CN113466865B - Combined mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm - Google Patents

Combined mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm Download PDF

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CN113466865B
CN113466865B CN202110936736.XA CN202110936736A CN113466865B CN 113466865 B CN113466865 B CN 113466865B CN 202110936736 A CN202110936736 A CN 202110936736A CN 113466865 B CN113466865 B CN 113466865B
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CN113466865A (en
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何兴宇
刘桃
郭艺夺
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Air Force Engineering University of PLA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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    • G01S13/9064—Inverse SAR [ISAR]
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Abstract

The invention relates to the technical field of signal processing, in particular to a joint mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm, which comprises the following steps: s1, order
Figure DDA0003213502800000011
And alpha is (0) Each element value in the algorithm is 1, and the maximum iteration number of the algorithm is assumed to be G; s2, p.g=0, 1,2, G, for alpha in the G-th iteration (g) According to
Figure DDA0003213502800000012
Calculating the mean M and covariance sigma of the posterior probability density function, then according to
Figure DDA0003213502800000013
To calculate maximum posterior probability estimates
Figure DDA0003213502800000015
S3, according to
Figure DDA0003213502800000016
To calculate u i Then according to
Figure DDA0003213502800000017
And
Figure DDA0003213502800000018
to update the super parameter to obtain a new super parameter estimation alpha (g+1) The method comprises the steps of carrying out a first treatment on the surface of the S4, if
Figure DDA0003213502800000019
Then the next iteration of the loop is performed; if it is
Figure DDA00032135028000000110
The iteration is stopped, and the final reconstruction result is
Figure DDA00032135028000000111
If it is
Figure DDA00032135028000000112
The final reconstruction result is
Figure DDA00032135028000000113

Description

Combined mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm
Technical Field
The invention relates to the technical field of signal processing, in particular to a joint mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm.
Background
The target aimed by inverse synthetic aperture radar (Inverse Synthetic Aperture Radar, ISAR) imaging is generally sparse in an observation scene, namely, the target image is sparse in the whole background domain, so that the condition of sparse reconstruction is met, and imaging can be performed through a sparse reconstruction method. In general, it is difficult to meet the requirement of high resolution imaging for wide-band and long-time continuous observation of a fixed scene, so that the radar is often faced with the problem of sparse aperture imaging. Under the sparse aperture condition, the traditional imaging method can cause strong side lobes and grating lobes of the image, and the imaging effect is poor. The ISAR imaging method based on compressed sensing can reconstruct a high-resolution image by using a small amount of observation data and sample numbers, and has unique advantages in radar target imaging.
When a sparse reconstruction algorithm is used for imaging a moving target, the imaging effect of the algorithm capable of obtaining the most sparse solution is generally better. Tipping proposes to reconstruct the original sparse signal based on a correlation vector machine (Relevance Vector Machine, RVM) by iterative optimization through a SBL-based sample learning method. The method is based on sparse probability learning, does not need additional prior information of signals, and can easily obtain the most sparse solution of the signals, so that the SBL algorithm is widely applied to the fields of signal and image processing, pattern recognition and the like. The super-resolution ISAR imaging based on SBL is researched, ISAR images of targets are acquired by using a small number of pulses, and the SBL-based imaging method has obvious advantages in the aspects of parameter estimation and selection, image reconstruction effect and the like compared with other CS-based imaging methods.
Most sparse signal reconstruction methods are directed to one-dimensional sparse signals, which can be considered as single observation vector (Single Measurement Vector, SMV) reconstruction methods. When the two-dimensional signal processing such as image processing is carried out by adopting the methods, the two-dimensional signal is required to be vectorized into a one-dimensional signal and then reconstructed, the processing can reduce the algorithm efficiency, and the reconstruction effect of the two-dimensional sparse signal is general. The current ISAR imaging method based on CS mostly carries out vectorization operation on the reconstructed signals, and then completes the reconstruction of the signals or carries out row-by-row reconstruction on the signals. However, these methods only make use of one-dimensional sparsity of the target image, and do not make use of two-dimensional joint sparsity of the image. Considering joint sparsity characteristics of a target ISAR image, the reconstruction of the ISAR image can be achieved by solving a multi-observation vector (Multiple Measurement Vector, MMV) joint sparsity optimization problem. The method has higher reconstruction precision and greatly reduces the operation complexity. Many reconstruction algorithms based on single observation vectors can be extended to the multi-observation vector problem.
