CN112269168A - SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition - Google Patents
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Abstract
The invention belongs to the technical field of microwave remote sensing, and discloses an SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition, which comprises the following steps: establishing an SAR echo representation model under a broadband interference condition; combining Laplace distribution prior assumption of time-frequency equivalent noise and low-rank characteristics of a broadband interference time-frequency matrix, and constructing an SAR broadband interference reconstruction model in the maximum likelihood sense; and estimating the model parameters by Bayesian inference to realize the reconstruction of the SAR broadband interference time-frequency matrix, and performing destructive processing in a data domain to obtain SAR echo data after interference suppression. The method can effectively inhibit the broadband interference and improve the robustness of the model to the SAR data containing the abnormal value and the double tail noise. Meanwhile, the SAR broadband interference suppression problem is converted into an optimization solving problem under a Bayesian framework, and the model parameter estimation precision is improved.
Description
Technical Field
The invention belongs to the technical field of microwave remote sensing, and particularly relates to an SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition. The method can be used for inhibiting broadband interference in SAR echo signals, recovering target information covered by the interference, obtaining a high-quality target imaging effect and obviously enhancing the interpretation capability of SAR images.
Background
The Synthetic Aperture Radar (SAR) has the characteristics of all-weather, high resolution, long action distance and the like, and is widely applied to the military and civil fields of imaging identification, resource exploration, ocean observation, geological mapping, environmental perception and the like. In general, SAR employs a transmission signal having a large bandwidth to achieve high resolution, which results in inevitable mixing of radio frequency interference in the same frequency band in SAR echo data. Radio frequency interference typically comes from airport radars, signal base stations, GPS devices, and the like. The presence of radio frequency interference can have a severe impact on SAR imaging quality. On the one hand, these radio frequency interferences have strong energy, which can significantly reduce the signal-to-noise ratio of the SAR echo signal and even cause saturation of the SAR receiver. On the other hand, the existence of radio frequency interference causes inaccurate estimation of the key Doppler parameters of the SAR system, thereby causing fuzzy and defocusing of SAR imaging results. In addition, the radio frequency interference can also reduce the accuracy of feature extraction, and is not beneficial to the interpretation of the SAR image. Therefore, the research of the effective SAR interference suppression algorithm has important application value.
Current interference suppression algorithms mainly include two main categories by principle: data driven classes and model driven classes. The data-driven algorithm mainly achieves the purpose of separating useful signals and interference in a specific data domain by designing a reasonable filter. In the data-driven interference suppression algorithm, Zhang Shuangxi combines short-time Fourier transform (STFT) with wavelet transform, maps the time domain SAR echo instantaneous frequency spectrum to a wavelet domain, and identifies and filters the wavelet coefficient corresponding to the interference component, thereby realizing the suppression of broadband interference. However, this method needs to perform multiple transformations, requires more computing resources, and causes a part of signal loss to some extent. The method comprises the steps of providing an interference suppression algorithm based on a deep residual error network, performing optimization training on the whole network through a large number of time-frequency pattern books simulating interference, extracting and reconstructing time-frequency characteristics of a target signal, and accordingly achieving effective suppression on actually-measured interference data. However, this approach relies on the fidelity and sample volume of the simulated SAR echo interference data.
The model-driven algorithm is mainly characterized by using a mathematical model to characterize SAR echoes and carrying out optimization solution on parameters according to a specific constraint optimization criterion. In the algorithm, Sejia and the like utilize the time-frequency low-rank characteristic of interference and the sparse hypothesis of target signals, and utilize GoDec (Go Decomposition) algorithm to decompose and reconstruct interference time-frequency information by a time-frequency matrix, so as to finally realize interference suppression. However, the suppression effect of this method is closely related to the accuracy of the model, and further analysis and improvement are required for the suppression effect of the broadband interference. On the basis of assuming that the interference has azimuth continuity, the xanthate and the like construct a time domain tensor model for the echo data and perform low-rank sparse decomposition, so that the separation of the interference and a target signal is realized. However, the assumption that the broadband interference is continuous along the azimuth direction is not effectively verified for the universality of the measured data.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide an SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition, provides prior distribution assumption of Laplace distribution, constructs a low-rank time-frequency matrix reconstruction model of broadband interference, can effectively suppress the broadband interference, and improves the robustness of the model to SAR data containing abnormal values and heavy tail noise. Meanwhile, the broadband interference suppression problem is expanded to a Bayesian framework, and model parameter estimation is simplified.
