CN113466864B - Rapid combined inverse-free sparse Bayes learning super-resolution ISAR imaging algorithm - Google Patents
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Abstract
The invention relates to the technical field of signal processing, in particular to a rapid combined inverse-free sparse Bayesian learning super-resolution ISAR imaging algorithm, which comprises the following steps: s1, initializing a parameter gamma, wherein gamma is a non-negative random initial value; s2, initializing a parameter Z, wherein
S3, according to
And
calculating the mean M and the variance Sigma of the posterior probability distribution by
And
to calculate q α (alpha) and q γ (gamma); s4, according to
Iteratively updating a parameter Z; s5, circularly carrying out S3 and S4 until M (t) ‑M (t‑1) || F And delta is less than or equal to the preset threshold value.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to a fast joint inverse-free 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.
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.
Disclosure of Invention
The invention aims to provide a rapid combined inverse-free sparse Bayesian learning super-resolution ISAR imaging algorithm, which solves the problems of complex imaging algorithm and large calculated amount in the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme:
a fast joint inverse-free sparse Bayesian learning super-resolution ISAR imaging algorithm is characterized by comprising the following steps:
s1, initializing a parameter gamma, wherein gamma is a non-negative random initial value;
s2, initializing a parameter Z, wherein
S3, according to
And->
Calculating the mean M and the variance Σ of the posterior probability distribution by +.>
And->
To calculate q α (alpha) and q γ (γ)；
S4, according to
Iteratively updating a parameter Z;
s5, circularly carrying out S3 and S4 until M (t) -M (t-1) || F And delta is less than or equal to the preset threshold value.
Before initializing parameters, the received signal can be expressed as:
the distance-compressed signal is expressed as:
dividing the pulse repetition frequency by assuming M pulses in the coherent accumulation timeFor N doppler cells, (2) where x (τ, t) is represented as: 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).
In a further technical solution, a bayesian method is used to reconstruct a signal X from the formula (3), and first, two layers of prior are given to X, wherein in the first layer, X is expressed as gaussian prior distribution represented by a parameter α, namely:
in the second layer, it is assumed that the super parameter α obeys the Gamma distribution, that is:
meanwhile, the mean value of V noise in the formula (3) needs to be zero, the covariance matrix is (1/Gamma) I, and Gamma estimation is realized through iterative learning, and meanwhile, V is required to be assumed to obey Gamma distribution, namely:
p(γ)＝Gamma(γ|c,d)＝Γ(c) -1 d c γ c-1 e -dγ (4)；
order the
Representing hidden variables of the hierarchical model in the formula (4), the variation distribution can be represented as:
q(θ)＝q X (X)q α (α)q γ (γ)；
let q be again X The iterative update of (X) obeys a gaussian distribution function, combines a likelihood function and a priori distribution, and the j-th column posterior probability density function of X can be expressed as:
the further technical scheme is that the solution of (5) is carried out by maximizing the unconstrained evidence lower bound, and the form of the evidence lower bound is as follows:
theorem is introduced: order the
Represents a continuous microtifunction and there are Lipschitz constants and Lipschitz continuous gradients for arbitrary +.>
And T.gtoreq.T (f), the following inequality holds:
and (3) combining the formula (6) and the formula (7) to obtain an unconstrained evidence lower bound, wherein the unconstrained evidence lower bound is expressed as follows:
the unconstrained evidence lower bound in equation (8) may be further expressed as:
the unconstrained evidence lower bound is then maximized by using a variational expectation maximization algorithm
In E-step, assuming that the other variables are constants, the posterior distribution function for each hidden variable is calculated, in M-step, q (θ) is fixed, and ≡is maximized>
Function about Z.
Further technical proposal is that the E-step calculation process comprises q X Iterative update of (X), q α Loop iteration sum q of (alpha) γ And (gamma) loop iteration.
