CN115963494A - Periodic segmented observation ISAR high-resolution imaging method based on rapid SBL algorithm - Google Patents

Abstract

The invention discloses a periodic sectional observation ISAR high-resolution imaging method based on a rapid SBL algorithm, which comprises the following steps: modeling by using the acquired periodic segmented observation data to obtain a reconstruction model of the original signal to be reconstructed; constructing a layered Bayesian prior model and obtaining layered prior distribution; obtaining posterior distribution of an original signal to be reconstructed according to the layered prior distribution and observation data; constructing an iterative formula of an SBL algorithm by using posterior distribution; calculating the diagonal elements of the posterior distribution mean and the posterior distribution covariance matrix in single iteration of the SBL algorithm by using a fast SBL algorithm based on a Fourier dictionary; and carrying out iterative calculation on diagonal elements of the posterior distribution mean value and the posterior distribution covariance matrix to obtain a final ISAR imaging result. The invention provides an imaging method based on a rapid SBL algorithm aiming at the condition of periodic segmented observation data, which can well inhibit side lobes, reduce the width of a main lobe and improve the resolution ratio, thereby realizing high-resolution imaging.

Description

Periodic segmented observation ISAR high-resolution imaging method based on rapid SBL algorithm

Technical Field

The invention belongs to the technical field of radars, and particularly relates to a periodic sectional observation ISAR high-resolution imaging method based on a rapid SBL algorithm.

Background

Inverse Synthetic Aperture Radar (ISAR) is capable of obtaining high-resolution radar images of moving objects in all-time and all-weather environments, and has been applied in various fields, such as space surveillance, radar astronomy, and the like. In high resolution radar imaging of an airborne target, the azimuthal resolution of the image is determined by the coherent accumulation angle. To obtain better azimuthal resolution, a larger coherent accumulation angle, i.e. a longer observation time, is required. During this time, when continuous measurement is impossible or measurement is invalid for some period of time, the observation data may be periodically lost. For example, interference and system instability will cause echo data at this time to be corrupted or lost. Furthermore, the data collected from multiple perspectives is discontinuous, which results in a phased loss of data, i.e., aperture sparsity. For some surveillance radars, the antenna is fixed to a rotating turntable to perform azimuth scanning throughout the airspace. Because the target is present in only one fixed surveillance zone, the collected echoes are discontinuous, with large gaps between the available samples. If the missing data is directly filled with zero padding and then azimuth compression is performed, the resulting image will have high side lobes and ghosts. Range resolution is inversely proportional to the bandwidth of the radar, so a straightforward way to increase range resolution is to increase the bandwidth and center frequency, but this approach is more hardware-intensive.

In order to achieve higher resolution without increasing a large hardware cost, numerous scholars have proposed a method for broadband synthesis using sparse subbands inherent to existing imaging radars. A key factor of this approach is the use of phased subband data to achieve accurate scatter center estimation. Therefore, it has become a challenge for researchers to obtain high-resolution images from ISAR raw data (or ISAR raw data called segmented observation) which are periodically missing in the azimuth dimension or the distance dimension. Segmented-view ISAR high-resolution imaging has received increasing attention in the radar imaging community.

In radar imaging, theoretical and experimental calculations show that when a radar echo has strong scattering points, the echo signal of a radar target can be regarded as a result of superposition of a few scattering center echo signals in a high-frequency band, and the target signal is sparse. In order to obtain a high-resolution radar image, a high-resolution radar generally works in a high-frequency region, so that a radar imaging technology based on a sparse representation theory is developed. The technology is characterized in that a radar imaging model is converted into a sparse representation model according to the sparse characteristic of radar target echo signals, and a sparse reconstruction method is adopted to carry out optimization solution on radar target parameters. The Sparse representation theory development has developed numerous Sparse reconstruction algorithms so far, and among the numerous algorithms, the Sparse Bayesian Learning (SBL) algorithm has stronger robustness and higher estimation accuracy, so that the Sparse Bayesian Learning algorithm has attracted research interest of researchers in both theory and application. The SBL algorithm is a very important Bayes statistical optimization algorithm, is developed on the basis of Bayes theory, and realizes signal reconstruction from the statistical angle. In the SBL framework, a signal to be recovered meets certain prior distribution, posterior distribution information of the signal is obtained through Bayesian analysis, and signal reconstruction is realized through continuous iteration.

However, the SBL algorithm requires solving an inverse matrix in each iteration, which has the same dimension as the observed data length. If the traditional direct inversion method is used for solving, the calculation complexity is in direct proportion to the cube of the observation data length. When the number of observation data samples is large, the calculation time tends to be long. In order to solve the problem, a plurality of scholars have already proposed some fast SBL algorithms, but the fast algorithms adopt some approximations, which can affect the accuracy of the imaging result. If the imaging method is used for segmented observation ISAR imaging, the imaging result is worse.

