A structured sparse ISAR imaging method combined with phase focusing

Abstract

The present invention provides a structured sparse ISAR imaging method with joint phase focusing. Under the premise of considering motion error, an azimuth sparse imaging optimization model of joint phase error and target structure characteristics is constructed; in order to solve the norm optimization problem, phase correction and target structure weighting are integrated into the fast iterative shrinkage threshold algorithm implementation process, and through the iteration of the algorithm, the correction of phase error and the update of structure weight information are simultaneously realized, and finally a high-resolution ISAR imaging result is obtained. The measured data experiment proves that compared with the traditional sparse imaging method, the proposed algorithm can not only realize high-precision ISAR imaging under the condition of phase error, but also further improve the processing performance under low signal-to-noise ratio because it makes full use of the structural sparse characteristics of the target.

Description

Technical Field

[0001] The invention relates to the field of radar imaging technology, and in particular to a structured sparse ISAR imaging method combined with phase focusing. Background Art

[0002] As a means of all-day and all-weather target perception, Inverse Synthetic Aperture Radar (ISAR) can obtain one-dimensional, two-dimensional and even high-dimensional information of non-cooperative targets, and can provide more fine features for back-end target recognition. Therefore, it plays an increasingly important role in military and civilian fields. For two-dimensional imaging, the bandwidth of the transmitted signal determines the range resolution capability, while the azimuth resolution capability depends on the relative rotation angle between the radar and the target. This requires the radar to continuously transmit multiple sub-pulse signals to obtain a longer virtual imaging aperture. However, with the diversification of application requirements, ISAR imaging is facing many new difficulties and challenges, especially the sparse aperture seriously restricts the imaging performance of the traditional range-Doppler (RD) algorithm. Applying the theory of Compressive Sensing (CS) to the field of ISAR imaging can obtain performance that cannot be matched by the traditional RD algorithm by utilizing the inherent sparse characteristics of the target, and has become an effective way to solve the sparse imaging problem.

[0003] Accurate motion compensation is the key to ISAR imaging, which can generally be achieved through two steps: envelope alignment and phase focusing. However, the sparse aperture will increase the difficulty of motion compensation, especially for phase focusing with high compensation accuracy requirements. Traditional phase focusing algorithms, such as Phase Gradient Autofocus (PGA) and Doppler Centre Tracking (DCT), cannot effectively compensate for the phase error introduced by motion, resulting in a decrease in imaging quality or even failure. In order to reduce the impact of sparse aperture on phase focusing and even imaging, the fast minimum entropy phase compensation method is usually combined with the smoothed l0 norm (SL0) algorithm to achieve joint processing of phase correction and azimuth imaging, but this method is sensitive to noise. And because this method needs to call the ADMM algorithm multiple times during implementation, its imaging performance and computational efficiency still have a lot of room for improvement. Summary of the invention

[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing, which makes full use of the structural sparse characteristics of the target, not only can achieve high-precision ISAR imaging under the condition of phase error, but also further improves the processing performance under low signal-to-noise ratio.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention provides a structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing, comprising the following steps:

[0007] S1. Construct sparse ISAR imaging echo model;

[0008] S2, using a structured fast iterative shrinkage threshold processing algorithm to solve the sparse ISAR imaging echo model;

[0009] S201, setting a structural weighting matrix of a target scattering point, and converting the sparse ISAR imaging echo model;

[0010] S202, after obtaining the converted sparse ISAR imaging echo model After that, an optimization model for estimating the phase error matrix E is constructed;

[0011] S203, after obtaining the converted sparse ISAR imaging echo model And the transformed estimated phase error matrix Finally update the structural weight matrix V l+1 ;

[0012] S204: Determine whether the update condition continues.

[0013] Further, the S1 is specifically:

[0014] Considering the sparse aperture condition, the sparse ISAR imaging echo model including phase error is written in matrix form as:

[0015] Y=EΘ a F a X+W=EΦ a X+W (1);

[0016] in, is a one-dimensional range image matrix containing phase error; M is the number of downsampling in azimuth, N is the number of units in range, and M≤Na; Φ a =Θ a F a ; is the azimuth downsampling matrix; is the azimuth Fourier matrix; a is the subscript; F a =exp(-j2πf a t a ), f a =[-1 / 2+1 / Na,-1 / 2+2 / Na,…,1 / 2] T , t a =[0,1,…,Na]; is the noise matrix; is the two-dimensional ISAR imaging matrix to be reconstructed; To estimate the phase error matrix, it is expressed as:

[0017]

[0018] Among them, diag(·) is the operation of constructing a diagonal matrix. Represents the phase information of the nth row of the data matrix.