Disclosure of Invention
The invention aims to provide a joint mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm, which solves the problem of poor ISAR imaging effect at present.
In order to solve the technical problems, the invention adopts the following technical scheme:
the joint mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm is characterized by comprising the following steps of:
s1, order
Figure BDA0003213502780000021
And alpha is (0) Each element value in the algorithm is 1, and the maximum iteration number of the algorithm is assumed to be G;
s2, p.g=0, 1,2, G, for alpha in the G-th iteration (g) According to
Figure BDA00032135027800000215
The mean M and covariance sigma of the posterior probability density function are calculated and then based on +.>
Figure BDA0003213502780000022
To calculate the mostBig posterior probability estimation +.>
Figure BDA0003213502780000023
Figure BDA0003213502780000024
S3, according to
Figure BDA0003213502780000025
To calculate u i Then according to->
Figure BDA0003213502780000026
And->
Figure BDA0003213502780000027
To update the super parameter to obtain a new super parameter estimation alpha (g+1) ；
S4, if
Figure BDA0003213502780000028
Then the next iteration of the loop is performed; if->
Figure BDA0003213502780000029
The iteration is stopped and the final reconstruction result is +.>
Figure BDA00032135027800000210
If->
Figure BDA00032135027800000211
The final reconstruction result is +>
Figure BDA00032135027800000212
Before initializing parameters, the received signal can be expressed as:
Figure BDA00032135027800000213
the distance-compressed signal is expressed as:
Figure BDA00032135027800000214
assuming that the number of pulses in the coherent accumulation time is M, dividing the pulse repetition frequency into N doppler cells, the expression of x (τ, t) in the expression (2) is: x= [ X ] nm ] N×M Applying sparse representation theory to echo distance signal direction, the matrix form of formula (1) is expressed as: y=Φx+v.
A further technical solution is to express the prior of the signal X as:
Figure BDA0003213502780000031
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000032
and p (x) ij |α i ,α i+1 ,α i-1 )＝N(x ij |0,(α i +βα i+1 +βα i-1 )- 1 )。
Further technical proposal is that the super parameter alpha is assumed i Is subjected to Gamma distribution, namely:
Figure BDA0003213502780000033
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000034
representing a Gamma function.
According to the further technical scheme, according to the likelihood function and the prior distribution, the probability density function of the j-th column of the signal X meets the following conditions:
Figure BDA0003213502780000035
the mean M and covariance Σ in S2 can be derived, i.e
Figure BDA0003213502780000036
Wherein D represents a diagonal matrix and the value of the ith diagonal element thereof is alpha i +βα i+1 +βα i-1 D can be expressed as:
Figure BDA0003213502780000037
further technical proposal is that the parameter alpha is assumed 0 ＝α N+1 =0, the maximum posterior probability estimate of the posterior probability density function p (α|y) is calculated using the expectation maximization algorithm, i.e. E X|Y,α [logp(α|X)]Wherein E is X|Y,α [·]Representation concerning p (x j |y j The method comprises the steps of carrying out a first treatment on the surface of the α) the MAP estimate of signal X corresponds to the mean of the posterior probability distribution function, then there is the one in S2:
Figure BDA0003213502780000038
the desired E-step and the maximized M-step steps are then performed alternately and iteratively to obtain an estimate of the parameter α in the g-th iteration as α (g) 。
Still further, it is desirable that the E-step comprises:
let the estimation of the superparameter in the g-th iteration be alpha (g) And knowing the observed signal as Y, then calculating the expected value of the log-likelihood estimate of α, i.e., the Q function of α, expressed as:
Figure BDA0003213502780000041
taking equation (3) into equation (4), and ignoring the constant term r that is independent of α, equation (4) can be rewritten approximately as:
Figure BDA0003213502780000042
according to p (X|Y; alpha) (g) ) The posterior probability distribution of (2) is a multivariate gaussian distribution, and the mean variance is known, (5) can be approximated by:
Figure BDA0003213502780000043
further, the maximizing M-step includes:
the new estimate of α is obtained by maximizing the Q function, namely:
Figure BDA0003213502780000044
for equation (6) to find the optimal solution using the gradient descent method, the first derivative of the Q function with respect to α at the optimal solution should be zero, assuming α is the optimal solution of equation (6), then:
Figure BDA0003213502780000045
bringing formula (5) into formula (7) yields:
Figure BDA0003213502780000046
wherein the method comprises the steps of
Figure BDA0003213502780000051
Then assume v 0 ＝0，v N+1 ＝0；
According to { alpha } i Both } and β are non-negative, and can be obtained:
Figure BDA0003213502780000052
thereby obtaining S3
Figure BDA0003213502780000053
And->
Figure BDA0003213502780000054
Compared with the prior art, the invention has the beneficial effects that: the algorithm in the scheme can obtain good imaging effect on the fast rotation target imaging due to the coupling characteristic among the distance units of the signals and the joint sparsity of the signals, and has the advantages of small reconstruction error, low reconstruction mean square error and good reconstruction result.