The segmented observation includes both aperiodic and periodic segmentation. Both of these situations are common. ISAR high resolution imaging has been studied for aperiodic segmented observational data, but less for periodic segmentation. Therefore, it is necessary to study periodic segmented observation ISAR high resolution imaging.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a periodic segmented observation ISAR high-resolution imaging method based on a rapid SBL algorithm. The technical problem to be solved by the invention is realized by the following technical scheme:

the invention provides a periodic sectional observation ISAR high-resolution imaging method based on a rapid SBL algorithm, which comprises the following steps:

s1: modeling by using the acquired periodic segmented observation data to obtain a reconstruction model of the original signal to be reconstructed, wherein the reconstruction model comprises the following steps:

wherein the dictionary matrix

x denotes the original signal to be reconstructed, v>

Represents observation noise, and->

Representing valid data in the observed data, D representing an overcomplete dictionary matrix, and->

Representing a selection matrix corresponding to the effective matrix;

s2: constructing a layered Bayesian prior model of an original signal to be reconstructed and obtaining layered prior distribution of the original signal to be reconstructed;

s3: obtaining posterior distribution of an original signal to be reconstructed according to the layered prior distribution and the periodic segmented observation data;

s4: constructing an iteration formula of an SBL algorithm by utilizing the posterior distribution;

s5: calculating the diagonal elements of the posterior distribution mean and the posterior distribution covariance matrix in single iteration of the SBL algorithm by using a fast SBL algorithm based on a Fourier dictionary;

s6: and substituting diagonal elements of the posterior distribution mean value and the posterior distribution covariance matrix into the iterative formula to carry out iterative computation so as to obtain a final ISAR imaging result.

In one embodiment of the present invention, the S2 includes:

constructing a layered Bayesian prior model, wherein a first layer of the layered Bayesian prior model is used for modeling an original signal x to be reconstructed and a noise e, and a probability density function of the original signal x to be reconstructed and the noise e is obtained:

wherein the content of the first and second substances,

representing obedience to a complex Gaussian distribution, x _k The (k + 1) th element, γ, representing the original signal vector x to be reconstructed _k Denotes x _k The inverse variance of Λ is from 1/γ _k A diagonal matrix formed in order, e _n Denotes the (n + 1) th element of the noisy data vector e, beta denotes e _n The inverse variance of (c);

setting a second layer of the hierarchical Bayesian prior model to gamma _k And β, the probability density function is:

wherein gamma (. Cndot.) represents a gamma distribution, and a and b represent γ, respectively _k C and d represent the shape and scale parameters of β, respectively, and Γ (a) represents the gamma function.

In one embodiment of the present invention, the S3 includes:

based on the prior distribution and the observation data of the sparse signal x, obtaining posterior distribution of the original signal x to be reconstructed by using a Bayesian formula and an expectation-maximization algorithm, wherein the covariance sigma and the mean mu of the obtained posterior distribution are respectively as follows:

wherein the content of the first and second substances,

in one embodiment of the invention, the iterative formula comprises:

ε ^(j) ＝diag(Σ ^(j) )

wherein the superscript (j) represents the number of iterations,

Σ represents the covariance of the posterior distribution of the signal, ∈ = diag (Σ) represents ∈ is a vector consisting of elements on the diagonal of the matrix Σ, μ represents the mean of the posterior distribution of the signal, β represents the precision of the noise, and/or>

Representing a dictionary matrix, Λ being a matrix of 1/γ _k A diagonal matrix, gamma, formed in sequence _k Indicating the precision of the (k + 1) th value in the signal vector x.

In one embodiment of the present invention, the S5 includes:

s51: constructing a Fourier dictionary matrix of periodic segmented observation data, and calculating by using the Fourier dictionary matrix to obtain

S52: by using

And solving parameters epsilon and mu in single iteration of the fast SBL algorithm.

In an embodiment of the present invention, the S51 includes:

s511: constructing a Fourier dictionary matrix of the periodic segmented observation data:

wherein, ω is _k ＝2πk/K,k＝0,...,K-1，

Representing a Fourier basis corresponding to the ith section of valid data;

s512: obtaining parameters using the constructed dictionary matrix

Expression (c): />

S513: setting permutation matrices

And utilizes the substitution matrix->

And a parameter>

Constructed parameter->

Acquire the parameter pick>

Is inverted matrix->

And the inverse matrix->

A shift expression of (a);

s514: based on the inverse matrix

Gets the inverse matrix +>

G-S decomposition formula and G-S decomposition factor of (1);

s515: solving for

G-S decomposition factor of (4);

s516: by using

Is obtained->

The calculation result of (2).

In one embodiment of the present invention, the S6 includes:

setting a convergence threshold delta, and judging whether the mu value obtained by each iteration meets the convergence condition

If the convergence condition is not met, repeating the steps S51 and S52 to continue iteration; and if the convergence condition is met, the obtained optimal mean value is the reconstructed sparse signal.

Another aspect of the present invention provides a storage medium, in which a computer program is stored, the computer program being configured to execute the steps of the periodic segmented observation ISAR high-resolution imaging method based on the fast SBL algorithm according to any one of the above embodiments.

Another aspect of the present invention provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the fast SBL algorithm-based periodic segmented observation ISAR high-resolution imaging method as described in any one of the above embodiments.

Compared with the prior art, the invention has the beneficial effects that:

1. the invention provides a high-resolution imaging method based on a rapid SBL algorithm aiming at the condition of periodic segmented observation data, which can well inhibit side lobes, reduce the width of a main lobe and improve the resolution. The fast SBL algorithm uses G-S decomposition and FFT (fast Fourier transform) to respectively solve an inverse matrix and multiplication operation related to the inverse matrix, and no approximation is adopted, so that the calculation amount can be reduced by several orders of magnitude while the result accuracy is ensured. Compared with the proposed fast SBL algorithm of aperiodic segmentation, the method of the invention has lower computational complexity.

2. The imaging method based on the rapid SBL algorithm improves the calculation speed without sacrificing the accuracy. The core of the fast SBL algorithm is to utilize a Fourier dictionary, a matrix to be inverted in each iteration of the SBL is a Toeplitz-block-Toeplitz matrix, and another Toeplitz-block-Toeplitz matrix can be constructed based on the matrix and can be quickly solved through FFT. The inverse matrix can be expressed through G-S decomposition, and the problem of high computational complexity caused by direct solving of the inverse matrix is avoided. It should be noted that the fast SBL algorithm proposed in the present invention is based on a fourier dictionary. Although SBL has no requirement on the type of dictionary, in many fields, signals are sparse in a dictionary composed of fourier bases.

