of spatial resolution units in the observation scene across the course, σ _j (t,n) is the complex scattering coefficient of the cross-course target after two-dimensional compression, f _i is the response frequency corresponding to the i-th array element across the course, i.e.

f _i =y _i /(λR ₀ ) (2)

表示散射点在方位-距离平面 的投影点与参考原点的斜距：In the formula, y _i is the coordinate of the i-th antenna element in the cross-course,

Represents the slant distance between the projected point of the scattering point on the azimuth-distance plane and the reference origin:

Converted to vector form as

S(t,n,i)=ψ(t,n) ^T α(t,n) (3)

In the formula,

ψ _i (t,n)=[exp(j2πf _i y ₁ ),exp(j2πf _i y ₂ ),…,exp(j2πf _i y _N )] ^T (4)

α(t,n)=[α ₁ (t,n),α ₂ (t,n),…,α _N (t,n)] ^T (5)

ψ _i (t,n) is the N×1-dimensional linear projection vector of the i-th array element; α(t,n) is the complex scattering coefficient vector of the cross-course target.

α is sparse, so the distributed array SAR echo S is also sparse under the basis function ψ, and the measurement matrix Φ∈R ^K×N is introduced (K is the number of sparse linear array elements, and N is the number of full array elements) , whose value is the corresponding K rows of the N×N identity matrix selected according to the sparse array element positions;

Then formula (6) can be transformed into

S _v = ΦΨα = Θα (8)

In the formula, S _v is the echo of the above-mentioned S thinning, and Θ=ΦΨ is the projection matrix;

According to the sparse representation theory, the scene α can be obtained by the sparse reconstruction of equation (9)

In the formula, ||·|| ₁ represents the l ₁ norm;

But α is a complex scene, the traditional method is to take the real part and the imaginary part of the complex signal to process separately, this method takes into account the amplitude sparsity of the SAR scene concentrated in the low frequency, and expresses the scene as a combination of amplitude and phase

α=G|α| (10)

是一个对角矩阵，

为α的相位，|α|为α的幅度；In the formula,

is a diagonal matrix,

is the phase of α, |α| is the amplitude of α;

Suppose that the scene magnitude can be sparsely represented by a basis P containing a sparse representation and sparse coefficients β

|α|=Pβ (11)

Then the scene is expressed as a combination of amplitude and phase, and after adding the constraint that |α|=Pβ itself is a real number, the distributed array SAR linear measurement model can be finally expressed as

In the formula, P contains the DCT base, and β* is the conjugate of β.

The above-mentioned distributed array SAR sparse representation 3D imaging algorithm considering the real value constraints of the scene amplitude, in the step R2, for the distributed array SAR linear measurement model, sparse 3D reconstruction is performed by means of a quasi-Newton algorithm, and the Specific steps are as follows:

Step 1, use the imaging result obtained by the three-dimensional RD imaging algorithm as the initial value of the scene α, and simultaneously obtain the initial values of G and β according to formula (10) and formula (11);

Step 2, select a suitable basis, and use the real-valued coefficient to represent the basis corresponding to the real-valued amplitude;

Step 3: According to G, transform the constrained optimization problem represented by equation (12) into an unconstrained optimization problem, and use the quasi-Newton algorithm to estimate β

In the formula, λ ₁ and λ ₂ are regularization parameters;

Step 4, according to the estimated value of β, also use the quasi-Newton algorithm to analytically solve equation (14), and re-estimate G

In the formula, Q=diag{α}, γ is a vector composed of G diagonal elements, and λ ₃ is a regularization parameter;

Step 5, repeat steps 3-4, when the changes of β and γ are less than the preset threshold, the iteration is terminated.

Compared with the prior art, the present application has the following advantages:

In this application, the distributed array SAR sparse representation 3D imaging algorithm considering the real-value constraints of the scene amplitude adopts the sparse representation theory to express the complex scene as a combination of amplitude and phase, and utilizes two a priori information of the sparseness of the 3D scene and the fact that the scene amplitude is a real number. , a real-valued constraint term of the scene amplitude is added to the regularization reconstruction model, and the quasi-Newton algorithm is used to estimate the scene amplitude and phase respectively, so as to complete the 3D reconstruction that is more in line with the actual situation; this method adds a real-valued amplitude constraint to the regularized reconstruction model. , making the measurement model more reasonable and in line with the actual situation, and can achieve higher super-resolution and stronger high-resolution 3D imaging.

Description of drawings

Figure 1 shows the sparsity in 3D space.

Fig. 2 is a flow chart of the 3D imaging algorithm of distributed array SAR sparse representation considering the real-value constraints of the scene amplitude.

Detailed ways

In order to make the technical problems, technical solutions and beneficial effects solved by the present application clearer, the present application will be described in further detail below 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, but not to limit the present application.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terms used herein in the description of the present invention are for the purpose of describing specific embodiments only, and are not intended to limit the present invention. As used herein, the indefinite articles "a (a)" or "an (an)" do not exclude a plurality, and the term "and/or" may include any and all combinations of one or more of the associated listed items.