The technical principle of the invention is as follows: first, a single-echo model of the SAR in the azimuth direction is established. And secondly, combining the Laplace distribution prior assumption of the echo signal time-frequency matrix and the low-rank characteristic of the broadband interference time-frequency matrix to form a broadband interference reconstruction model in the maximum likelihood meaning. And then, forming complete model parameter posterior probability under a Bayesian framework, estimating the model parameters by utilizing Bayesian inference, realizing reconstruction of a broadband interference time-frequency matrix, and performing destructive processing in a data domain to obtain echo data after interference suppression. And finally, obtaining a high-quality SAR image through SAR imaging processing, and evaluating the interference suppression effect.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
and 4, carrying out inverse short-time Fourier transform on the reconstructed broadband interference, and then carrying out cancellation processing on the reconstructed broadband interference and the original echo signal to obtain a time domain echo signal after broadband interference suppression.
Compared with the prior art, the invention has the beneficial effects that:
(1) on the basis of fully analyzing SAR echo and interference time-frequency characteristics, the time-frequency statistical characteristics of the target signal and the time-frequency low-rank characteristics of broadband interference are fully utilized, the prior distribution assumption of Laplace distribution is put forward, a low-rank time-frequency matrix reconstruction model of the broadband interference is constructed, the broadband interference can be effectively inhibited, and the robustness of the model to SAR data containing abnormal values and heavy tail noise is improved.
(2) The invention expands the broadband interference suppression problem to a Bayes framework, and utilizes a variational Bayes method to carry out parameter estimation on a Bayes posterior probability model, thereby effectively simplifying the direct inference problem of complex probability model parameters in the broadband interference time-frequency matrix reconstruction process.
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The invention is described in further detail below with reference to the figures and specific embodiments.
Fig. 1 is a flowchart of an implementation of an SAR broadband interference suppression method based on bayesian theory and low rank decomposition according to the present invention;
FIG. 2 is a time-frequency domain statistical result diagram of non-interference single SAR echo data in the embodiment of the present invention; wherein, (a) is a single SAR echo time-frequency diagram; (b) fitting a result graph for the probability density of the SAR echo;
FIG. 3 is a time-frequency domain representation result diagram of two times of actual measurement of broadband interference SAR echo data in the embodiment of the present invention; wherein, (a) corresponds to the echo data of the one-time actual measurement azimuth; (b) corresponding to the other measured azimuth echo data;
FIG. 4 is a comparison of an original non-interfering signal and an emulated wideband interfering echo in an embodiment of the present invention; wherein, (a) is a time domain interference pre-and post-contrast graph; (b) a comparison graph before and after frequency domain interference is obtained; (c) the time-frequency diagram of the signal before interference, (d) the time-frequency diagram of the signal after interference;
FIG. 5 is a diagram illustrating the interference suppression processing result of simulation data according to an embodiment of the present invention; wherein, (a) is a reconstructed interference signal time-frequency domain representation diagram; (b) recovering a time-frequency domain representation of a target signal; (c) a time domain comparison graph of the recovered signal and the original signal is obtained; (d) fitting a result graph for the recovered signal probability density function;
FIG. 6 is a comparison graph of interference suppression results of measured data of a coast scene in the Sentinel-1A VH polarization mode according to an embodiment of the present invention; wherein, (a) is the imaging result of the original SAR data; (b) imaging results after GoDee algorithm interference suppression processing are obtained; (c) the imaging result after the interference suppression processing is carried out by the method;
FIG. 7 is a comparison graph of interference suppression results of ship scene measured data in the Sentinel-1B VH polarization mode in the embodiment of the present invention; wherein, (a) is the imaging result of the original SAR data; (b) imaging results after GoDee algorithm interference suppression processing are obtained; (c) the imaging result after the interference suppression processing of the method is shown.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only illustrative of the present invention and should not be construed as limiting the scope of the present invention.
Referring to fig. 1, the SAR broadband interference suppression method based on bayesian theory and low rank decomposition provided by the present invention includes the following steps:
because the SAR data are processed by the azimuth pulse, only the single echo model along the azimuth direction is needed to be constructed. The azimuth single echo model can be expressed as a linear superposition form of signals, interference and noise:
s(k)＝x(k)+i(k)+n(k)
wherein s (k) represents the original echo signal of the kth range snapshot unit, x (k) represents the target echo signal of the kth range snapshot unit, i (k) represents the interference of the kth range snapshot unit, and n (k) represents the noise signal of the kth range snapshot unit.