3. The rapid algorithm provided by the invention also utilizes the property of displacement rank, so that the calculation complexity of the algorithm is related to the number of divided sections in the periodic segmented observation data, and the imaging time is shorter as the number of divided sections is less.

The present invention will be described in further detail with reference to the accompanying drawings and examples.

Drawings

FIG. 1 is a flowchart of a periodic segmented observation ISAR high-resolution imaging method based on a fast SBL algorithm according to an embodiment of the present invention;

FIG. 2 is a model diagram of periodically segmented observation data according to an embodiment of the present invention;

FIG. 3 is a graph of periodic segmented data imaging results for various methods;

FIG. 4 is a graph of periodic segmented data imaging performance as a function of length of observed data for various methods;

FIG. 5 is a graph of periodic segmented data imaging performance as a function of observed data loss rate for various methods;

FIG. 6 is a graph of periodic segmented data imaging performance as a function of the number of segments into which observed data is segmented for various methods;

FIG. 7 is a graph of the high resolution range profile of the complete survey data and the imaging results of the conventional range-Doppler algorithm and SBL method;

fig. 8 is a high resolution range profile of periodically segmented measured data and a graph of the imaging results of a conventional range-doppler algorithm and FD-gps bl algorithm.

Detailed Description

To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined invention purpose, the following describes in detail a periodic segmented observation ISAR high-resolution imaging method based on a fast SBL algorithm according to the present invention with reference to the accompanying drawings and the detailed description.

The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.

It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Furthermore, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or device that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrases "comprising one of \8230;" does not exclude the presence of additional like elements in an article or device comprising the element.

Example one

Referring to fig. 1, fig. 1 is a flowchart of a periodic segmented observation ISAR high-resolution imaging method based on a fast SBL algorithm according to an embodiment of the present invention. The imaging method comprises the following steps:

s1: and modeling by using the acquired periodic segmented observation data to obtain a reconstruction model of the original signal to be reconstructed.

The original signal to be reconstructed is a sparse signal, and the reconstruction of the sparse signal refers to a process of solving the original signal x to be reconstructed according to the observation data y on the premise that the original signal x to be reconstructed has certain sparsity. The model of the observation y can be described by a noisy underdetermined linear system, such as:

y＝Dx+e

wherein the content of the first and second substances,

is the observed data; />

Is an overcomplete dictionary matrix and K > N; x represents the original sparse signal to be reconstructed, i.e. most of the elements in the vector x are zero; />

Represents the observation noise, N represents the observation data length, and K/N is the super-resolution multiple. />

For segmented observation data, a schematic diagram of signal reconstruction is shown in fig. 2. The grey boxes represent valid sample samples and the white boxes represent missing sample samples. All the observed data y can be converted according to the positions of the missing samples _Ns Divided into q segments, each segment of data having a length of N _sp Validity of each data containedThe length of the data is N _gp Length of missing data is N _mp . All observed data are of length N _s Total valid data length is N _g The total length of the missing data is N _m . Their relationship is: qN _gp ＝N _g ，qN _mp ＝N _m ，qN _sp ＝N _s ＝N _g +N _m . As can be seen, the total valid data

And total missing data>

The data are respectively the collection of each segment of valid data and missing data, and the data have the following relations:

wherein the content of the first and second substances,

represents observed data, is greater than or equal to>

And &>

Respectively represent and valid data>

And the missing data->

A corresponding selection matrix. The missing rate of the raw observation is->

The reconstruction model is as follows:

wherein the dictionary matrix

x denotes the original signal to be reconstructed, and>

represents observational noise, <' > based on>

Representing valid data in the observed data.

S2: and constructing a layered Bayesian prior model of the original signal to be reconstructed and obtaining the layered prior distribution of the original signal to be reconstructed.

First, a simple description is given of an SBL (Sparse Bayesian Learning) algorithm. The SBL is based on a bayesian framework, and the original signal to be reconstructed is assumed to be a heavy tail density distribution, such as laplace or Student's T distribution. For the convenience of derivation, a scale-mixing distribution based on a hierarchical Bayesian model is usually adopted to replace the original heavy-tail distribution. Gaussian Scale Mixtures (GSMs) and Laplace Scale Mixtures (LSMs) are commonly used in SBL. The SBL then estimates the parameters of these distribution models from the observation data to reconstruct the signal.

In order to effectively improve the sparsity of the signal, a hierarchical bayesian prior model is usually used to describe the signal in the SBL. The first layer of the hierarchical bayesian prior model is the modeling of the original signal x to be reconstructed and the noise e. It is assumed that the original sparse signal x to be reconstructed obeys a zero mean covariance complex gaussian distribution Λ and the noise e obeys a zero mean covariance complex gaussian distribution β ^-1 I, the Probability Density Functions (PDF) of the original signal x to be reconstructed and the noise e are respectively:

wherein, the first and the second end of the pipe are connected with each other,

the representation obeys a complex Gaussian distribution, x _k Representing the (k + 1) th element of the original sparse signal vector x and each element in the original sparse signal vector x is independent of each other, γ _k Denotes x _k Is a function of 1/gamma _k A diagonal matrix formed in sequence. e.g. of the type _n Denotes the (n + 1) th element of the noisy data vector e, beta denotes e _n Accuracy (inverse variance). />

The second layer of the hierarchical Bayesian prior model is γ _k And modeling of beta, which are both in accordance with gamma distribution, and the probability density functions are respectively as follows:

wherein gamma (. Cndot.) represents a gamma distribution, and a and b represent γ, respectively _k C and d denote the shape and scale parameters of β, respectively, which are called hyper-parameters. To achieve a broad over-test, a, b, c, d are typically set to very small normal numbers. Γ (a) represents a gamma function.