Drawings
Fig. 1 is a graph of signal amplitude after vectorization of the first two columns of the original signal.
Fig. 2 is a graph of reconstruction errors for corresponding portions of different algorithm reconstruction results.
Fig. 3 is a reconstructed MSE for different algorithms at different sparsities K.
Fig. 4 shows the reconstructed MSE for each algorithm at different signal-to-noise ratios.
Fig. 5 is a graph of the average calculated time for each algorithm at different sparsities.
Fig. 6 is a view of a model of a scattering point of interest.
FIG. 7 is a two-dimensional ISAR image of a target using the RD algorithm.
Fig. 8 is a partial enlarged view of fig. 7.
Fig. 9 is a graph of imaging results using a two-dimensional OMP algorithm.
FIG. 10 is a graph of imaging results using a two-dimensional SBL algorithm.
FIG. 11 is an ISAR image reconstructed by the M-SBL algorithm.
FIG. 12 is an ISAR image reconstructed by the M-FOCUSS algorithm.
Fig. 13 is an ISAR image reconstructed by the SBL algorithm.
FIG. 14 is an ISAR image reconstructed by the PC-SBL algorithm.
Fig. 15 is an ISAR image reconstructed by the present algorithm.
Fig. 16 is a partial enlarged view of fig. 15.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Examples:
FIGS. 1-16 show a preferred embodiment of the present invention, a joint-mode-coupling sparse Bayesian learning super-resolution ISAR imaging algorithm, which specifically includes the following steps:
s1, order
Figure BDA0003213502780000061
And alpha is (0) Each element value in the algorithm is 1, and the maximum iteration number of the algorithm is assumed to be G;
s2, p.g=0, 1,2, G, for alpha in the G-th iteration (g) According to
Figure BDA00032135027800000613
The mean M and covariance sigma of the posterior probability density function are calculated and then based on +.>
Figure BDA0003213502780000062
To calculate the maximum posterior probability estimate +.>
Figure BDA0003213502780000063
Figure BDA0003213502780000064
S3, according to
Figure BDA0003213502780000065
To calculate u i Then according to->
Figure BDA0003213502780000066
And->
Figure BDA0003213502780000067
To update the super parameter to obtain a new super parameter estimation alpha (g+1) ；
S4, if
Figure BDA0003213502780000068
Then the next iteration of the loop is performed; if->
Figure BDA0003213502780000069
The iteration is stopped and the final reconstruction result is +.>
Figure BDA00032135027800000610
If->
Figure BDA00032135027800000611
The final reconstruction result is +>
Figure BDA00032135027800000612
The algorithm in the scheme can obtain good imaging effect on the fast rotation target imaging due to the coupling characteristic among the distance units of the signals and the joint sparsity of the signals, and has the advantages of small reconstruction error, low reconstruction mean square error and good reconstruction result.
Before initializing parameters, the radar is assumed to transmit linear radio frequency signals, and the received signals can be expressed as:
Figure BDA0003213502780000071
the distance-compressed signal is expressed as:
Figure BDA0003213502780000072
wherein c represents the propagation velocity of electromagnetic wave, ω 0 R is the rotation angular velocity of uniform rotation 0 Representing the distance from the center of the rotating shaft to the radar, wherein tau is the fast time, t m Is slow time, T p Representing pulse width, f c For carrier frequency, μ represents tone frequency. B represents the bandwidth of the transmitted signal, A k Representing the kth scattering center P k (x k ，y k ) Scattering coefficient T of (1) a The coherent integration time is represented, and K represents the number of scattering points.