In general, wideband Interference can be characterized in two typical forms, namely Chirp modulated wideband Interference (CMWBI) and Sinusoidal modulated wideband Interference (SVMWBI).
Specifically, the mathematical characterization form of the chirp broadband interference is as follows:
wherein, an、fn、γnRespectively representing the amplitude, frequency and frequency modulation rate of the nth chirp broadband interference. Similarly, the mathematical characterization of sinusoidal fm broadband interference is in the form of:
wherein, am、βm、fm、φmRespectively representing the amplitude of the m-th sinusoidal FM broadband interferenceDegree, modulation factor, frequency, initial phase.
Of course, the wideband radio frequency interference in an actual SAR echo is relatively complex, but can be characterized by a combination of these two basic interference types.
Compared with strong broadband interference, the target signal presents a noise-like distribution. Therefore, the single echo of the azimuth direction can be simplified into the following form:
s(k)＝i(k)+nx(k)
wherein n isx(k) N (k) + x (k) is equivalent noise, representing the superposition of the signal and the noise. s (k) is denoted as the original echo signal.
And 2, according to the statistical characteristic analysis of the echo signal time-frequency matrix, adopting Laplace prior distribution hypothesis and combining with the broadband interference time-frequency low-rank characteristic to construct a broadband interference reconstruction model in the maximum likelihood meaning.
Specifically, the method comprises the following substeps:
and a substep 2a, adopting a Laplace prior distribution hypothesis to construct a broadband interference recovery model in the maximum likelihood sense.
In order to fully mine echo signal characteristics, a single azimuth echo (an original echo signal) is mapped to a distance time-frequency domain by using a short-time Fourier transform for processing. In the time-frequency domain, the original echo signal model is:
S＝WBI+N
wherein the content of the first and second substances,
respectively representing an original echo time-frequency matrix, a broadband interference time-frequency matrix and an equivalent noise time-frequency matrix.
In order to fully utilize the time-varying and non-stationary characteristics of the signal, the invention adopts a strategy of reconstructing interference in a time-frequency domain and then restoring a target signal by data cancellation so as to reserve the characteristics of the signal to the maximum extent.
Firstly, statistical distribution fitting is carried out on the time-frequency transformation result of the interference-free SAR echo data, as shown in the attached figure 2. Wherein, (a) is a time-frequency diagram of a single SAR echo, and (b) is a probability density fitting result of the SAR echo. The probability density statistical distribution of the measured data is more consistent with Laplace distribution, and the Laplace distribution can better process abnormal values and heavy tail noise in the data. Therefore, it is assumed that the equivalent noise time-frequency matrix N in the time-frequency domain original echo signal model follows Laplace prior distribution. Whereas for the reconstruction problem of wideband interference the reconstruction error needs to be minimized, the present invention uses a likelihood function to determine the loss function of the reconstruction problem:
wherein S isijFor the ith row and jth column element, WBI, of the matrix SijIs the ith row and the jth column element of the matrix WBI; omega represents a subscript set of time-frequency matrix elements, | | · | | non-woven air1Represents L1Norm, C is a constant independent of the variable, p (· |0, b) represents the Laplace distribution with a location parameter of 0 and a scale parameter of b. Therefore, after unnecessary coefficients and constant terms are omitted, the optimization function of the broadband interference time-frequency matrix reconstruction problem is obtained as follows:
this converts the wideband interference time-frequency matrix reconstruction problem into L1And (5) optimizing the norm.
And the substep 2b is used for forming a broadband interference low-rank time-frequency matrix accurate reconstruction model in the maximum likelihood sense by combining the low-rank characteristic of the broadband interference time-frequency matrix and utilizing a matrix full-rank decomposition principle.
