A radar high-resolution imaging method based on compressed sensing

Abstract

The application discloses a radar high-resolution imaging method based on compressed sensing. The application comprises the following steps: step 1, an imaging model is established according to the joint block sparse characteristics of a random sequence stepped echo signal; step 2, a criterion of a block sparse signal space matching pursuit (BSSMP) algorithm is determined; step 3, the BSSMP algorithm is constructed according to the criterion; step 4, a sensing matrix Θ is constructed, so that the column full rank is satisfied, and a column set T∪T k is represented in the sensing matrix Θ; step 5, a condition that all the indexes selected by the BSSMP in the k+1th iteration are correct is established under the premise that at least K-r correct support elements are selected in the first k iterations of the BSSMP algorithm; and step 6, a condition and a required number of times for reconstructing X by the BSSMP algorithm are given. The application can effectively recover a signal, the established model fully considers the structural characteristics of the block sparse and joint sparse of the sequence echo signal, realizes joint processing of multidimensional signals, improves the imaging performance, and has high application value.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of engineering technology, and relates to a radar high-resolution imaging method. BACKGROUND

[0002] High-resolution radar imaging has high resolution, strong anti-interference, all-weather and all-day applicability, and becomes one of the widespread applications of radar technology. It has very important military and civil values. One of the most common imaging radars is a synthetic aperture radar (SAR). This radar is usually equipped on an airplane or a satellite to image a stationary target on the ground. The essence of imaging is to synthesize a huge effective antenna aperture in the direction of the relative motion between the radar and the imaging target. However, imaging of a moving target on the ground also has equal application value. Inverse synthetic aperture radar (ISAR) is another radar imaging technology developed for this problem. It can image a moving target (such as an airplane or a missile) with high resolution. ISAR can not only be fixed on the ground to image a moving target, but also can be equipped on a moving platform such as an airplane, a ship or a satellite to image a moving target with high resolution. The imaging principle of ISAR is roughly the same as that of SAR, and both of them are two-dimensional imaging based on the range-Doppler (RD) principle. In recent years, with the progress of science and technology, the requirement for the resolution of images is also higher and higher, and the research on the imaging method of radar has brought many challenges. The emergence of the theory of compressed sensing provides a good idea for solving the above problems. The target scattering points of ISAR have the characteristic of sparsity, that is, the main energy is scattered by only a few scattering centers. After the target scattering points are regarded as a whole, the target shape has the characteristic of sparse structure. By fully utilizing the structural characteristics, the imaging performance of ISAR can be improved. At present, the ISAR imaging methods mainly include the following three aspects:

[0003] (1). Mode-coupled sparse structure, in which there are other scattering points around the strong scattering points of the target with a high probability;

[0004] (2). Block sparse structure, that is, the strong scattering points of the target are gathered in a certain area and are distributed in blocks;

[0005] (3). Joint sparse structure, that is, the echo signals have the same sparse structure.

[0006] Although previous studies have taken into account the three different target sparse structure features respectively, and proposed some imaging algorithms. But in practical applications, the three cases are not alone, so it is necessary to fully consider the multiple sparse structure features and propose effective sparse reconstruction algorithm. We consider the random chirp frequency-stepped (RCFS) signal, make full use of the joint block sparse structure features of the random chirp frequency-stepped (RCFS) signal itself, and design a reasonable and effective imaging method.

[0007] In summary, the present application will be based on the random sequence step echo signal, establish a joint block sparse model, and propose a new sparse reconstruction method. This method not only makes full use of the joint block sparse actual characteristics of the random sequence step echo (RCFS) signal, realizes the joint processing of multi-dimensional signal, but also improves the performance of imaging. SUMMARY

[0008] The present application establishes a joint block sparse model for random sequence step echo signals and proposes a block-subspace matching pursuit sparse reconstruction algorithm.

[0009] The specific steps of the method of the present application include the following:

[0010] Step 1: According to the joint block sparse characteristics of the random sequence step echo signal, an imaging model is established.