Assuming that the number of pulses in the coherent accumulation time is M, dividing the pulse repetition frequency into N doppler cells, the expression of x (τ, t) in the expression (2) is: x= [ X ] nm ] N×M Applying sparse representation theory to echo distance signal direction, the matrix form of formula (1) is expressed as: y=Φx+v.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000073
in the form of a matrix of y (τ, t) in formula (1)>
Figure BDA0003213502780000074
Representing noise matrix, sparse dictionary Φ N×N Can be expressed as:
Figure BDA0003213502780000075
if it is
Figure BDA0003213502780000076
Then->
Figure BDA0003213502780000077
Representing a super-resolution range profile.
Matrix X T Can be expressed in the following form: x is X T ＝FA；
Wherein a= [ a ] mn ]Representation of
Figure BDA0003213502780000078
Is a two-dimensional super-resolution ISAR image of the target, and the element values in the matrix represent the scattering amplitudes of the scattering points. Parameter->
Figure BDA0003213502780000079
And->
Figure BDA00032135027800000710
Representing super resolution multiple of range profile, parameter +.>
Figure BDA00032135027800000711
And
Figure BDA00032135027800000712
super-resolution multiples of azimuth are shown. />
Figure BDA00032135027800000713
Representing a partial fourier matrix, namely:
Figure BDA0003213502780000081
after the joint reconstruction of the range profile is completed, the X is solved by a traditional CS reconstruction method T Reconstruction problem of FA, to obtain an ISAR image of the target. Assuming that the noise V obeys a mean of 0 and the variance is sigma 2 I, multivariate gaussian distribution.
Considering the recovery of the original sparse signal from the noise observations, the observed signal can be expressed as follows: y is m ＝Φx m +v m . It can be seen that the sparse signal shown can be seen as the mth column of the medium signal matrix X of y=Φx+v. For the purpose of facilitating subsequent analysis, the ith row of signal X is denoted as X (i) The j-th column of signal X is denoted as X j ，x ij Representing the ith element in the jth column of signal X. Under the traditional SBL framework, signal x is generally assumed m Obeying a given gaussian a priori distribution as follows:
Figure BDA0003213502780000082
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000083
for controlling signal x m Parameters of sparsity. It can be seen that when the parameter gamma i Towards infinity, the corresponding coefficient x im And tends to zero.
For fast rotating type targets, there is typically a range cell migration using conventional imaging methods, while the scattering characteristics of scattering points of adjacent range cells are correlated. In the scheme, the Gaussian likelihood function model of each distance unit is not only related to the corresponding super-parameter, but also related to the adjacent parameter of the corresponding super-parameter.
Thus, the a priori representation of signal X is:
Figure BDA0003213502780000084
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000085
and p (x) ij |α i ，α i+1 ，α i-1 )＝N(x ij |0，(α i +βα i+1 +βα i-1 ) -1 )。
Wherein, the parameter 0 is more than or equal to beta is more than or equal to 1 and represents the distance unit signal x (i) Adjacent distance element signal { x }, thereto (i+1) ，x (i-1) Correlation coefficient of }. For an initial distance cell x (1) And last distance element x (N) Let alpha be 0 =0 and α N+1 =0. When β=0, the gaussian prior model also corresponds to the gaussian prior model of the conventional M-SBL. The coefficients of adjacent distance units are coupled and associated through the common super-parameters, and the coupling association relationship is always kept through the common super-parameters in the iterative learning process.
Supposing a super parameter alpha i Is subjected to Gamma distribution, namely:
Figure BDA0003213502780000091
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000092
representing a Gamma function.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003213502780000093
representing a Gamma function. The parameter b is typically chosen to be a very small value, such as 10 -4 In contrast, parameter a is typically chosen to be a larger value, typically chosen as aε [0,1 ]]。
According to the likelihood function and the prior distribution, the probability density function of the j-th column of the signal X meets the following conditions:
Figure BDA0003213502780000094
the mean M and covariance Sigma in S2 can be derived, i.e
Figure BDA0003213502780000095
Wherein D represents a diagonal matrix and the value of the ith diagonal element thereof is alpha i +βα i+1 +βα i-1 D can be expressed as:
Figure BDA0003213502780000096
let parameter alpha 0 ＝α N+1 =0, the maximum posterior probability estimate of the posterior probability density function p (α|y) is calculated using the expectation maximization algorithm, i.e. E XY，α [logp(α|X)]Wherein E is xY，α [·]Representation concerning p (x j |y j The method comprises the steps of carrying out a first treatment on the surface of the α) the MAP estimate of signal X corresponds to the mean of the posterior probability distribution function, then there is the one in S2:
Figure BDA0003213502780000097
the desired E-step and the maximized M-step steps are then performed alternately and iteratively to obtain an estimate of the parameter α in the g-th iteration as α (g) G=1, 2,3, G, wherein, G represents the maximum number of iterations.