A further technical proposal is that q is as follows X In the iterative update of (X), the posterior probability distribution q X The iterative update of (X) is expressed as:
wherein,,
<α n >representing alpha n Regarding q α The expectation of (α) can be derived from equation (9) to yield q X (X) obeys a gaussian distribution whose mean and variance are respectively:
A further technical proposal is that q is as follows α In cyclic iteration of (α), posterior distribution q α (α) is expressed as:
wherein,,
is->
Regarding q X (X) expectation, X nl The first element of line n in X, i.e., α satisfies the Gamma distribution in S3 +.>
Wherein the method comprises the steps of
A further technical proposal is that q is as follows γ (gamma) iteration of the loop, for q γ The variation optimization of (γ) can be obtained:
namely, gamma satisfies Gamma distribution in S3
Wherein the method comprises the steps of
In a further technical scheme, q (theta; Z) old ) Carry-in
The +.about.in S4 can then be obtained by optimization problems>
Let the gradient of the above formula with respect to Z be zero, it is possible to obtain:
(10) TI-2Φ in T Phi is a positive definite matrix and satisfies T>T(f)＝2λ max (Φ T Φ), wherein λ is max (Φ T Φ) represents Φ T Maximum eigenvalue of Φ.
Compared with the prior art, the invention has the beneficial effects that: in the scheme, although the inverse of the N multiplied by N matrix still needs to be calculated in the process of iteratively updating the variance sigma, the matrix inversion operation at the moment is applied to the diagonal matrix, the inverse can be rapidly obtained, and the matrix inversion operation with high calculation complexity can be avoided by the algorithm, so that the calculation amount of the algorithm is greatly reduced.
Drawings
Fig. 1 is a graph of reconstructed MSEs for each algorithm at different sparsities K, with other parameters set as follows: m=250, n=500, l=20.
Fig. 2 is a graph of the reconstructed MSE for each algorithm for different parameters M, where the other parameters are set as follows: n=500, l=20, k=120.
Fig. 3 is a graph of reconstructed MSEs for various algorithms at different signal-to-noise ratios.
Fig. 4 is an average operation time chart of each algorithm under different parameters N, and other parameters are set as follows: m=n/2,K =n/10, l=20, snr=20 dB.
FIG. 5 is a graph of the result of super-resolution ISAR imaging of B727 data by the PC-SBL algorithm.
FIG. 6 is a graph showing the results of super-resolution ISAR imaging of B727 data by the M-FOCUSS algorithm.
FIG. 7 is a graph of the results of super-resolution ISAR imaging of B727 data by the M-SBL algorithm.
FIG. 8 is a graph of the result of super-resolution ISAR imaging of B727 data by the algorithm of the present invention.
FIG. 9 is a MSE plot of super-resolution ISAR imaging of B727 for different algorithms.
FIG. 10 is a graph showing the time contrast of super-resolution ISAR imaging of B727 by different algorithms.
FIG. 11 is a graph showing the results of super-resolution ISAR imaging of Yak-42 by the PC-SBL algorithm.
FIG. 12 is a graph showing the results of super-resolution ISAR imaging of Yak-42 by the M-FOCUSS algorithm.
FIG. 13 is a graph showing the results of the M-SBL algorithm on the super-resolution ISAR imaging of Yak-42.
FIG. 14 is a graph showing the results of the algorithm of the present invention on the super-resolution ISAR imaging of Yak-42.
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:
fig. 1-14 show a preferred implementation manner of the fast joint inverse-free sparse bayesian learning super-resolution ISAR imaging algorithm according to the present invention, where the fast joint inverse-free sparse bayesian learning super-resolution ISAR imaging algorithm in this embodiment specifically includes the following steps:
s1, initializing a parameter gamma, wherein gamma is a non-negative random initial value;
s2, initializing a parameter Z, wherein
S3, according to
And->
Calculating the mean M and the variance Σ of the posterior probability distribution by +.>
And->
To calculate q α (alpha) and q γ (γ)；
S4, according to
Iteratively updating a parameter Z;
s5, circularly carrying out S3 and S4 until M (t) -M (t-1) || F And delta is less than or equal to the preset threshold value.
Before initializing parameters, the radar is assumed to transmit linear radio frequency signals, and the received signals can be expressed as:
the distance-compressed signal is expressed as:
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, the pulse repetition frequency is divided into N doppler cells, and 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).
Wherein,,
in the form of a matrix of y (τ, t) in formula (1)>
Representing noise matrix, sparse dictionary Φ N×N Can be expressed as:
if it is
Then->
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
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->
And->
Representing super resolution multiple of range profile, parameter +.>
And
super-resolution multiples of azimuth are shown. />
Representing a partial fourier matrix, namely:
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.
Reconstructing a signal X from the formula (3) by using a Bayesian method, firstly endowing X with two layers of prior, and expressing X as Gaussian prior distribution characterized by a parameter alpha in a first layer, namely:
wherein,,
to control the non-negative hyper-parameters of a priori variance of each row of X, X (n) Represents the nth row of X.