[0019] For the problem shown in formula (1), it is converted into the sparse ISAR imaging echo model for solution:

[0020]

[0021] where λ is the regularization parameter, ||·||1 and ||·|| F They represent l1 norm and F norm respectively, where l1 is 1 norm.

[0022] Further, in S201, the converted sparse ISAR imaging optimization model is:

[0023]

[0024] in, is a matrix of all 1s; is the structural weighting matrix of the target scattering point; l represents the number of cycles.

[0025] Further, the S201 is specifically as follows:

[0026] S2011, Order Z l =(1+V l )⊙X, then:

[0027]

[0028] Among them, Z l is the target matrix; is the optimized target matrix;

[0029] For formula (5), we can obtain The optimal solution is:

[0030]

[0031] else if

[0032]

[0033] in,

[0034] c l is the auxiliary parameter set, and c0=0; τ is a constant satisfying τ≥Q(h), Q(h) is The Lipschitz constant; for exist The gradient value at U l is the substitution matrix in the lth cycle,

[0035] The calculation method is μ is the set threshold.

[0036] S2012, after getting the update Then, the converted sparse ISAR imaging echo model is obtained according to formula (6):

[0037]

[0038] Where ⊙ represents the Hadamard product of the matrix.

[0039] Further, the S202 is specifically as follows:

[0040] The optimization model of the estimated phase error matrix E is:

[0041]

[0042] in, is the estimated phase error matrix after conversion.

[0043] S2021. Find the first-order derivative of E for formula (7): get The estimated value of is:

[0044] S2022, use Get phase update value;

[0045] Wherein, j is a complex number sign; angle(·) represents a phase operation.

[0046] Further, in S3, the structural weight matrix V is updated l+1 , specifically:

[0047]

[0048] in, for The first (n,n a ) elements; is the updated structural weight matrix; Ω:p,q∈{-1,0,1}, and p 2 +q 2 ≠0; η∈(0,1), ε is a positive number.

[0049] Further, the S204 is specifically:

[0050]

[0051] else if Break;

[0052] Among them, ξ is the estimated error value of the setting.

[0053] The beneficial effects of the present invention are as follows: under the premise of considering the motion error, an azimuth sparse imaging optimization model combining phase error and target structure characteristics is constructed; in order to solve the norm optimization problem, phase correction and target structure weighting are integrated into the fast iterative shrinkage threshold algorithm implementation process, and through the iteration of the algorithm, the correction of phase error and the update of structure weight information are simultaneously realized, and finally a high-resolution ISAR imaging result is obtained. The measured data experiment proves that compared with the traditional sparse imaging method, the proposed algorithm can not only realize high-precision ISAR imaging under the condition of phase error, but also further improve the processing performance under low signal-to-noise ratio because it makes full use of the sparse structural characteristics of the target. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow chart of a structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing;

[0055] Figure 2 This is a comparison chart of imaging results of different algorithms under the condition of 30% echo data;

[0056] Figure 3 This is a comparison chart of imaging indicators of different algorithms under different sampling rates;

[0057] Figure 4 This is a comparison chart of imaging results of different algorithms under the condition of 0dB signal-to-noise ratio;

[0058] Figure 5 This is a comparison chart of imaging indicators of different algorithms under different signal-to-noise ratio conditions;

[0059] Figure 6 This is a comparison chart of imaging time of different algorithms under different signal-to-noise ratio conditions. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0061] See also Figure 1 , a structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing, comprising the following steps:

[0062] S1. Construct sparse ISAR imaging echo model;

[0063] S2, using a structured fast iterative shrinkage threshold processing algorithm to solve the sparse ISAR imaging echo model;

[0064] S201, setting a structural weighting matrix of a target scattering point, and converting the sparse ISAR imaging echo model;

[0065] S202, after obtaining the converted sparse ISAR imaging echo model After that, an optimization model for estimating the phase error matrix E is constructed;

[0066] S203, after obtaining the converted sparse ISAR imaging echo model And the transformed estimated phase error matrix Finally update the structural weight matrix V l+1 ;

[0067] S204: Determine whether the update condition continues.