Desirably, the E-step includes:
let the estimation of the superparameter in the g-th iteration be alpha (g) And knowing the observed signal as Y, then calculating the expected value of the log-likelihood estimate of α, i.e., the Q function of α, expressed as:
Figure BDA0003213502780000098
taking equation (3) into equation (4), and ignoring the constant term r that is independent of α, equation (4) can be rewritten approximately as:
Figure BDA0003213502780000101
according to p (X|Y; alpha) (g) ) The posterior probability distribution of (2) is a multivariate gaussian distribution, and the mean variance is known, (5) can be approximated by:
Figure BDA0003213502780000102
the maximizing M-step includes:
the new estimate of α is obtained by maximizing the Q function, namely:
Figure BDA0003213502780000103
for equation (6) to find the optimal solution using the gradient descent method, the first derivative of the Q function with respect to α at the optimal solution should be zero, assuming α is the optimal solution of equation (6), then:
Figure BDA0003213502780000104
bringing formula (5) into formula (7) yields:
Figure BDA0003213502780000105
Figure BDA0003213502780000106
wherein the method comprises the steps of
Figure BDA0003213502780000107
Then assume v 0 ＝0，v N+1 ＝0；
According to { alpha } i Both } and β are non-negative, and can be obtained:
Figure BDA0003213502780000108
thereby obtaining S3
Figure BDA0003213502780000109
And->
Figure BDA00032135027800001010
Experimental example one:
the reconstruction effect of the algorithm in the simulation generation signal is compared with the reconstruction effect of the algorithms such as PC-SBL, M-FOCUSS, M-SBL and the like. Assuming an original sparse signal X 0 Is 100X 20, and X 0 Each column of the array contains K non-zero elements, and the positions of the non-zero elements of each column are the same. The dimension of the matrix Φ is 40×100. Suppose that non-zero elements in each column are centrally distributed in 5 dense blocks, i.e. signal X 0 Satisfying a mode coupling model。
For the PC-SBL and PC-MSBL (i.e. algorithm of the present scheme) algorithms, the parameter β=1. For the M-FOCUSS and M-SBL algorithms, each parameter is selected as a default. In view of the large amount of computation by the vectorization operation, when reconstructing the original signal using the PC-SBL algorithm, the reconstruction of the two-dimensional sparse signal is achieved by sequentially reconstructing each column of the original signal.
The sparseness of each column of the original signal is k=15. Definition of signal to noise ratio as
Figure BDA0003213502780000111
And the signal-to-noise ratio was set to 30dB. Due to the original signal X 0 For a multi-channel signal it is difficult to represent the complete signal with a signal amplitude diagram, as shown in fig. 1 and 2, by graphically giving a partial signal of the original signal and the reconstructed signal for comparison. As can be seen from fig. 2, compared with other algorithms, the reconstruction error of the algorithm of the present solution is minimal, and the reconstruction result is the best.
To further quantify the reconstruction effect of each algorithm, a mean square error (Mean Square Error, MSE) parameter is introduced here. Assume that the parameters are shifted from 6 to 30 at 1 intervals. For each value, 100 monte carlo experiments were performed. The reconstructed mean square error for each algorithm at different parameters is shown in fig. 3 when SNR = 30dB. As can be seen from fig. 3, the reconstructed mean square error of the algorithm of the present scheme is the lowest compared to other algorithms, and especially when K > 18, the reconstruction advantage of the algorithm of the present scheme is more obvious.
And (5) examining the reconstruction performance of each algorithm under different signal-to-noise ratios. The sparsity is set to k=15 and the reconstructed mean square error of each algorithm with respect to the parameter SNR is shown in fig. 4. The SNR is assumed to be shifted from-20 dB to 30dB at intervals of 2 dB. As shown in fig. 5, the calculation complexity of each algorithm was also measured using the average CPU calculation time, and 100 monte carlo experiments were also performed for each different SNR value and K value.