As shown in Figure 1 and Figure 2, in the real three-dimensional world, the scattering target (as shown in Figure 1) only occupies a small part of the entire space, which is sparse, and the array SAR has three-dimensional resolution. Therefore, the sparseness of the scattering target is also maintained in the three-dimensional imaging space, that is, the scattering coefficients of only K elements in the target echo signal are non-zero values.

The idea of sparse representation can be used for reference, and only a small amount of sparse array element echo data can be used to achieve high-precision 3D reconstruction of the target area, which greatly reduces the number of array elements and solves the bottleneck of low resolution across heading dimensions. Figure 2 shows the flow of the distributed array SAR sparse representation 3D imaging algorithm proposed by the present invention considering the real-value constraints of the scene amplitude.

A distributed array SAR sparse representation 3D imaging algorithm considering the real-value constraints of the scene amplitude mainly includes the following steps:

Step R1, construct a sparse array SAR complex signal linear measurement model:

Step R2, sparse three-dimensional reconstruction is performed by means of a quasi-Newton algorithm.

A distributed array SAR sparse representation three-dimensional imaging algorithm considering the real-value constraints of the scene amplitude as described above, in the step R1, based on the full array linear array, the echo data of the i-th receiving array element of the array SAR passes through. Range compression, range migration correction and azimuth compression can be expressed as

where t is the range fast time, n is the azimuth slow time, N is the number of spatial resolution units in the observation scene across the course, σ _j (t,n) is the complex scattering coefficient of the cross-course target after two-dimensional compression, f _i is the response frequency corresponding to the i-th array element across the course, i.e.

f _i =y _i /(λR ₀ ) (2)

表示散射点在方位-距离平面 的投影点与参考原点的斜距：In the formula, y _i is the coordinate of the i-th antenna element in the cross-course,

Represents the slant distance between the projected point of the scattering point on the azimuth-distance plane and the reference origin:

Converted to vector form as

S(t,n,i)=ψ(t,n) ^T α(t,n) (3)

In the formula,

ψ _i (t,n)=[exp(j2πf _i y ₁ ),exp(j2πf _i y ₂ ),…,exp(j2πf _i y _N )] ^T (4)

α(t,n)=[α ₁ (t,n),α ₂ (t,n),…,α _N (t,n)] ^T (5)

ψ _i (t,n) is the N×1-dimensional linear projection vector of the i-th array element; α(t,n) is the complex scattering coefficient vector of the cross-course target.

α is sparse, so the distributed array SAR echo S is also sparse under the basis function ψ, and the measurement matrix Φ∈R ^K×N is introduced (K is the number of sparse linear array elements, and N is the number of full array elements) , whose value is the corresponding K rows of the N×N identity matrix selected according to the sparse array element positions;

Then formula (6) can be transformed into

S _v = ΦΨα = Θα (8)

In the formula, S _v is the echo of the above-mentioned S thinning, and Θ=ΦΨ is the projection matrix;

According to the sparse representation theory, the scene α can be obtained by the sparse reconstruction of equation (9)

In the formula, ||·|| ₁ represents the l ₁ norm;

But α is a complex scene, the traditional method is to take the real part and the imaginary part of the complex signal to process separately, this method takes into account the amplitude sparsity of the SAR scene concentrated in the low frequency, and expresses the scene as a combination of amplitude and phase

α=G|α| (10)

是一个对角矩阵，

为α的相位，|α|为α的幅度；In the formula,

is a diagonal matrix,

is the phase of α, |α| is the amplitude of α;

Suppose that the scene magnitude can be sparsely represented by a basis P containing a sparse representation and sparse coefficients β

|α|=Pβ (11)

Then the scene is expressed as a combination of amplitude and phase, and after adding the constraint that |α|=Pβ itself is a real number, the distributed array SAR linear measurement model can be finally expressed as

In the formula, P contains the DCT base, and β* is the conjugate of β.

The above-mentioned distributed array SAR sparse representation 3D imaging algorithm considering the real value constraints of the scene amplitude, in the step R2, for the distributed array SAR linear measurement model, sparse 3D reconstruction is performed by means of a quasi-Newton algorithm, and the Specific steps are as follows:

Step 1, use the imaging result obtained by the three-dimensional RD imaging algorithm as the initial value of the scene α, and simultaneously obtain the initial values of G and β according to formula (10) and formula (11);

Step 2, select a suitable basis, and use the real-valued coefficient to represent the basis corresponding to the real-valued amplitude;

Step 3: According to G, transform the constrained optimization problem represented by equation (12) into an unconstrained optimization problem, and use the quasi-Newton algorithm to estimate β

In the formula, λ ₁ and λ ₂ are regularization parameters;

Step 4, according to the estimated value of β, also use the quasi-Newton algorithm to analytically solve equation (14), and re-estimate G

In the formula, Q=diag{α}, γ is a vector composed of G diagonal elements, and λ ₃ is a regularization parameter;

Step 5, repeat steps 3-4, when the changes of β and γ are less than the preset threshold, the iteration is terminated.