[0011] Step 2: Determine the criterion for constructing the block signal space matching pursuit BSSMP algorithm;

[0012] Step 3: Construct the BSSMP algorithm according to the criterion;

[0013] Step 4: Construct the perception matrix Θ, so that it satisfies The column is full rank, The column set T∪T k The column set.

[0014] Step 5: Under the premise that the BSSMP algorithm selects at least K-r correct support elements in the first k iterations, establish the condition that all the indicators selected by the BSSMP algorithm in the k+1 iteration are correct;

[0015] Step 6: Give the condition and the number of times required for the BSSMP algorithm to reconstruct X;

[0016] Further, step 1 is specifically implemented as follows:

[0017] 1.1: Description of the ISAR imaging process of RCFS signal:

[0018] The ISAR imaging process for RCFS signals includes range synthesis and Doppler focusing. The motion-compensated subpulse compressed sampling signal can be expressed as:

[0019]

[0020] in, For the first The scattering intensity at each scattering point, f c For carrier frequency, Γ n,na Here, Δf represents the sub-pulse step sequence, and Δf is the carrier frequency step size. For the first The position of the target scattering point in the target coordinate system, where Δθ is the equivalent angular rotation step.

[0021] The above sub-pulse compressed sampling signals are then combined for range and then subjected to Doppler focusing. Due to the sparsity of target range imaging, the nth... a The downsampling sparse reconstruction model for each distance image is as follows:

[0022] s(n a )=Θ(n a )x(n a ),n a =1,…,N a (2)

[0023] in For downsampling vectors, For the perception matrix, For target scattering point information, i.e., the nth scattering point a A 1D distance image. When n a After taking all the samples, set N to a The group distance image sparse recovery model is described as follows:

[0024] S=ΘX (3)

[0025] in, N a =d×r, N=Md. d represents the length of each block after X is uniformly divided into rows, and M represents the number of sub-blocks after X is uniformly divided into rows.

[0026] 1.2 Based on the structural characteristics of block joint sparseness, X and the perception matrix Θ are divided into blocks;

[0027] Divide X into evenly distributed blocks along the rows, and consider X as a series of concatenated sub-blocks X[i].

[0028] Right now:

[0029] X = [X[1]] H ,…,X[M]H ] H (4)

[0030] Where, N a =d×r, N=Md; d represents the length of each block after X is uniformly divided into rows; M represents the number of sub-blocks after X is uniformly divided into rows; for a single distance image, x(n a ) is the distance image to be reconstructed.

[0031] Divide the perception matrix Θ into uniform blocks along its columns, and consider Θ as a concatenation of each column sub-block matrix, that is:

[0032] Θ=[Θ[1],…,Θ[M]] (5)

[0033] Furthermore, the recognition criteria constructed in step 2 are as follows:

[0034]

[0035] Among them, R k The residual is generated at step k. Indicates that by R k The space formed by the columns, Indicates in Orthogonal projection on column space It is T k The index sub-block matrix is ​​formed by concatenation; where T k Let the estimated support set be:

[0036]

[0037] Here, matrix B is formed by concatenating B[i], and the calculation... For each submatrix, the F-norm is calculated, and the top L largest submatrix indices λ1,...,λ are selected. L , Indicates in Orthogonal projection on column space.

[0038] Furthermore, the algorithm for step 3 is described as follows:

[0039] Input: Perception matrix Θ, measurement S, block sparsity K, and number of indicators selected each time L;

[0040] Initialization: k = 0, R 0 =S;

[0041] Determine if the stopping condition is met. If the stopping condition is not met, k = k + 1, and continue the iteration to construct B[i] as follows:

[0042]

[0043] calculate For each submatrix, the F-norm is calculated, and the top L largest submatrix indices λ1, ..., λ2 are selected. L ;T k =T k-1 ∪{λ1,...,λ L};

[0044]

[0045] R k =S-ΘX k ;

[0046] Stopping condition met:

[0047] Output: It is X k The set of K row block indicators with the largest F-norm in the matrix satisfy and It is a matrix The row block indicator in The corresponding row block matrices are connected together; It is a submatrix of Θ, formed by the index in It is formed by connecting the column sub-matrices of Θ corresponding to it, and 0 is a matrix with all elements being 0.