[0068] The S1 is specifically:

[0069] Considering the sparse aperture condition, the sparse ISAR imaging echo model including phase error is written in matrix form as:

[0070] Y=EΘ a F a X+W=EΦ a X+W (1);

[0071] in, is a one-dimensional range image matrix containing phase error; M is the number of downsampling in azimuth, N is the number of units in range, and M≤Na; Φ a =Θ a F a ; is the azimuth downsampling matrix; is the azimuthal Fourier matrix; a is the subscript;

[0072] F a =exp(-j2πf a t a ), f a =[-1 / 2+1 / Na,-1 / 2+2 / Na,…,1 / 2] T , t a =[0,1,…,Na]; is the noise matrix; is the two-dimensional ISAR imaging matrix to be reconstructed; To estimate the phase error matrix, it is expressed as:

[0073]

[0074] Where diag(·) is the operation of constructing a diagonal matrix;

[0075] For the problem shown in formula (1), it is converted into the sparse ISAR imaging echo model for solution:

[0076]

[0077] where λ is the regularization parameter, ||·||1 and ||·|| F They represent l1 norm and F norm respectively, where l1 is 1 norm.

[0078] In S201, the converted sparse ISAR imaging echo model is:

[0079]

[0080] in, is a matrix of all 1s; is the structural weighting matrix of the target scattering point; l represents the number of cycles.

[0081] The S201 is specifically:

[0082] S2011, Order Z l =(1+V l )⊙X, then:

[0083]

[0084] Among them, Z l is the target matrix; is the optimized target matrix;

[0085] For formula (5), we can obtain The optimal solution is:

[0086]

[0087] else if

[0088]

[0089] in,

[0090] c l is the auxiliary parameter set, and c0=0; τ is a constant satisfying τ≥Q(h), Q(h) is The Lipschitz constant, for exist The gradient value at; U l is the replacement matrix in the lth cycle, calculated as μ is the set threshold.

[0091] S2012, after getting the update Then, the converted sparse ISAR imaging echo model is obtained according to formula (6):

[0092]

[0093] Where ⊙ represents the Hadamard product of the matrix.

[0094] The S202 is specifically as follows:

[0095] The optimization model of the estimated phase error matrix E is:

[0096]

[0097] in, is the estimated phase error matrix after conversion.

[0098] S2021. Find the first-order derivative of E for formula (7): get The estimated value of is:

[0099] S2022, use Get phase update value;

[0100] Wherein, j is a complex number sign; angle(·) represents a phase operation.

[0101] In S3, the structural weight matrix V is updated l+1 , specifically:

[0102]

[0103] in, for The first (n,n a ) elements; is the updated structural weight matrix; Ω:p,q∈{-1,0,1}, and p 2 +q 2 ≠0; η∈(0,1), ε is a positive number.

[0104] The S204 is specifically:

[0105]

[0106] else if Break;

[0107] Among them, ξ is the estimated error value of the setting.

[0108] Example

[0109] In order to verify the effectiveness of the structured sparse inverse synthetic aperture radar (ISAR) imaging method with joint phase focusing, the Yak-42 measured data was used for simulation analysis. The data was acquired by a C-band radar with a bandwidth of 400MHz and an echo dimension of 256╳256. The imaging results have strong structured sparse features.

[0110] For measured data, since it is impossible to obtain the correct imaging results in advance, image entropy (IE) and image contrast (IC) are used as indicators to measure imaging quality.

[0111] For the convenience of comparison, the experiment also gives the imaging results of the FMEPC+SL0 processing method, which is Method 1, the joint phase focusing and ISAR imaging method based on ADMM, which is Method 2, and the reweighted fast iterative shrinkage threshold algorithm, which is Method 3. In addition, the azimuth sampling rate (SPR) is defined, which is the ratio of the number of randomly selected pulses to the total number of azimuth pulses. Therefore, when the SPR is 1, it means that all azimuth pulses participate in the ISAR imaging process.

[0112] First, the sampling rate SPR is set to 0.3, that is, 30% of the data in the azimuth direction is randomly sampled, and the signal-to-noise ratio is set to 10dB. After the sparse echo signal is envelope aligned, the results obtained by using the above four methods are as follows Figure 2 As shown in Figure 2, it can be seen that this method has the best sidelobe effect and is the most focused.

[0113] Figure 3The entropy value (IE) and contrast (IC) curves of different algorithms under different sampling rates are further given. The comparison results in the figure further verify that this method has the best performance under different sampling rates.