How this application works:

The algorithm adopts the sparse representation theory to represent the complex scene as a combination of amplitude and phase, and uses two prior information, namely, the sparseness of the three-dimensional scene and the scene amplitude as a real number. The quasi-Newton algorithm is used to estimate the amplitude and phase of the scene separately, so as to complete the 3D reconstruction that is more in line with the actual situation; this method adds amplitude real-value constraints to the regularized reconstruction model, which makes the measurement model more reasonable and in line with the actual situation, and can achieve higher super-resolution capability. and more robust high-resolution 3D imaging.

The above is one or more embodiments provided in conjunction with specific contents, and it is not construed that the specific implementation of the present application is only limited to these descriptions. Any method, structure, etc. similar to or similar to the application, or some technical deductions or replacements are made under the premise of the concept of the application should be regarded as the protection scope of the application.

Claims (3)

1. a distributed array SAR sparse representation three-dimensional imaging algorithm taking into account the real-value constraint of scene amplitude, is characterized in that, mainly comprises the steps: Step R1, construct a linear measurement model of the sparse array SAR complex signal: Step R2, sparse three-dimensional reconstruction is performed by means of a quasi-Newton algorithm. 2. A distributed array SAR sparse representation three-dimensional imaging algorithm according to claim 1, characterized in that, in the step R1, based on the full array line array, the i-th array SAR After range compression, range migration correction and azimuth compression, the echo data of each receiving array element can be expressed as

In the formula, t is the range fast time, n is the azimuth slow time, N is the number of spatial resolution units in the observation scene across the course, σ _j (t,n) is the complex scattering coefficient of the cross-course target after two-dimensional compression, f _i is the response frequency corresponding to the i-th array element across the course, i.e. f _i =y _i /(λR ₀ ) (2) In the formula, y _i is the coordinate of the i-th antenna element in the cross-course,

Represents the slant distance between the projected point of the scattering point on the azimuth-distance plane and the reference origin: Converted to vector form as S(t,n,i)=ψ(t,n) ^T α(t,n) (3) In the formula, ψ _i (t,n)=[exp(j2πf _i y ₁ ),exp(j2πf _i y ₂ ),…,exp(j2πf _i y _N )] ^T (4) α(t,n)=[α ₁ (t,n),α ₂ (t,n),…,α _N (t,n)] ^T (5) ψ _i (t,n) is the N×1-dimensional linear projection vector of the i-th array element; α(t,n) is the complex scattering coefficient vector of the cross-course target.

α is sparse, so the distributed array SAR echo S is also sparse under the basis function ψ, and the measurement matrix Φ∈R ^K×N is introduced (K is the number of sparse linear array elements, and N is the number of full array elements) , whose value is the corresponding K rows of the N×N unit matrix selected according to the position of the sparse array element;

Then formula (6) can be transformed into S _v = ΦΨα = Θα (8) In the formula, S _v is the echo of the above-mentioned S thinning, and Θ=ΦΨ is the projection matrix; According to the sparse representation theory, the scene α can be obtained by the sparse reconstruction of equation (9)

In the formula, ||·|| ₁ represents the l ₁ norm; However, α is a complex scene. The traditional method is to take the real part and the imaginary part of the complex signal to process separately. This method takes into account the amplitude sparsity of the SAR scene concentrated at low frequencies, and expresses the scene as a combination of amplitude and phase. α=G|α| (10) In the formula,

is a diagonal matrix,

is the phase of α, |α| is the amplitude of α; Suppose that the scene magnitude can be sparsely represented by a basis P containing a sparse representation and sparse coefficients β |α|=Pβ (11) Then the scene is expressed as a combination of amplitude and phase, and after adding the constraint that |α|=Pβ itself is a real number, the distributed array SAR linear measurement model can be finally expressed as

In the formula, P contains the DCT base, and β* is the conjugate of β. 3. a kind of distributed array SAR sparse representation three-dimensional imaging algorithm taking into account the real value constraint of scene amplitude according to claim 1-2, is characterized in that, in described step R2, for distributed array SAR linear measurement model, The sparse 3D reconstruction is carried out with the help of the quasi-Newton algorithm, and the specific steps are as follows: Step 1, use the imaging result obtained by the three-dimensional RD imaging algorithm as the initial value of the scene α, and simultaneously obtain the initial values of G and β according to formula (10) and formula (11); Step 2, select a suitable basis, and use the real-valued coefficient to represent the basis corresponding to the real-valued amplitude; Step 3: According to G, transform the constrained optimization problem represented by equation (12) into an unconstrained optimization problem, and use the quasi-Newton algorithm to estimate β

In the formula, λ ₁ and λ ₂ are regularization parameters; Step 4, according to the estimated value of β, also use the quasi-Newton algorithm to analytically solve equation (14), and re-estimate G

In the formula, Q=diag{|α|}, γ is a vector composed of G diagonal elements, and λ ₃ is a regularization parameter; Step 5, repeat steps 3-4, when the changes of β and γ are less than the preset threshold, the iteration is terminated.

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