S3: and obtaining posterior distribution of the original signal to be reconstructed according to the layered prior distribution and the periodic segmented observation data.

Specifically, based on the layered prior distribution and the observation data y obtained in step S21, a posterior distribution of the original signal x to be reconstructed is obtained by using a bayesian formula and an expectation-maximization (EM) algorithm, and the posterior distribution can be analytically expressed as a complex gaussian distribution:

wherein the covariance Σ = (β D) of the complex gaussian distribution ^H D+Λ ^-1 ) ^-1 Mean μ = β Σ D ^H y。

According to the identity of the wood-Berry matrix, Σ and μ can be expressed again as:

μ＝βΛD ^H Q ^-1 y

wherein Q = I + β D Λ D ^H 。

In the segmented observation model, effective measurement data is obtained

And the dictionary matrix->

Substituting the above equation, Σ and μ can be represented as:

wherein, the first and the second end of the pipe are connected with each other,

s4: constructing an iteration formula of an SBL algorithm by utilizing the posterior distribution;

in the SBL algorithm, signal reconstruction is achieved iteratively. The optimal mean value of the posterior distribution constructed in step S3 is the reconstructed signal. The following are iterative steps of the SBL algorithm, referred to herein as the direct-inversion SBL (DI-SBL):

/>

ε ^(j) ＝diag(Σ ^(j) )

wherein e = diag (Σ) means that e is a vector formed by elements on the diagonal of the matrix Σ, e _k Represents the (k + 1) th element of epsilon,

denotes γ obtained after the jth iteration _k Mu and sigma respectively represent the mean and covariance of the posterior probability of the original signal x to be reconstructed. Unknown parameter gamma of mu _k And β is called the hyperparameter and can be solved by the max-expectation algorithm. I | · | live through ₂ Represents->

And (4) norm.

As can be seen from the above iteration process of DI-SBL, the key steps of the single iteration process of SBL are to calculate ε and μ, but the calculation process needs to be solved

The computational complexity of the conventional direct inversion method is proportional to the cube of the matrix dimension, and the matrix ≧>

Is compared with the observation vector->

Are the same. If the observed data is more, the calculation time is often very long, and the actual engineering is difficult to realize.

S5: and calculating diagonal elements of a posterior distribution mean and a posterior distribution covariance matrix in single iteration of the SBL algorithm by using a fast SBL algorithm based on a Fourier dictionary.

In order to solve the above problems, the embodiment of the present invention provides a fast SBL algorithm based on a fourier dictionary to implement periodic segmented observation ISAR high-resolution imaging. The innovation of the algorithm is as follows: in the SBL algorithm based on the fourier dictionary,

is a Topritz-block-Topritz matrix, and another Topritz-block-Topritz matrix->

Solving for->

Then the result is resolved to>

The greater computational complexity caused by direct inversion is avoided. In addition, based on the G-S decomposition factor, epsilon and mu can be solved through FFT/IFFT, and the calculation time is greatly shortened.

Specifically, step S5 of the present embodiment includes:

s51: constructing a Fourier dictionary matrix of periodic segmented observation data, and obtaining the periodic segmented observation data by utilizing the Fourier dictionary matrix for calculation

In the present embodiment, step S51 includes:

s511: and constructing a Fourier dictionary matrix of the periodic segmented observation data.

Since the embodiment of the invention uses the dictionary formed by Fourier basis, when the data is missing, the dictionary matrix is not a complete Fourier dictionary, and is used

Means for>

The Fourier basis of column (k + 1) in (M) is expressed as:

/>

wherein, ω is _k ＝2πk/K,k＝0,...,K-1，

The fourier basis corresponding to the ith segment of valid data can be represented as:

wherein the content of the first and second substances,

representing a length of N _gp A complete Fourier basis of, i.e.

S512: obtaining parameters using the constructed dictionary matrix

The expression (c).

Based on the obtained dictionary matrix

Can be expressed as:

wherein, the first and the second end of the pipe are connected with each other,

is a Toplitz-block-Toplitz matrix, i.e.:

further, the air conditioner is provided with a fan,

one of the sub-matrices R of _i Comprises the following steps:

R _i the element expression of (1) is:

from the above formula, r _m Can be prepared by mixing 1/gamma _k And performing fast calculation on the formed vector by K-point FFT. Then, can obtain

And->

It can be seen that the SBL algorithm has an inversion matrix to be evaluated in each iteration &>

Can be quickly calculated by FFT. And also,

is also a Topritz-block-Topritz matrix, ->

Structure and>

the same is true.

S513: setting permutation matrices

And utilizes said permutation matrix>

And a parameter->

Constructed parameter->

Acquire the parameter pick>

Is inverted matrix->

And said inverse matrix>

The shifting expression of (2).

Specifically, by setting a permutation matrix

Parameter->

Can be expressed as: />

Wherein, the first and the second end of the pipe are connected with each other,

is a Topritz-block-Topritz matrix of the form:

wherein, the first and the second end of the pipe are connected with each other,

superscript here<·>Represents->

In a corresponding sub-matrix, e.g. </or>

Represents Q ₀ Q in (1) _i . Accordingly, are combined>

It can also be calculated quickly by FFT.