[0048] Furthermore, step 4 is implemented as follows:

[0049] Based on the block-RIP theoretical framework, the condition for the BSSMP algorithm to select at least Kr support elements in the first Kr iterations is that the perceptron matrix Θ satisfies the L(Kr)+r+1 order block-RIP condition and the corresponding block-RIP constant is... The following conditions must be met:

[0050]

[0051] Where r indicates that any r non-zero row blocks in X are linearly independent, rank(X[i]) = d, and L is the number of indicators selected by the BSSMP algorithm each time.

[0052] Furthermore, the condition for establishing in step 5 that the metrics selected by BSSMP in the (k+1)th iteration are all correct is:

[0053] Bkrank(Θ)≥|T∪T k +1 (9)

[0054] Furthermore, the specific implementation steps for step 5 are as follows:

[0055] 5.1 Introduce the definition of Bkrank(Θ): Bkrank(Θ) is the maximum number of linearly independent column sub-blocks in Θ when Θ is uniformly partitioned into column sub-blocks.

[0056] 5.2 Determine the intermediate value p i and the intermediate value q j respectively:

[0057]

[0058] 5.3 By calculating step 5.2, p i = 1 and q j < 1. Therefore, under the condition of Bkrank(Θ) ≥ |T∪T k | + 1, p i > q j holds. Thus, it is proved that the indicators selected by the BSSMP algorithm at the k+1th iteration are all support elements.

[0059] Further, step 6 is specifically implemented as follows:

[0060] 6.1 When K = r and Θ satisfies Bkrank(Θ) ≥ K + 1, BSSMP can recover X after iterations;

[0061] 6.2 When K > r, and the sensing matrix Θ satisfies the L(K-r)+r+1 order block-RIP condition, and the corresponding block-RIP constant satisfies the formula in step 4, then BSSMP can recover X after iterations.

[0062] The present application has the following advantages:

[0063] According to the random sequence stepped echo signal and the joint block sparsity structure characteristics thereof, the present application proposes an effective high-resolution imaging method for the ISAR radar high-resolution imaging problem, so that the signal can be effectively recovered. The model established by the present application fully considers the block sparsity and joint sparsity structure characteristics of the sequence echo signal, and has high application value. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 ERR performance comparison of the recovery algorithm as a function of block sparsity degree;

[0065] Figure 2 ERR performance comparison of the recovery algorithm as a function of block sparsity degree; DETAILED DESCRIPTION

[0066] The invention will now be further described with reference to the accompanying drawings.

[0067] like Figure 1 As shown, for a single distance image x(n) a For x(n), it has a block-sparse structural characteristic. Divide it evenly into M sub-blocks, with each sub-block having a length of d. Then x(n) a The non-zero elements of the signal are distributed in only a few sub-blocks. For the Na-group range image, since the target observed in each sub-pulse signal is the same, each echo signal has the same sparse structural characteristics. When we put the Na-group signals together, they form X, which then has the sparse structural characteristics of a joint block. Figure 2 This is a structural feature diagram of X.

[0068] A high-resolution radar imaging method based on compressed sensing includes the following steps:

[0069] Step 1: Establish an imaging model based on the joint block sparsity characteristics of random sequence step echo signals.

[0070] Step 2: Determine the criteria for constructing the Block Signal Spatial Matching Pursuit (BSSMP) algorithm;

[0071] Step 3: Construct the BSSMP algorithm according to the criteria;

[0072] Step 4: Construct the perception matrix Θ such that it satisfies The ranks are full. T∪T represents the set of columns in the perception matrix Θ. k Column set.

[0073] Step 5: Given that at least Kr correct support elements were selected in the first k iterations of the BSSMP algorithm, establish the condition that all the indicators selected by BSSMP in the (k+1)th iteration are correct.