And characterizing the azimuth echo of the broadband interference data in a time-frequency domain. As shown in fig. 3, the time-frequency domain characterization results of different measured broadband interference data are shown. As can be seen from the time-frequency characterization result of the measured data broadband interference in fig. 3, the broadband interference occupies only a limited time-frequency spectrum unit, and therefore, the time-frequency matrix of the broadband interference can be considered to have a low-rank characteristic. Generally, for airborne SAR and spaceborne SAR, the frequency band of the radio frequency broadband interference is limited and approximately stable. In combination with the aggregation characteristic of the radio frequency broadband interference in the time-frequency domain, it can be further assumed that the broadband interference is low-rank compared with the time-frequency matrix of the whole echo signal. Therefore, the problem of recovering the wideband interference time-frequency matrix in the substep 2a is the problem of recovering the low-rank component of the time-frequency matrix of the original echo.
According to the matrix full rank decomposition theorem, any matrix which is not zero can be decomposed into a form of a product of two full rank matrices, and a broadband interference time-frequency low-rank matrix is decomposed, wherein the expression is as follows:
WBI＝LHR
wherein the content of the first and second substances,
and
q, T are the dimensionalities of the time-frequency matrix, r is the rank of the broadband interference time-frequency matrix, r is less than or equal to min { Q, T }, and superscript H represents the conjugate transpose operation of the matrix.
The recovery of the wideband interference time-frequency matrix can be characterized as the following optimization problem:
and 3, introducing complex Gaussian prior distribution constraint of decomposition factors of the broadband interference time-frequency matrix, constructing a posterior model of the broadband interference time-frequency matrix under a Bayes framework, deducing and estimating parameters of a signal posterior probability model by using variational Bayes, and accurately reconstructing the broadband interference time-frequency matrix. Meanwhile, cancellation processing is carried out in a time-frequency domain, and time domain echo data after interference suppression are obtained by combining with the ISTFT.
Specifically, the method comprises the following substeps:
a substep 3a, constructing a posterior model of a broadband interference time-frequency matrix under a Bayes framework;
firstly, transforming the Laplace distribution of an equivalent noise time-frequency matrix N into a Gaussian scale mixed expression form:
wherein, CN (N)ij|0，zij) Means zero mean and z varianceijComplex Gaussian distribution of (i), p (z)ij| λ) represents an exponential distribution with a parameter λ, NijAnd the ith row and the jth column of the noise time-frequency matrix N are represented.
Secondly, an ith column vector L of a decomposition factor L of the broadband interference time-frequency matrix is setiAnd j column vector R of decomposition factor R of broadband interference time-frequency matrixjAll obey complex Gaussian distribution, corresponding accuracy
And
obey a Gamma distribution, i.e.:
wherein, a0，b0，c0，d0Respectively, the hyper-parameters of Gamma distribution, I is a unit matrix, and the superscript-1 represents the inverse operation.
Finally, a complete Bayesian posterior probability model of the model parameters is given by using Bayesian theorem:
wherein, tauLIs composed of
Formed vector of τRIs composed of
The constructed vector. Z is a group consisting ofijForming a matrix.
Substep 3b, estimating Bayes posterior probability model parameters by using variational Bayes, and reconstructing a low-rank broadband interference time-frequency matrix;
factorizing the approximate distribution of the Bayes posterior probability model, and expressing the approximate distribution as the following form:
parameter estimation by using variation inference can obtain:
thus, the specific parameter estimation result is:
wherein E [. cndot. ] represents the expectation.
Determining the low-rank factor of the broadband interference time-frequency matrix according to the estimated value of the Bayes posterior probability model parameters, thereby obtaining the reconstruction form of the broadband interference time-frequency matrix as
WBI＝(L*)HR*
Wherein L is*And R*And representing the convergence estimation result of the low-rank broadband interference time-frequency matrix factor.
And 4, carrying out inverse short-time Fourier transform on the reconstructed broadband interference, and then carrying out cancellation processing on the reconstructed broadband interference and the original echo signal to obtain a time domain echo signal after broadband interference suppression.
Utilizing the reconstructed broadband interference time-frequency matrix to perform cancellation processing on the original echo signal in a data domain to obtain an SAR target echo signal, namely a time domain echo signal after broadband interference suppression:
where ISTFT is an inverse Fourier transform operation, L*And R*Respectively representing the estimation results of the low-rank factors of the broadband interference time-frequency matrix, and the superscript H representing the conjugate transpose operation of the matrix.
Simulation experiment
After the broadband interference suppression, the method carries out simulation data interference suppression analysis and actual measurement data SAR imaging processing, and evaluates the interference suppression result.