In view of

Is a Toplitz-block-Toplitz matrix that can be written in two different forms:

wherein the content of the first and second substances,

is->

One of (N) _g -q)×(N _g -q), and also a toprizz-block-toprizz matrix. />

Their relationship is->

Wherein it is present>

Is oneA matrix in which all elements on the minor diagonal are 1 and the remaining elements are 0, i.e. < >>

For the above

Respectively using a matrix inversion formula to obtain:

wherein the content of the first and second substances,

/>

will be provided with

And &>

Substituted into the above>

Obtaining:

based on the obtained

Ask for->

Is expressed by the following formula.

Defining a matrix:

wherein the content of the first and second substances,

I _q is an identity matrix with dimension q x q. It is clear that the following description of the preferred embodiments,

and &>

Then, the user can use the device to perform the operation,

is indicative of->

Can be expressed as:

order to

Can be further expressed as:

s514: based on the inverse matrix

Gets the inverse matrix +>

And a G-S decomposition factor.

Based on

Is expressed by (1), can find out->

The G-S decomposition formula (II) of (II), namely: />

Wherein the content of the first and second substances,

is a toeplitz-block matrix. />

And &>

Is called->

G-S decomposition factor of (2). And is->

Is 2q.

S515: solving for

G-S decomposition factor of (1).

The embodiment utilizes an iterative mode to quickly calculate

Is influenced by the Levinson-Durbin (L-D) algorithm, an embodiment of the present invention provides an iterative method for calculating ^ based on the G-S decomposition factor>

G-S decomposition factor of (1). The iterative process is as follows:

inputting: g ₀ And G ₁

Calculating an initial value:

and (3) an iterative process:

wherein, alpha =1, \8230, N _gp -2。

And (3) outputting:

w in S513 _q Can be further written as

Will be known as G ₀ ，/>

And calculated->

Substituting to obtain W _q . Will->

And W _q Substituted into>

Is further obtained/>

And &>

I.e. based on>

G-S decomposition factor of (1).

S516, based on the inverse matrix

Get the inverse matrix->

G-S decomposition formula (2).

In particular, based on

Is broken down by G-S of (4)>

The decomposition formula of G-S is:

/>

wherein the content of the first and second substances,

is a block-toeplitz matrix. Thus, a>

The solution of (a) is converted into some block-toeplitz matrix operations. And, at this time->

The displacement rank of (2 q), therefore, the calculation complexity of the FD-GPSBL algorithm is related to q, and the larger the value of q is, the longer the calculation time is.

S52: using the solution obtained in S516Obtained by

And solving epsilon and mu in single iteration of the rapid SBL algorithm, wherein the specific process is as follows:

based on the obtained dictionary matrix

ε and μ are expressed as:

ε＝diag(Σ)

specifically, the fast calculation of ε is as follows:

because Λ is a diagonal matrix, the calculation of epsilon can be divided into two steps, and the specific steps are as follows:

wherein epsilon _k And delta _k Representing the (k + 1) th values of ε and δ, respectively. And because of gamma _k And β can be calculated by an iterative formula of the SBL algorithm in (S22), and therefore only δ needs to be calculated quickly. Will be in step S511

And ^ in S516>

Substituting the above expression for delta to obtain delta _k The expression of (a) is:

wherein the content of the first and second substances,

is a block matrix, the dimensions of the sub-matrices are all N _gp ×N _gp . In units of matrix blocks, U ^l,m Representing a matrix formed by the sum of all sub-matrices on the mth diagonal of the block matrix, with dimension N _gp ×N _gp 。/>

Is called a polynomial coefficient and is U ^l,m The sum of all elements on the nth diagonal line of (1) can be quickly solved through FFT/IFFT, and the specific solving process is as follows:

order to

Wherein->

Represents->

The ith sub-vector of (4), based on the comparison result>

In which the dimension of each sub-vector is q, and the total is N _gp And (4) respectively. Then->

Wherein->

Means by>

The vector formed by the ith element in each sub-vector. Make->

Its dimension is N _gp . Order to

The expression is as follows:

wherein the content of the first and second substances,

is one dimension of N _gp ×N _gp The toplitz matrix of (a). Is visible and/or is present>

The solution can be solved by the sum of some toplitz matrices and vector products. And the product of the Topritz matrix and the vector may be converted to an FFT/IFFT. Thus, c ^l,m The solution can be fast through FFT/IFFT. In the same way, is based on>

Can be solved in the same way and have +>

Then, δ can be quickly calculated by FFT:

wherein the content of the first and second substances,

means that the vector in the brackets is subjected to K-point FFT, an

Finally, by delta, beta and 1/gamma _k The dot product of (c) calculates epsilon.

Further, the fast calculation process of μ is as follows:

from the expression of μ in step S4, the calculation of μ can be divided into three steps:

subjecting the obtained in S516

Substituted into>

Is expressed, visible->

To the right of (c) are some of the products of the toplitz matrix and the vector, and therefore ≥ s>

The calculation can be fast through FFT/IFFT. Then will->

Divided into q sections, each section having a length of N _gp And is provided with

Represents->

The ith sub-vector of (1). Make/combine>

Wherein it is present>

The calculation formula of (A) is as follows:

wherein the content of the first and second substances,

indicating that the vector in brackets is subjected to a K-point IFFT. />

Finally, by

Beta and 1/gamma _k The dot product of (d) calculates μ.

S6: and substituting the posterior distribution mean and the posterior distribution covariance into the iterative formula to carry out iterative computation so as to obtain the final ISAR high-resolution imaging.