[0074] Step 6: Give the conditions for reconstructing X using the BSSMP algorithm and the number of iterations required;

[0075] Furthermore, step 1 is implemented as follows:

[0076] 1.1: Description of the ISAR imaging process for RCFS signals:

[0077] The ISAR imaging process for RCFS signals includes range synthesis and Doppler focusing. The motion-compensated subpulse compressed sampling signal can be expressed as:

[0078]

[0079] in, For the first The scattering intensity at each scattering point, fc is the carrier frequency, Γ n,na is the sub-pulse stepping sequence, Δf is the carrier frequency stepping amount, is the position of the nth target scattering point in the target coordinate system, and Δθ is the equivalent angular rotation step.

[0080] After distance synthesis is performed on the above-mentioned sub-pulse compression sampling signal, Doppler focusing is performed. Since target distance imaging presents sparsity, the down-sampling sparse reconstruction model of the nth a distance image is:

[0081] s(n a )=Θ(n a )x(n a ),n a =1,…,N a (2)

[0082] wherein is a down-sampling vector, is a sensing matrix, is target scattering point information, i.e., the nth a 1-dimensional distance image. When n a is taken through, the N a group distance image sparse recovery model is described as:

[0083] S=ΘX (3)

[0084] wherein, N a =d×r, N=Md. d represents the length of each block after X is uniformly blocked by rows, and M represents the number of sub-blocks after X is uniformly blocked by rows;

[0085] 1.2 According to the structural characteristics of the block joint sparsity, X and the sensing matrix Θ are blocked.

[0086] X is uniformly blocked by rows, and X is regarded as being composed of each sub-block X[i] in series,

[0087] i.e.:

[0088] X=[X[1] H ,…,X[M] H ] H (4)

[0089] wherein, N a =d×r, N=Md; d represents the length of each block after X is uniformly blocked by rows; M represents the number of sub-blocks after X is uniformly blocked by rows; for a single distance image, x(n a ) is the distance image to be reconstructed.

[0090] Divide the perception matrix Θ into uniform blocks along its columns, and consider Θ as a concatenation of each column sub-block matrix, that is:

[0091] Θ=[Θ[1],…,Θ[M]] (5)

[0092] Furthermore, the recognition criteria constructed in step 2 are as follows:

[0093]

[0094] Among them, R k The residual is generated at step k. Indicates that by R k The space formed by the columns, Indicates in Orthogonal projection on column space It is T k The index sub-block matrix is ​​formed by concatenation; where T k Let the estimated support set be:

[0095]

[0096] Here, matrix B is formed by concatenating B[i], and the calculation... For each submatrix, the F-norm is calculated, and the top L largest submatrix indices λ1, ..., λ2 are selected. L , Indicates in Orthogonal projection on column space.

[0097] Furthermore, the algorithm for step 3 is described as follows:

[0098] Input: Perception matrix Θ, measurement S, block sparsity K, and number of indicators selected each time L;

[0099] Initialization: k = 0, R 0 =S;

[0100] Determine if the stopping condition is met. If the stopping condition is not met, k = k + 1, and continue the iteration to construct B[i] as follows:

[0101]

[0102] calculate For each submatrix, the F-norm is calculated, and the top L largest submatrix indices λ1,...,λ are selected. L ;T k =T k-1 ∪{λ1,...,λ L};

[0103]

[0104] R k =S-ΘX k ;

[0105] Stopping condition met:

[0106] Output: It is X k The set of K row block indicators with the largest F-norm in the matrix satisfy and It is a matrix The row block indicator in The corresponding row block matrices are connected together; It is a submatrix of Θ, formed by the index in It is formed by connecting the column sub-matrices of Θ corresponding to it, and 0 is a matrix with all elements being 0.

[0107] Furthermore, step 4 is implemented as follows:

[0108] Based on the block-RIP theoretical framework, the condition for the BSSMP algorithm to select at least Kr support elements in the first Kr iterations is that the perceptron matrix Θ satisfies the L(Kr)+r+1 order block-RIP condition and the corresponding block-RIP constant is... The following conditions must be met:

[0109]

[0110] Where r indicates that any r non-zero row blocks in X are linearly independent, rank(X[i]) = d, and L is the number of indicators selected by the BSSMP algorithm each time.