(1) The method is adopted to carry out interference suppression processing on the broadband interference simulation data, and the effectiveness of the method is verified.
The invention adopts the non-interference actual measurement radar echo data with the bandwidth of 200MHz, and additive noise with the signal-to-interference ratio of-15.16 dB and the signal-to-noise ratio of 10dB, which obeys the Laplace distribution, is superposed on the data, and finally, the radar echo data containing the broadband interference is formed. Figure 4 is a graph comparing an original interference-free echo signal with a post-interference echo signal. Fig. 4(a) and 4(b) are time domain and frequency domain analysis results of signals before and after interference, respectively, and it can be seen from the graphs that the time domain and frequency domain characteristics of the signals are seriously damaged by broadband interference, so that useful information of target signals under interference concealment cannot be acquired. Fig. 4(c) and 4(d) respectively show the time-frequency diagrams of signals before and after the interference, and it can be seen that the existence of strong broadband interference enables the time-frequency information of the signals after the interference to be completely suppressed and cannot be visually displayed.
The interference suppression processing is performed by adopting the method provided by the invention, and fig. 5 is an analysis result of the interference suppression processing. Fig. 5(a) and (b) are respectively a reconstructed wideband interference time-frequency matrix and a time-frequency matrix for recovering a target signal, which shows that the method extracts a low-rank wideband interference matrix in an echo time-frequency matrix more completely, and realizes the separation of wideband interference and the target signal. Fig. 5(c) shows the time domain characterization comparison result of the original non-interference and interference-suppressed restored signal, and it can be seen that the method of the present invention better retains the signal characteristics and has less signal distortion while suppressing interference. Fig. 5(d) shows the probability density function of the recovered signal after interference suppression, and it can be seen that the probability density distribution function of the recovered target signal conforms to the proposed prior assumption.
(2) And (3) pulse-by-pulse processing sentinel actual measurement broadband interference data, and performing comparative analysis with a GoDec method by combining an SAR imaging algorithm.
The interference suppression method provided by the invention is used for carrying out a broadband interference suppression test on the actual measurement SAR echo data. The measured data was recorded from a C-band Sentinel-1 satellite from European Space Agency (ESA) with a resolution of 5m × 20m (distance × azimuth).
FIG. 6 shows experimental results on SAR echo data acquired from a Sentinel-1A VH polarization mode satellite. Fig. 6(a) shows the SAR imaging result without any interference suppression algorithm, and it is obvious that the broadband interference completely covers the entire scene, and the SAR imaging result is blurred. Fig. 6(b) and fig. 6(c) are SAR imaging results after the wide-band interference suppression processing is performed by using the GoDec algorithm and the method of the present invention, respectively. It can be seen that a part of interference residues still exist in the SAR image processed by the GoDec algorithm, so that the image is fuzzy, and the contrast between land and sea is poor. Compared with the SAR imaging result processed by the GoDec algorithm, the SAR image target processed by the method for broadband interference suppression is clearer, and the land and ocean contrast is higher.
In order to further verify the superiority of the method provided by the invention, broadband interference suppression processing is performed on the SAR echo data with interference recorded by the Sentinel-1B VH polarization mode satellite, and the obtained result is shown in FIG. 7. Fig. 7(a) is an imaging result of raw SAR echo data, in which a ship target is completely covered by broadband interference, resulting in a certain degree of defocusing of the target point. Fig. 7(b) and fig. 7(c) are SAR imaging results after the wide-band interference suppression processing is performed by using the GoDec algorithm and the algorithm proposed by the present invention, respectively. Obviously, the SAR imaging result after the broadband interference suppression processing by using the GoDec algorithm still has stripe-shaped broadband interference residues, and the ship target is blurred and defocused. In the SAR imaging result after the broadband interference suppression processing is carried out by the algorithm provided by the invention, the interference suppression is more sufficient, the ship target focusing performance is good, and the image is clearer.
(3) The advantage of the method of the present invention over the conventional method is analyzed by quantitative comparison of additive noise ratio (MNR).
In order to quantitatively evaluate the interference suppression effect of the algorithm provided by the invention, a representative MNR is adopted as an evaluation index. The MNR represents the average energy ratio of the weakly scattering region to the strongly scattering region in the SAR image, which is mathematically defined as:
wherein, N and InThe number of pixels representing the weakly scattering region and the corresponding pixel value, M and ImThe number of pixels representing the strongly scattering region and the corresponding pixel value size. The smaller the MNR index value is, the stronger the SAR image contrast is, and the better the SAR data information is recovered. Table 1 shows the MNR index of the SAR imaging result after two sets of measured data are processed by different interference suppression algorithms.