Specifically, the steps of S51 (S512-S516) and S52 are repeated until the convergence condition is satisfied and the iteration is stopped, thereby completing the high-resolution imaging. In this embodiment, a convergence threshold δ is set, and whether the μ value obtained by each iteration satisfies the convergence condition is determined according to the following formula

If the convergence condition is not met, continuing to repeat the steps S512-S516 and S52 for iteration; if the convergence condition is met, the optimal mean value which is the reconstructed sparse signal can be obtained, and high-resolution imaging is realized.

The periodic sectional observation ISAR high-resolution imaging method provided by the embodiment of the invention is further explained by a simulation experiment.

(1.1) Experimental conditions:

setting parameters of the SBL algorithm: initial value

Hyperparametric a = b = c = d =10 ^-6 (ii) a Convergence threshold δ =10 ^-3 (ii) a Frequency sampling factor K/N _s And =4. In order to clearly see the performance of the imaging method based on the fast SBL algorithm, some typical existing sparse signal reconstruction methods are added in the embodiment for comparison, including fast iterative adaptive iterative algorithm (FIAA), and orthogonal matchingMatching Pursuit (OMP), S-ESBL, and DI-SBL algorithms. Here, the S-ESBL algorithm is an approximate fast SBL algorithm that has been proposed, and DI-SBL refers to a direct calculation SBL algorithm.

Simulation experiment: the analog observation data is from an analog signal with 25 random frequency points. The signal-to-noise ratio is 10dB.

Actually measured data experiment: the measured observations were from the Jack-42 plane. The radar used to collect ISAR data operates in the c-band, with a frequency band of 400mhz and a pulse repetition frequency of 300hz. There are 256 sample points from the window and the imaging time contains 256 pulses.

To demonstrate the signal reconstruction performance of the various methods, the normalized root mean square error (nRMSE) of the signal reconstruction is defined as:

wherein, the first and the second end of the pipe are connected with each other,

representing the reconstructed signal value and x the true signal value.

(1.2) contents and results of the experiment

The method comprises the following steps: and performing signal reconstruction on the simulated observation data by using software MATLAB R2020 b. The analog data length is 512, and the analog data length is divided into 8 sections, and each section of data length is 64. The missing rate is 50%, that is, the effective data length in each piece of data is 32. The reconstruction results of the various algorithms are shown in fig. 3. Wherein, fig. 3 (a) is a reconstruction result diagram of an imaging method based on the FIAA algorithm; fig. 3 (b) is a diagram of a reconstruction result of an imaging method based on the OMP algorithm; fig. 3 (c) is a diagram of a reconstruction result of an imaging method based on the S-ESBL algorithm; FIG. 3 (d) is a graph of the reconstructed results of an imaging method based on the DI-SBL algorithm; fig. 3 (e) is a diagram of a reconstruction result of an imaging method based on the FD-GPSBL algorithm, that is, the imaging method according to the embodiment of the present invention.

Table 1 shows the time and normalized root mean square error of signal reconstruction for the various methods described above.

TABLE 1 time and normalized RMS error comparisons for signal reconstruction for various algorithms

	FIAA	OMP	S-ESBL	DI-SBL	FD-GPSBL
						Reconstruction time/s	0.8519	0.0204	5.2275	13.1587	0.6844
nRMSE	0.1781	0.6650	0.3123	0.0675	0.0675

Step two: monte Carlo experiments were performed to compare the performance plots of the various methods under different parameters. The results are shown in fig. 4, 5 and 6. FIG. 4 is a graph of performance of various methods with varying observed data lengths, wherein FIG. 4 (a) is a graph of reconstructed computation time, noting that the time values on the graph are logarithmic; FIG. 4 (b) is the reconstructed normalized root mean square error; FIG. 4 (c) is the variance of the normalized root mean square error. FIG. 5 is a graph showing performance of various methods for observing different data loss rates, wherein FIG. 5 (a), FIG. 5 (b), and FIG. 5 (c) represent the calculation time, normalized root mean square error, and variance, respectively. FIG. 6 is a graph of performance of various algorithms when the number of segments in the periodic segmented observation data is different, wherein FIG. 6 (a), FIG. 6 (b), and FIG. 6 (c) represent the computation time, normalized root mean square error, and variance, respectively.

Step three: the measured data was imaged using software MATLAB R2020 b. In order to demonstrate the imaging effect of the periodically segmented observation data, first, an imaging result graph of the complete "Jack-42" airplane data is shown in FIG. 7 for comparison, wherein FIG. 7 (a) is a High Resolution Range Profile (HRRP), the abscissa of the graph represents the fast time dimension, and the ordinate represents the distance dimension; FIG. 7 (b) is an imaging result of a conventional range-Doppler algorithm; FIG. 7 (c) is the imaging result of the DI-SBL algorithm. The abscissa of fig. 7 (b) and 7 (c) represents an azimuth dimension, and the ordinate represents a distance dimension. For the segmented observations, assume that the "Jack-42" aircraft data is periodically missing in the azimuth dimension with an MR of 50% and q of 4. The HRRP of the periodically segmented "jacqa-42" data and the imaging results using the conventional range-doppler algorithm and FD-gps bl algorithm are shown in fig. 8 (a), 8 (b), and 8 (c), respectively. The distance dimension over-sampling factor for both full and missing data imaging is 4. The dynamic display range of all imaging plots is 40dB.

Table 2 shows the average running time of DI-SBL in the above periodic segmented observation measured data imaging experiment and the FD-GPSBL algorithm implementation method proposed by the embodiment of the present invention.