In the second layer, it is assumed that the super parameter α obeys the Gamma distribution, that is:
wherein,,
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 ]]。
Meanwhile, the mean value of V noise in the formula (3) needs to be zero, the covariance matrix is (1/Gamma) I, and Gamma estimation is realized through iterative learning, and meanwhile, V is required to be assumed to obey Gamma distribution, namely:
p(γ)＝Gamma(γ|c,d)＝Γ(c) -1 d c γ c-1 e -dγ (4)；
order the
Representing hidden variables of the hierarchical model in the formula (4), the variation distribution can be represented as:
q(θ)＝q X (X)q α (α)q γ (γ)；
let q be again X The iterative update of (X) obeys a gaussian distribution function, combines a likelihood function and a priori distribution, and the j-th column posterior probability density function of X can be expressed as:
wherein the mean and variance can be expressed as follows:
Wherein,,
Σ t ＝γI+ΦDΦ T from equation 2, it can be seen that in the iteration of the posterior distribution based on the M-SBL algorithm, the inverse of one M x M matrix needs to be calculated each time. Thus, the computational complexity of the variational M-SBL algorithm is approximately O (M 3 ). Such high computational complexity can limit its application to many problems requiring handling large amounts of data.
In the scheme, the (5) solution is carried out by maximizing the unconstrained evidence lower bound, and the evidence lower bound is in the form of:
theorem is introduced: order the
Represents a continuous microtifunction and there are Lipschitz constants and Lipschitz continuous gradients for arbitrary +.>
And T.gtoreq.T (f), the following inequality holds:
according to the above theorem, the lower bound of p (y|x, γ) can be found by:
wherein,,
when the inequality relation in the formula (a) holds for any Z, and when z=x, the inequality in the formula becomes an equation.
And (3) combining the formula (6) and the formula (7) to obtain an unconstrained evidence lower bound, wherein the unconstrained evidence lower bound is expressed as follows:
wherein,,
the unconstrained evidence lower bound in equation (8) may be further expressed as:
wherein,,
h (Z) can be expressed as:
the unconstrained evidence lower bound is then maximized by using a variational expectation maximization (expectation maximization, EM) algorithm
In E-step, assuming that the other variables are constants, the posterior distribution function for each hidden variable is calculated, in M-step, q (θ) is fixed, and ≡is maximized>
Function about Z.
The E-step calculation process includes q X Iterative update of (X), q α Loop iteration sum q of (alpha) γ And (gamma) loop iteration.
q X In the iterative update of (X), the posterior probability distribution q X The iterative update of (X) is expressed as:
wherein,,
<α n >representing alpha n Regarding q α The expectation of (α) can be derived from equation (9) to yield q X (X) obeys a gaussian distribution whose mean and variance are respectively:
Where < γ > represents the desire for γ.
q α In cyclic iteration of (α), posterior distribution q α (α) is expressed as:
wherein,,
is->
Regarding q X (X) expectation, X nl Represents the first element of the nth row in X, i.e., alpha satisfies S3Gamma distribution->
Wherein the method comprises the steps of
q γ (gamma) iteration of the loop, for q γ The variation optimization of (γ) can be obtained:
namely, gamma satisfies Gamma distribution in S3
Wherein the method comprises the steps of
In summary, E-step mainly implements iterative updating of posterior probability distributions of hidden variables X, α and γ. In the iterative update process, part of the parameters are given by:
wherein Tr (A) represents the trace of matrix A, Σ n,n Represents the nth diagonal element of the matrix Σ.
In M-step, q (θ; Z) old ) Carry-in
The optimization problem can be obtained in S4
Let the gradient of the above formula with respect to Z be zero, it is possible to obtain:
(10) The derivation is true because of TI-2Φ T Phi is a positive definite matrix and satisfies T>T(f)＝2λ max (Φ T Φ), wherein λ is max (Φ T Φ) represents Φ T Maximum eigenvalue of Φ.
In summary, the observation data is assumed to be Y, and the structured sparse dictionary is Φ.
In the scheme, although the inverse of the N multiplied by N matrix still needs to be calculated in the process of iteratively updating the variance sigma, the matrix inversion operation at the moment is applied to the diagonal matrix, the inverse can be rapidly obtained, and the matrix inversion operation with high calculation complexity can be avoided by the algorithm, so that the calculation amount of the algorithm is greatly reduced.