As can be seen from fig. 4, as the signal-to-noise ratio increases, the reconstructed signal MSE of each algorithm decreases, and under different signal-to-noise ratios, the reconstructed MSE of the algorithm of the present scheme is the smallest, and the reconstruction effect is the best. As seen in FIG. 5, the algorithm of this scheme requires a computation time similar to that of the M-FOCUSS and M-SBL algorithms. Although the reconstruction effect of the PC-SBL algorithm under certain conditions is similar to that of the PC-MSBL algorithm of the scheme, the required operation time is longest in each algorithm.
Experimental example two:
an extended boeing 747 scattering point model was created, as shown in fig. 6, with a transmitted chirp signal carrier frequency of 6GHz, a bandwidth of 600MHz, a pulse width of 20us, and a pulse repetition frequency of 1500Hz. Assuming that 300 pulse signals are received in total for coherent processing and translational compensation is completed, the equivalent turntable rotation angular velocity is 0.5rad/s, which is much larger than the equivalent turntable target rotation angular velocity of a general target.
The two-dimensional ISAR image of the target obtained by the RD algorithm is shown in fig. 7 and 8, and a plurality of scattering points in the model have defocus problems, which are mainly caused by the migration problem of the range-beyond units. Two-dimensional super-resolution images obtained by the two-dimensional CS method (using two-dimensional OMP and two-dimensional SBL) are shown in fig. 9 and 10. At this time, the number of consecutive pulses was selected to be 16, and the dimension of the f function was set to be 16×256.
As in fig. 11-14, a major problem with target ISAR images based on the M-focus, M-SBL, and SBL algorithms is that the scattering points do not lie exactly on the grid divided by the sparse basis of these algorithm constructs, i.e., fig. 11-13 face the basis mismatch problem. Although the PC-SBL algorithm can better utilize the characteristics of the target ISAR image to obtain a target image with better resolution, the joint sparse characteristic of each echo signal is not utilized, so that the most sparse solution is not obtained, and the imaging effect of the target image needs to be further improved.
As shown in fig. 15 and 16, the target image reconstructed by the algorithm has higher resolution, and has the best imaging effect compared with other algorithms, mainly because the algorithm utilizes the ISAR image characteristic and the joint sparse characteristic among signals. (wherein parameter β=1.)
The average operation time of each algorithm was calculated by 100 simulation experiments, and the results are shown in table 1.
Table 1 average calculation time for different algorithms
Figure BDA0003213502780000121
The simulation experiment shows that the algorithm reconstruction effect of the scheme is best, the obtained imaging quality is highest, and the operation complexity is low.
Although the invention has been described herein with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the scope and spirit of the principles of this disclosure. More specifically, various variations and modifications may be made to the component parts and/or arrangements of the subject combination arrangement within the scope of the disclosure, drawings and claims of this application. In addition to variations and modifications in the component parts and/or arrangements, other uses will be apparent to those skilled in the art.

Claims (5)

1. The joint mode coupling sparse Bayesian learning super-resolution ISAR imaging algorithm is characterized by comprising the following steps of:
s1, order
Figure FDA0004245246340000011
And alpha is (0) Each element value in the algorithm is 1, and the maximum iteration number of the algorithm is assumed to be G;
s2, p.g=0, 1,2, G, for alpha in the G-th iteration (g) According to
Figure FDA0004245246340000012
Calculating the mean M and covariance sigma of the posterior probability density function and then according to +.>
Figure FDA0004245246340000013
To calculate the maximum posterior probability estimate +.>
Figure FDA0004245246340000014
S3, according to
Figure FDA0004245246340000015
To calculate u i Then according to->
Figure FDA0004245246340000016
And->
Figure FDA0004245246340000017
To update the super parameter to obtain a new super parameter estimation alpha (g+1) ；
S4, if
Figure FDA0004245246340000018
Then the next iteration of the loop is performed; if->
Figure FDA0004245246340000019
The iteration is stopped and the final reconstruction result is +.>
Figure FDA00042452463400000110
If->
Figure FDA00042452463400000111
The final reconstruction result is +>
Figure FDA00042452463400000112