TABLE 2 average run-time comparison of DI-SBL and FD-GPSBL algorithms in experiments

Algorithm	DI-SBL	FD-GPSBL
			Time/s	9.1078	1.8541

(1.3) analysis of results

It can be seen from fig. 3 that when the two frequency values of the signal differ by one minimum frequency resolution unit, the signal reconstruction results based on FIAA, DI-SBL and FD-GPSBL algorithms are very good, indicating that they have higher resolution. The signal reconstruction results of DI-SBL and FD-GPSBL algorithms proposed by the embodiments of the present invention are the same. Furthermore, the nRMSE for the various methods listed in Table 1 also demonstrates the above conclusion, i.e., the nRMSE for the FIAA, DI-SBL, and FD-GPSBL algorithms are relatively small and the nRMSE for the DI-SBL and FD-GPSBL algorithms are the same. By comparing the computation times in table 1, we note that the computation time of the OMP algorithm is the shortest. FD-GPSBL is more than 19 times faster than DI-SBL.

Fig. 4, 5 and 6 illustrate the effect of some variables on algorithm performance. As can be seen from fig. 4 (a) and 4 (b), as the total length of the observed data increases, the calculation time of the algorithm becomes longer, and nRMSE gradually decreases; for different MRs, the larger the MR of data, the less valid data. The time for a single iteration of the SBL-like algorithm decreases, but the total number of iterations increases when the convergence threshold is reached. As shown in fig. 5 (a) and 5 (b), as MR increases, the calculation time of the algorithm decreases within a certain range, while nRMSE increases. The computation time of the FD-GPSBL algorithm is several times shorter than that of the DI-SBL algorithm. Further, when the MR is greater than 40%, nRMSE of the S-ESBL algorithm becomes large and increases rapidly as the MR increases. This is because the S-ESBL adopts a certain approximation, and the reconstruction effect is worse when more missing samples are available; when MR is more than 70%, nRMSE of FIAA becomes large; the nRMSE of the DI-SBL and FD-GPSBL algorithms also increased, but the amplification was small, and the error values were acceptable even at an MR of 80%. From FIG. 6 (a)) And (b) knowing that the q value only affects the computational complexity of the FIAA and FD-GPSBL algorithms, and has no effect on their reconstruction errors. Furthermore, as the q value increases, the computation time of the FD-GPSBL algorithm proposed by the embodiment of the present invention becomes longer, and the computation time of the FIAA algorithm becomes shorter. This is because the shift rank of the inverse matrix in the FD-GPSBL algorithm is 2q and the shift rank of the inverse covariance matrix in the FIAA algorithm is 2N _gp . Here, since the FD-gps bl algorithm has a large calculation time when the q value is higher than 16, only the calculation time, normalized root mean square error, and variance when the q value is small are shown in fig. 6. In addition, to compare the stability of the algorithm, the variance maps of the nRMSE of the algorithm are also given in fig. 4 (c), 5 (c) and 6 (c). Obviously, the variance values of the algorithms are all less than 0.03, which shows that the algorithms have good stability.

In order to verify the effectiveness of the rapid algorithm provided by the invention, the traditional distance-Doppler algorithm and the SBL/FD-GPSBL algorithm are used for respectively imaging the measured data of the Jack-42 airplane. The high resolution range profile and imaging results of the complete measurement data are shown in fig. 7, and the high resolution range profile and imaging results of the periodic segmented measurement data are shown in fig. 8. As can be seen from fig. 7, the range-doppler algorithm has a high side lobe level in the imaging result, and the SBL algorithm has a good imaging result. As can be seen from fig. 8, compared with the imaging result of the complete data, the range-doppler algorithm has a higher side lobe level for the imaging result of the segmented data, while the imaging result of the FD-gps bl algorithm proposed by the present invention is better, which indicates that the FD-gps bl algorithm has a higher imaging resolution.

Table 2 shows the calculated time for DI-SBL and FD-GPSBL algorithms for periodic segment observation in the experimental study. It is clear that the computation time of the FD-GPSBL algorithm is very short compared to the DI-SBL. The actual measurement data used in the experiment is only 128, the MR is 50%, and the effective data amount is small, so the acceleration effect of the FD-GPSBL algorithm is not obvious. In conclusion, it can be seen that the FD-gps bl algorithm can obtain better imaging results even in the case of a large MR, and the calculation time is short.

In summary, the embodiment of the invention provides a high-resolution imaging method based on a fast SBL algorithm for periodically and sectionally observing data, which can well inhibit side lobes, reduce the width of a main lobe and improve the resolution. The fast SBL algorithm is to use GS decomposition and FFT (fast Fourier transform) to respectively solve an inverse matrix and multiplication operation related to the inverse matrix, and no approximation is adopted, so that the calculation amount can be reduced by several orders of magnitude while the result accuracy is ensured. Compared with the proposed fast SBL algorithm of aperiodic segmentation, the method of the invention has lower computational complexity. The imaging method based on the rapid SBL algorithm improves the calculation speed without sacrificing the accuracy. The core of the fast SBL algorithm is to utilize a Fourier dictionary, a matrix to be inverted in each iteration of the SBL is a Toeplitz-block-Toeplitz matrix, and another Toeplitz-block-Toeplitz matrix can be constructed based on the matrix and can be quickly solved through FFT. The inverse matrix can be expressed through G-S decomposition, and the problem of high calculation complexity caused by directly solving the inverse matrix is avoided. It is noted that the fast SBL algorithm proposed by the present invention is based on a fourier dictionary. Although SBL has no requirement on the type of dictionary, in many areas, signals are sparse in a dictionary of fourier bases.