The advantages of the algorithm are demonstrated by several experiments:
experimental example one:
the effectiveness of the algorithm of the scheme is verified by using the simulation signal. The parameters a, b, u and v are all set to 10 -6 . Setting the parameter T to a value slightly greater than the Lipschitz constant, such that t=λ max (2Φ T Φ)+10 -6 . In experiments, the reconstruction performance of the algorithm of the scheme is compared with that of a PC-SBL algorithm, a continuous block original dual active set algorithm (group primal dual active set with continuation algorithm, GPDASC algorithm), an M-FOCUSS algorithm, an M-SBL algorithm and a T-MSBL algorithm. In the simulation experiment, the L sparse vectors of the original data all contain K non-zero elements, and the non-zero element positions of the vectors are the same. At the same time, the non-zero element positions are random, and the amplitudes thereof follow a standard normal distribution. Matrix array
Is a Gaussian random matrix, and each vector element in the matrix obeys standard Gaussian distribution of independent same distribution. The experiments are all 100 Monte Carlo simulation results.
The reconstruction performance of each algorithm is quantitatively analyzed by means of a mean square error, which is defined as MSE= |R-R 0 || F /||R 0 || F Wherein R is 0 Representing a full aperture ISAR image data matrix obtained using the RD algorithm, R representing a sparse aperture imaging data matrix obtained using three different other algorithms.
As can be seen in fig. 1-3, the PC-SBL algorithm and the GPDASC algorithm are relatively inefficient to reconstruct, mainly because both algorithms require that each vector of the signal be block sparse and require knowledge of part of the a priori information. The reconstruction effect of other algorithms is similar, and the original signal can be better reconstructed. Here, the CPU average calculation time is also used to measure the calculation complexity of each algorithm. As can be seen from fig. 4, the algorithm of the present solution avoids matrix inversion operation, and has the lowest calculation complexity and the shortest calculation time. Therefore, the algorithm reconstruction effect and the operation complexity are comprehensively considered, and the algorithm performance of the scheme is best.
Experimental example two:
ISAR imaging experiments are carried out by using the wave sound 727 simulation data to verify the effectiveness of the algorithm of the scheme, the radar transmits linear frequency modulation signals, the carrier frequency is 9GHz, the signal bandwidth is 150MHz, and the pulse repetition frequency is 20KHz. The values of the setting parameters a, b, u, v and T are consistent with those in experiment one,
is a partial fourier matrix. Firstly, ISAR super-resolution imaging is realized by 128 pulses, as shown in fig. 5-8, because the reconstruction error is larger when the T-MSBL algorithm reconstructs a complex signal, and the GPDASC algorithm mainly aims at the reconstruction problem of a block sparse signal, the reconstructed ISAR image results of the two algorithms are not continuously given here, and only the reconstructed ISAR image results are compared with the other three algorithms in experimental example I.
As can be seen from the figures 5-8, compared with other algorithms, the algorithm reconstruction of the scheme has the advantages that the ISAR image resolution is higher, and the focusing performance is good. In order to quantitatively analyze the imaging effect of each algorithm, the reconstructed mean square error of each algorithm is also calculated. As can be seen in fig. 9-10 (all 200 monte carlo experimental results), the reconstructed ISAR image MSE of the algorithm of the present scheme is minimal. In addition, compared with the average operation time of each algorithm, the algorithm operation time of the scheme is shortest, and the calculation complexity of the algorithm of the scheme is proved to be smaller than that of other algorithms.
Experimental example three:
the effectiveness of the algorithm is verified by using the Yak-42 measured data, the radar also transmits a linear frequency modulation signal, the center frequency is 10GHz, the signal bandwidth is 400MHz, the pulse repetition frequency is 100Hz, and 256 pulses are acquired within the coherent accumulation time of 2.56 s. The values of parameters a, b, u, v and T were consistent with the settings of the parameters in experiment one.
Is a partial fourier matrix. As shown in FIGS. 11-14, ISAR high resolution imaging is achieved with 128 pulses.
Compared with other algorithms, the ISAR image obtained by the algorithm reconstruction of the scheme has higher resolution and good focusing performance. The imaging effect of each algorithm is quantitatively analyzed by comparing and analyzing the reconstructed mean square error of each algorithm, and as can be seen from fig. 11-14, the reconstructed ISAR image MSE of the algorithm of the scheme is minimum, the average operation time of each algorithm is compared, and the result is also 200 Monte Carlo experimental results, and as can be seen, the operation time required by the algorithm of the scheme is shortest compared with other Bayesian learning algorithms, and the superiority of the algorithm of the scheme in calculation complexity is further proved.