TABLE 1 SAR image MNR index evaluation results
| Name of algorithm | Sentinel-1A VH polarization | Sentinel-1B VV polarization |
| Original image | 5.4917dB | -7.0768dB |
| GoDec algorithm | -5.8736dB | -12.4061dB |
| Proposed algorithm | -10.0862dB | -14.9031dB |
The above results show that: the GoDec algorithm and the algorithm provided by the invention can improve the contrast of the SAR image, but in two groups of data, the MNR index of the algorithm provided by the invention is superior to that of the GoDec algorithm, which shows that the contrast of the SAR imaging result after the interference suppression treatment by adopting the method provided by the invention is higher, the target contour is clearer than that of a ship target, and is consistent with the qualitative analysis result, further showing that the broadband interference suppression effect of the invention is better.
Although the present invention has been described in detail in this specification with reference to specific embodiments and illustrative embodiments, it will be apparent to those skilled in the art that modifications and improvements can be made thereto based on the present invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (8)
1. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition is characterized by comprising the following steps of:
step 1, establishing a single echo model of the SAR along the azimuth direction to obtain an original echo signal;
step 2, constructing a broadband interference reconstruction model in the maximum likelihood meaning by adopting a Laplace prior distribution hypothesis and combining the time-frequency low-rank property of broadband interference;
step 3, introducing complex Gaussian prior distribution constraint of the broadband interference time-frequency matrix decomposition factor, and constructing a posterior probability model of the broadband interference time-frequency matrix recovery model parameters under a Bayes framework; estimating posterior probability model parameters of the broadband interference by adopting variational Bayes inference, and accurately reconstructing the broadband interference;
and 4, carrying out inverse short-time Fourier transform on the reconstructed broadband interference, and then carrying out cancellation processing on the reconstructed broadband interference and the original echo signal to obtain a time domain echo signal after broadband interference suppression.
2. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition according to claim 1, wherein the establishing of the SAR single-echo model along the azimuth direction specifically comprises:
firstly, the azimuth single echo model is expressed as a linear superposition form of signals, interference and noise:
s(k)＝x(k)+i(k)+n(k)
wherein s (k) represents the original echo signal of the kth range snapshot, x (k) represents the target echo signal of the kth range snapshot, i (k) represents the interference of the kth range snapshot, and n (k) represents the noise of the kth range snapshot;
then, since the target signal exhibits a noise-like distribution, the single echo in the azimuth direction is simplified into the following form:
s(k)＝i(k)+nx(k)
wherein n isx(k) N (k) + x (k) is equivalent noise, representing the superposition of the signal and the noise; s (k) is denoted as the original echo signal.
3. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition as claimed in claim 2, wherein the Laplace prior distribution assumption is adopted, and the time-frequency low-rank property of broadband interference is combined to construct a broadband interference reconstruction model in the maximum likelihood sense, and the specific steps are as follows:
step 2a, constructing a broadband interference recovery model in the maximum likelihood sense by adopting a Laplace prior distribution hypothesis;
and the substep 2b is used for forming a broadband interference low-rank time-frequency matrix accurate reconstruction model in the maximum likelihood sense by combining the low-rank characteristic of the broadband interference time-frequency matrix and utilizing a matrix full-rank decomposition principle.
4. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition as recited in claim 3, wherein the Laplace prior distribution assumption is adopted to construct a broadband interference recovery model in the maximum likelihood sense, specifically:
firstly, mapping an original echo signal to a distance time-frequency domain by using short-time Fourier transform, wherein in the time-frequency domain, an original echo signal model is as follows:
S＝WRI+N
wherein the content of the first and second substances,
respectively representing an original echo signal time-frequency matrix, a broadband interference time-frequency matrix and an equivalent noise time-frequency matrix;
then, if the equivalent noise time-frequency matrix N obeys Laplace prior distribution, the reconstruction error needs to be minimized for the reconstruction problem of the broadband interference, and the likelihood function is used for determining the loss function of the reconstruction problem:
wherein S isijFor the ith row and jth column element, WBI, of the matrix SijIs the ith row and the jth column element of the matrix WBI; omega represents a subscript set of time-frequency matrix elements, | | · | | non-woven air1Represents L1Norm, C is a constant term, p (· |0, b) represents Laplace distribution with a position parameter of 0 and a scale parameter of b;
omitting a coefficient item and a constant item, and obtaining an optimization function of the broadband interference time-frequency matrix reconstruction problem as follows:
the above equation is the wideband interference recovery model in the maximum likelihood sense.
5. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition as claimed in claim 4, wherein the accurate reconstruction model of the broadband interference low-rank time-frequency matrix under the maximum likelihood meaning is formed by combining the low-rank characteristic of the broadband interference time-frequency matrix and utilizing the matrix full-rank decomposition principle, and the specific process is as follows:
firstly, setting a time-frequency matrix of broadband interference to have low-rank characteristics, and considering that the broadband interference is low-rank compared with the time-frequency matrix of an original echo signal by combining the aggregation characteristics of the broadband interference in a time-frequency domain; the problem of recovering the broadband interference time-frequency matrix is the problem of recovering the low-rank component of the time-frequency matrix of the original echo signal;
then, according to the matrix full rank decomposition theorem, any non-zero matrix can be decomposed into a form of a product of two full rank matrices, and a broadband interference time-frequency low-rank matrix is decomposed, which is expressed as:
WRI＝LHR
wherein the content of the first and second substances,
to know
The low-rank decomposition factor of the broadband interference time-frequency matrix is represented by Q, T, the dimension of the time-frequency matrix is represented by r, the rank of the broadband interference time-frequency matrix is represented by r, and min { T, Q } is less than or equal to r; superscript H represents the conjugate transpose operation of the matrix;
the recovery problem of the wideband interference time-frequency matrix is characterized as the following optimization problem:
6. the SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition according to claim 5, wherein the introducing of complex Gaussian prior distribution constraint of broadband interference time-frequency matrix decomposition factors constructs a posterior probability model of broadband interference time-frequency matrix recovery model parameters under a Bayesian framework, specifically:
firstly, transforming the Laplace distribution of an equivalent noise time-frequency matrix N into a Gaussian scale mixed expression form:
wherein, CN (N)ij|0，zij) Means zero mean and z varianceijComplex Gaussian distribution of (i), p (z)ij| λ) represents an exponential distribution with a parameter λ, NijRepresenting the ith row and the jth column of the equivalent noise time frequency matrix N;
secondly, an ith column vector L of a decomposition factor L of the broadband interference time-frequency matrix is setiAnd j column vector R of decomposition factor R of broadband interference time-frequency matrixjAll obey complex Gaussian distribution, corresponding accuracy
And
obey a Gamma distribution, i.e.:
wherein, a0，b0，c0，d0Respectively, hyper-parameters of Gamma distribution, I is a unit matrix, and the superscript-1 represents the inversion operation;
finally, a complete Bayesian posterior probability model of the model parameters is given by using Bayesian theorem:
wherein, tauLIs composed of
Formed vector of τRIs composed of
A vector formed by ZijA matrix of components.
7. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition as recited in claim 6, wherein the estimation of the posterior probability model parameters of the broadband interference by the variational Bayes inference is adopted to accurately reconstruct the broadband interference, and the specific process is as follows:
first, the approximate distribution of the bayesian posterior probability model is factorized, expressed as follows:
secondly, parameter estimation is carried out by utilizing variation deduction, and the following results can be obtained:
thus, the specific parameter estimation result is:
wherein E [. cndot. ] represents expectation;
finally, according to the estimated value of the Bayes posterior probability model parameters, determining the low-rank factor of the broadband interference time-frequency matrix, thereby obtaining the reconstruction form of the broadband interference time-frequency matrix as
WBI＝(L*)HR*
Wherein L is*And R*Respectively representing the estimation results of the low-rank factors of the broadband interference time-frequency matrix.
8. The SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition according to claim 1, wherein the reconstructed broadband interference is subjected to inverse short-time Fourier transform and then subjected to cancellation processing with an original echo signal, and the specific expression is as follows:
where s (k) is the original echo signal of the kth range snapshot, ISTFT is the inverse Fourier transform operation, L*And R*Respectively representing the estimation results of the low-rank factors of the broadband interference time-frequency matrix, and the superscript H representing the conjugate transpose operation of the matrix.
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