[0111] Furthermore, the condition for establishing in step 5 that the metrics selected by BSSMP in the (k+1)th iteration are all correct is:

[0112] Bkrank(Θ)≥|T∪T k |+1 (9).

[0113] Furthermore, the specific implementation steps for step 5 are as follows:

[0114] 5.1 Introducing the definition of Bkrank(Θ): When Θ is uniformly divided into columns, Bkrank(Θ) refers to the maximum number of linearly independent columns in Θ when the column sub-block matrix of Θ is full rank.

[0115] 5.2 Determining the intermediate value p i and the median value q jrespectively.

[0116]

[0117] 5.3 Compute p i = 1 and q j < 1. Therefore, under the condition that Bkrank(Θ) ≥ |T∪T k | + 1, p i > q j holds. Thus, it is proved that the selected indices by BSSMP algorithm at the k+1th iteration are all support elements.

[0118] Further, the step 6 is implemented as follows:

[0119] 6.1 When K = r and Θ satisfies Bkrank(Θ) ≥ K + 1, BSSMP can recover X after iterations.

[0120] 6.2 When K > r and the sensing matrix Θ satisfies the L(K-r)+r+1 order block-RIP condition, and the corresponding block-RIP constant satisfies the formula in step 4, then BSSMP algorithm can recover X after iterations.

[0121] Example 1: Numerical simulation

[0122] To verify the effectiveness of BSSMP algorithm, we conducted numerical experiments and compared it with the existing algorithm BMMV. In each iteration, a 128x256 Gaussian matrix is randomly generated. The matrix is divided into 128 blocks by column, and the length of each block is d = 2. We mainly examine the performance of the algorithm by calculating the accurate reconstruction rate (ERR) of support elements K = r, whose calculation formula is:

[0123]

[0124] In addition, joint block sparsity also belongs to joint sparse model, so we also consider the existing SSMP algorithm. We consider two cases K = r and K > r, (r = 7) respectively, and the relevant test results are shown in Figure 1 and Figure 2 .

Claims

1. A radar high resolution imaging method based on compressed sensing, characterized in that The following steps are: Step 1, according to the joint block sparse characteristics of the random sequence stepped echo signal, an imaging model is established; Step 2, the criterion of the block sparse signal space matching pursuit BSSMP algorithm is determined; Step 3, the BSSMP algorithm is constructed according to the criterion; Step 4, construct the perception matrix Θ such that column full rank, denotes a set of columns T U T k ;T k denotes the estimated support set; Step 5, under the premise that the BSSMP algorithm selects at least K-r correct support elements in the first k iterations, the condition that the BSSMP selects all correct indicators in the k+1 iteration is established; wherein K is the block sparsity; Step 6, the condition and the number of times required for the BSSMP algorithm to reconstruct the target scattering point information matrix X are given; The identification criterion constructed in step 2 algorithm is as follows: where R k is the residual produced at the kth iteration, denotes the space spanned by R k , and denotes the orthogonal projection onto the column space of , and is the orthogonal projection onto the column space of T k ; where T k denotes the estimated support set, and let where the matrix B is concatenated from B[i], and the computation F-norm of each sub-matrix, select the first L largest sub-block indices λ1,..., λ L , denotes the orthogonal projection onto the column space of ​ The algorithm description of step 3 algorithm is as follows: Input: sensing matrix Θ, measurement S, block sparsity K and the number of selected indicators L each time; Initialization: k = 0, R 0 = S; Determine whether the stop condition is met, if the stop condition is not met, k=k+1, continue the following iteration to construct B[i]: Computing the F-norm of each sub-matrix, select the first L largest sub-block indices λ1,..., λ L ; T k = T k-1 ∪{λ1,..., λ L} R k = S-ΘX k ; Satisfy the stop condition: Output: is X k the K sets of row-block indices with the largest F-norm in satisfies and is formed by the row-block matrix concatenation of the row-block indices of in ; is a submatrix of Θ, is formed by the column sub-block matrix concatenation of the indices of in , and 0 is a matrix with all elements equal to 0.