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 (3)
1. A fast joint inverse-free sparse Bayesian learning super-resolution ISAR imaging algorithm is characterized by comprising the following steps:
s1, initializing a parameter gamma, wherein gamma is a non-negative random initial value;
s2, initializing a parameter Z, wherein
S3, according to
And->
Calculating the mean M and the variance Σ of the posterior probability distribution by +.>
And->
To calculate q α (alpha) and q γ (γ)；
S4, according to
Iteratively updating a parameter Z;
s5, circularly carrying out S3 and S4 until M (t) -M (t-1) || F Delta is less than or equal to delta, wherein delta is a preset threshold value;
before initializing parameters, the radar is assumed to transmit linear radio frequency signals, and the received signals can be expressed as:
applying sparse representation theory to echo distance signal direction, and (1) expressing the matrix form of formula as: y=Φx+v (3);
suppose V obeys the Gamma distribution, namely:
p(γ)＝Gamma(γ|c,d)＝Γ(c) -1 d c γ c-1 e -dγ (4)；
order the
Representing hidden variables of the hierarchical model in the formula (4), the variation distribution can be represented as:
q(θ)＝q X (X)q α (α)q γ (γ)；
let q be again X The iterative update of (X) obeys a gaussian distribution function, combines a likelihood function and a priori distribution, and the j-th column posterior probability density function of X can be expressed as:
solving (5) by maximizing unconstrained lower bound of evidence in the form of:
theorem is introduced: order the
Represents a continuous microtifunction and there are Lipschitz constants and Lipschitz continuous gradients for arbitrary +.>
And T.gtoreq.T (f), the following inequality holds:
and (3) combining the formula (6) and the formula (7) to obtain an unconstrained evidence lower bound, wherein the unconstrained evidence lower bound is expressed as follows:
the unconstrained evidence lower bound in equation (8) may be further expressed as:
the unconstrained evidence lower bound is then maximized by using a variational expectation maximization algorithm
In E-step, assuming that the other variables are constants, the posterior distribution function for each hidden variable is calculated, in M-step, q (θ) is fixed, and ≡is maximized>
A function about Z;
the E-step calculation process includes q X Iterative update of (X), q α Loop iteration sum q of (alpha) γ (γ) loop iteration; the q is X In the iterative update of (X), the posterior probability distribution q X The iterative update of (X) is expressed as:
wherein,,
<α n >representing alpha n Regarding q α The expectation of (α) can be derived from equation (9) to yield q X (X) obeys a gaussian distribution whose mean and variance are respectively:
The q is α In cyclic iteration of (α), posterior distribution q α (α) is expressed as:
wherein,,
is->
Regarding q X (X) expectation, X nl The first element of line n in X, i.e., α satisfies the Gamma distribution in S3 +.>
Wherein the method comprises the steps of
The q is γ (gamma) iteration of the loop, for q γ The variation optimization of (γ) can be obtained:
namely, gamma satisfies Gamma distribution in S3
Wherein the method comprises the steps of
In the M-step, q (θ; Z) old ) Carry-in
The optimization problem can be obtained in S4
Let the gradient of the above formula with respect to Z be zero, it is possible to obtain:
(10) TI-2Φ in T Phi is a positive definite matrix and satisfies T > T (f) =2λ max (Φ T Φ), wherein λ is max (Φ T Φ) represents Φ T Maximum eigenvalue of Φ.
2. The rapid joint inverse free sparse bayesian learning super-resolution ISAR imaging algorithm according to claim 1, wherein: the distance-compressed signal is expressed as:
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 。
3. The rapid joint inverse free sparse bayesian learning super-resolution ISAR imaging algorithm according to claim 2, wherein: reconstructing a signal X from the formula (3) by using a Bayesian method, firstly endowing X with two layers of prior, and expressing X as Gaussian prior distribution characterized by a parameter alpha in a first layer, namely:
in the second layer, it is assumed that the super parameter α obeys the Gamma distribution, that is:
meanwhile, the mean value of V noise in the formula (3) is zero, the covariance matrix is (1/gamma) I, and gamma estimation is realized through iterative learning.
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