Yet another embodiment of the present invention provides a storage medium having a computer program stored therein for executing the steps of the periodic segmented observation ISAR high resolution imaging method described in the above embodiments. Yet another aspect of the present invention provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the periodic segmented observation ISAR high-resolution imaging method according to the above embodiment when calling the computer program in the memory. Specifically, the integrated module implemented in the form of a software functional module may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes several instructions to enable an electronic device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute some steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (9)

1. A periodic segmented observation ISAR high-resolution imaging method based on a rapid SBL algorithm is characterized by comprising the following steps:

s1: modeling is carried out by utilizing the acquired periodic segmented observation data to obtain a reconstruction model of the original signal to be reconstructed,

the reconstruction model is as follows:

wherein the dictionary matrix

x denotes the original signal to be reconstructed, v>

Which is indicative of the observed noise,

representing valid data in the observation data, D representing an overcomplete dictionary matrix, and->

Representing a selection matrix corresponding to the effective matrix;

s2: constructing a layered Bayesian prior model of an original signal to be reconstructed and obtaining layered prior distribution of the original signal to be reconstructed;

s3: obtaining posterior distribution of an original signal to be reconstructed according to the layered prior distribution and the periodic segmented observation data;

s4: constructing an iterative formula of an SBL algorithm by utilizing the posterior distribution;

s5: calculating the posterior distribution mean value and the diagonal elements of a posterior distribution covariance matrix in single iteration of the SBL algorithm by using a fast SBL algorithm based on a Fourier dictionary;

s6: and substituting diagonal elements of the posterior distribution mean value and the posterior distribution covariance matrix into the iterative formula to carry out iterative computation so as to obtain a final ISAR imaging result.

2. The method of ISAR high resolution imaging based on periodic segmented observation based on fast SBL algorithm according to claim 1, wherein said S2 comprises:

constructing a layered Bayesian prior model, wherein a first layer of the layered Bayesian prior model is used for modeling an original signal x to be reconstructed and a noise e, and a probability density function of the original signal x to be reconstructed and the noise e is obtained:

wherein the content of the first and second substances,

the representation obeys a complex Gaussian distribution, x _k The (k + 1) th element, γ, representing the original signal vector x to be reconstructed _k Represents x _k Of Λ is from 1/γ _k A diagonal matrix formed in sequence, e _n (n + 1) th element representing a noisy data vector eBeta represents e _n The inverse variance of (d);

setting a second layer of the hierarchical Bayesian prior model to gamma _k And β, the probability density functions are:

wherein gamma (. Gamma.) represents a gamma distribution, and a and b represent γ, respectively _k C and d represent the shape and scale parameters of β, respectively, and Γ (a) represents the gamma function.

3. The method of claim 2, wherein the S3 comprises:

based on the prior distribution and the observation data of the sparse signal x, obtaining posterior distribution of the original signal x to be reconstructed by using a Bayesian formula and an expectation-maximization algorithm, wherein the covariance sigma and the mean mu of the obtained posterior distribution are respectively as follows:

wherein the content of the first and second substances,

4. the fast SBL algorithm based periodic segmented observation ISAR high resolution imaging method of claim 3, wherein the iterative formula comprises:

ε ^(j) ＝diag(Σ ^(j) )

wherein the superscript (j) denotes the number of iterations,

Σ represents the covariance of the posterior distribution of the signal, e = diag (Σ) represents e is a vector formed by elements on the diagonal of the matrix Σ, μ represents the mean of the posterior distribution of the signal, β represents the accuracy of the noise, and ÷ represents the ratio of the mean to the mean of the posterior distribution of the signal>

Representing a dictionary matrix, Λ being a matrix of 1/γ _k A diagonal matrix, gamma, formed in sequence _k Indicating the precision of the (k + 1) th value in the signal vector x.

5. The method of ISAR high resolution imaging based on periodic segmented observation based on fast SBL algorithm according to claim 4, wherein said S5 comprises:

s51: constructing a Fourier dictionary matrix of periodic segmented observation data, and calculating by using the Fourier dictionary matrix to obtain

S52: by using

And solving parameters epsilon and mu in a single iteration of the rapid SBL algorithm.

6. The method of claim 5, wherein the S51 comprises:

s511: constructing a Fourier dictionary matrix of the periodic segmented observation data:

wherein, ω is _k ＝2πk/K,k＝0,...,K-1，

Representing a Fourier basis corresponding to the ith section of valid data;

s512: obtaining parameters using the constructed dictionary matrix

The expression of (c):

s513: setting permutation matrices

And utilizes said permutation matrix>

And a parameter->

Construction parameter>

Obtaining parameters

In an inverse matrix>

And the inverse matrix->

A shift expression of (a); />

S514: based on the inverse matrix

Gets the inverse matrix pick>

G-S (Gohberg-Semencult) decomposition formula of (a) and a G-S decomposition factor;

s515: solving for

G-S decomposition factor of (1);

s516: by using

Is obtained->

The calculation result of (2).

7. The method of ISAR high resolution imaging based on periodic segmented observation based on fast SBL algorithm according to claim 6, wherein said S6 comprises:

setting a convergence threshold delta, and judging whether the mu value obtained by each iteration meets the convergence condition

If the convergence condition is not met, repeating the steps S51 and S52 to continue iteration; and if the convergence condition is met, the obtained optimal mean value is the reconstructed sparse signal.

8. A storage medium, characterized in that the storage medium has stored therein a computer program for executing the steps of the periodic segmented observation ISAR high resolution imaging method based on the fast SBL algorithm according to any one of claims 1 to 7.

9. An electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor when calling the computer program in the memory implements the steps of the fast SBL algorithm based periodic segmented observation ISAR high resolution imaging method according to any one of claims 1 to 7.

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