2. The radar high-resolution imaging method based on compressed sensing according to claim 1, characterized in that Step 1 is implemented as follows: 1.1: ISAR imaging process description of RCFS signal in random sequence stepping: The ISAR imaging process of RCFS signal includes range synthesis and Doppler focusing; the sub-pulse compression sampling signal after motion compensation is represented as: wherein is the scattering intensity of the th scattering point, f c is the carrier frequency, Γ n,na is the sub-pulse stepping sequence, Δf is the carrier frequency stepping amount, is the scattering intensity of the th target scattering point in the target coordinate system, Δθ is the equivalent angular rotation step; The above sub-pulse compressed sampling signals are then combined for range and then Doppler focusing is performed; due to the sparsity of target range imaging, the nth... a The downsampling sparse reconstruction model for each distance image is as follows: s(n a ) = Θ(n a )x(n a ), n a = 1,..., N a (2) wherein is a down-sampled vector, is a sensing matrix, is the target scattering point information, i.e., the nth a 1-D range profile; when n a goes through all, the N a range profile sparse recovery model is described as: S=ΘX (3) wherein, N a = d x r, N = Md; d represents the length of each block after X is uniformly divided by rows, and M represents the number of sub-blocks after X is uniformly divided by rows. 1.2 According to the structural characteristics of block joint sparsity, X and the sensing matrix Θ are blocked; X is uniformly divided into blocks by row, X is regarded as being composed of each sub-block X[i] in series, That is, X = [X[1] H ,…, X[M] H ] H (4) where N a = d x r, N = Md; d denotes the length of each block after X is uniformly divided by rows; M denotes the number of sub-blocks after X is uniformly divided by rows; for a single range image, x(n a ) is the range image to be reconstructed; The sensing matrix Θ is uniformly blocked by column, and the sensing matrix Θ is regarded as the concatenation of each column sub-block matrix, that is: Θ=[Θ[1],…,Θ[M]] (5).

3. The radar high-resolution imaging method based on compressed sensing according to claim 2, characterized in that Step 4 is implemented as follows: Based on the block-RIP theoretical framework, it is derived that the condition for BSSMP algorithm to select at least K-r support elements in the first K-r iterations is that the sensing matrix Θ satisfies the L(K-r)+r+1 order block-RIP condition and the corresponding block-RIP constant satisfies the following condition: Wherein, r represents that any r nonzero row blocks in X are linearly independent, rank(X[i])=d, and L is the number of indicators selected by the BSSMP algorithm each time.

4. The radar high-resolution imaging method based on compressed sensing according to claim 3, characterized in that The condition that the BSSMP selects all correct indicators in the k+1 iteration is established in step 5. Bkrank(Θ) ≥ | T U T k | + 1 (9).

5. The radar high-resolution imaging method based on compressed sensing according to claim 4, characterized in that The implementation steps of step 5 are as follows: 5.1 Introduce the definition of Bkrank(Θ): when the column sub-block matrix array of Θ is full rank, Bkrank(Θ) refers to the maximum number of linearly independent column sub-blocks in Θ; 5.2 Determine intermediate values p i and q j respectively: 5.3 Compute p by step 5.2 i = 1 and q j < 1; therefore, under the condition that Bkrank(Θ) ≥ |T U T k | + 1, p i > q j holds; thus, it is shown that the index selected by the BSSMP algorithm at the k+1 iteration is always a support element.

6. The radar high-resolution imaging method based on compressed sensing according to claim 5, characterized in that The implementation steps of step 6 are as follows: 6.1 When K = r and Θ satisfies Bkrank(Θ) ≥ K + 1, BSSMP proceeds sub-iterations can recover X; 6.2 When K>r, and the sensing matrix Θ satisfies the L(K-r)+r+1 order block-RIP condition, and the corresponding block-RIP constant satisfies the formula in Step 4, then the BSSMP algorithm recovers X in O(1) iterations.

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