[0114] To further verify the performance of the proposed algorithm, Figure 4 The comparison of imaging results of different algorithms when the signal-to-noise ratio is 0dB and the azimuth sampling rate is 0.8 is given in Figure 2. The comparison results also further verify that the imaging performance of this method is optimal under low signal-to-noise ratio conditions.

[0115] to this end, Figure 5 The comparison of imaging performance indicators of different algorithms under different signal-to-noise ratio conditions is given in . It can be seen that the present method has good imaging performance indicators, which is consistent with the imaging display results.

[0116] Finally, the imaging time comparison of different algorithms is given, such as Figure 6 As shown in the figure, it can be seen that the proposed algorithm needs to update the phase error and the structural weight at the same time.

[0117] The above-mentioned embodiments only express the implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be based on the attached claims.

Claims

1. A structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing, characterized in that: The following steps are involved: S1. Construct sparse ISAR imaging echo model; S2, using a structured fast iterative shrinkage threshold processing algorithm to solve the sparse ISAR imaging echo model; S201, setting a structural weighting matrix of a target scattering point, and converting the sparse ISAR imaging echo model; S202, after obtaining the converted sparse ISAR imaging echo model After that, an optimization model for estimating the phase error matrix E is constructed; S203, after obtaining the converted sparse ISAR imaging echo model And the transformed phase matrix Finally update the structural weight matrix V l+1 ; S204: Determine whether the update condition continues.

2. The structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing according to claim 1, characterized in that: The S1 is specifically: Considering the sparse aperture condition, the sparse ISAR imaging echo model including phase error is written in matrix form as: Y=EΘ a F a X+W=EΦ a X+W (1); in, is a one-dimensional range image matrix containing phase error; M is the number of downsampling in azimuth, N is the number of units in range, and M≤Na; Φ a =Θ a F a ; is the azimuth downsampling matrix; is the azimuth Fourier matrix; a is the subscript; F a =exp(-j2πf a t a ), f a =[-1 / 2+1 / Na,-1 / 2+2 / Na,…,1 / 2] T , t a =[0,1,…,Na]; is the noise matrix; is the two-dimensional ISAR imaging matrix to be reconstructed; is the phase error matrix to be estimated, expressed as: Where diag(·) is the operation of constructing a diagonal matrix; Represents the phase information of the nth row of the data matrix; For the problem shown in formula (1), it is converted into the sparse ISAR imaging echo model for solution: where λ is the regularization parameter, ||·||1 and ||·|| F They represent l1 norm and F norm respectively, and l1 is the l norm.

3. The structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing according to claim 2, characterized in that: In S201, the converted sparse ISAR imaging echo model is: in, is a matrix of all 1s; l is the number of cycles; is the structural weighting matrix of the target scattering point.

4. The structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing according to claim 3, characterized in that: The S201 is specifically as follows: S2011, Order Z l =(1+V l )⊙X, then: Among them, Z l is the target matrix; is the optimized target matrix; For formula (5), we can obtain The optimal solution is: else if in, c l is the auxiliary parameter set, and c0=0; τ is a constant satisfying τ≥Q(h), Q(h) is The Lipschitz constant; for exist The gradient value at U l is the substitution matrix in the lth cycle, The calculation method is μ is the set threshold; S2012, after getting the update Then, the converted sparse ISAR imaging echo model is obtained according to formula (6): Where ⊙ represents the Hadamard product of the matrix.

5. The structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing according to claim 4, characterized in that: The S202 is specifically as follows: The optimization model of the estimated phase error matrix E is: in, is the estimated phase error matrix after transformation; S2021. Find the first-order derivative of E for formula (7): get The estimated value of is: S2022, use Get phase update value; Wherein, j is a complex number sign; angle(·) represents a phase operation.

6. The structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing according to claim 5, characterized in that: In S203, the structural weight matrix V is updated. l+1 , specifically: in, for The first (n,n a ) elements; is the updated structural weight matrix; Ω:p,q∈{-1,0,1}, and p 2 +q 2 ≠0; η∈(0,1), ε is a positive number.

7. The structured sparse inverse synthetic aperture radar (ISAR) imaging method combined with phase focusing according to claim 6, characterized in that: The S204 is specifically: Among them, ξ is the estimated error value of the setting.

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