Let parameter alpha 0 ＝α N+1 =0, the maximum posterior probability estimate of the posterior probability density function p (α|y) is calculated using the expectation maximization algorithm, i.e. E X|Y,α [logp(α|X)]Wherein E is X|Y,α [·]Representation concerning p (x j |y j The method comprises the steps of carrying out a first treatment on the surface of the α) the MAP estimate of signal X corresponds to the mean of the posterior probability distribution function, then there is the one in S2:
Figure FDA00042452463400000113
the desired E-step and the maximized M-step steps are then performed alternately and iteratively to obtain an estimate of the parameter α in the g-th iteration as α (g) ；
Desirably, the E-step includes:
let the estimation of the superparameter in the g-th iteration be alpha (g) And knowing the observed signal as Y, then calculating the expected value of the log-likelihood estimate of α, i.e., the Q function of α, expressed as:
Figure FDA0004245246340000021
taking equation (3) into equation (4), and ignoring the constant term r that is independent of α, equation (4) can be rewritten approximately as:
Figure FDA0004245246340000022
according to p (X|Y; alpha) (g) ) The posterior probability distribution of (2) is a multivariate gaussian distribution, and the mean variance is known, (5) can be approximated by:
Figure FDA0004245246340000023
desirably, the E-step includes:
let the estimation of the superparameter in the g-th iteration be alpha (g) And knowing the observed signal as Y, then calculating the expected value of the log-likelihood estimate of α, i.e., the Q function of α, expressed as:
Figure FDA0004245246340000024
taking equation (3) into equation (4), and ignoring the constant term r that is independent of α, equation (4) can be rewritten approximately as:
Figure FDA0004245246340000025
according to p (X|Y; alpha) (g) ) The posterior probability distribution of (2) is a multivariate gaussian distribution, and the mean variance is known, (5) can be approximated by:
Figure FDA0004245246340000026
the maximizing M-step includes:
the new estimate of α is obtained by maximizing the Q function, namely:
Figure FDA0004245246340000031
for equation (6) to find the optimal solution using gradient descent, the first derivative of the Q function with respect to α at the optimal solution is required to be zero, assuming α * For the optimal solution of equation (6), then:
Figure FDA0004245246340000032
bringing formula (5) into formula (7) yields:
Figure FDA0004245246340000033
wherein the method comprises the steps of
Figure FDA0004245246340000034
Then assume v 0 ＝0，v N+1 ＝0；
According to { alpha } i Both } and β are non-negative, and can be obtained:
Figure FDA0004245246340000035
thereby obtaining S3
Figure FDA0004245246340000036
And->
Figure FDA0004245246340000037
2. The joint-mode coupled sparse bayesian learning super-resolution ISAR imaging algorithm according to claim 1, wherein: before initializing parameters, the radar is assumed to transmit linear radio frequency signals, and the received signals can be expressed as:
Figure FDA0004245246340000038
the distance-compressed signal is expressed as:
Figure FDA0004245246340000041
assuming that the number of pulses in the coherent accumulation time is M, dividing the pulse repetition frequency into N doppler cells, the expression of x (τ, t) in the expression (2) is: x= [ X ] nm ] N×M Applying sparse representation theory to echo distance signal direction, the matrix form of formula (1) is expressed as: y=Φx+v.
3. The joint-mode coupled sparse bayesian learning super-resolution ISAR imaging algorithm according to claim 2, wherein: the prior of signal X is expressed as:
Figure FDA0004245246340000042
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004245246340000043
and p (x) ij |α i ,α i+1 ,α i-1 )＝N(x ij |0,(α i +βα i+1 +βα i-1 ) -1 )。
4. A joint-mode coupled sparse bayesian learning super-resolution ISAR imaging algorithm according to claim 3, wherein: supposing a super parameter alpha i Is subjected to Gamma distribution, namely:
Figure FDA0004245246340000044
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004245246340000045
representing a Gamma function.
5. The joint-mode coupled sparse bayesian learning super-resolution ISAR imaging algorithm according to claim 4, wherein: according to the likelihood function and the prior distribution, the probability density function of the j-th column of the signal X meets the following conditions:
Figure FDA0004245246340000046
the mean M and covariance Σ in S2 can be derived, i.e
Figure FDA0004245246340000047
Wherein D represents a diagonal matrix and the value of the ith diagonal element thereof is alpha i +βα i+1 +βα i-1 D can be expressed as:
Figure FDA0004245246340000048
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