CN101908138A - Target Recognition Method in Synthetic Aperture Radar Image Based on Independent Component Analysis of Noise - Google Patents

Abstract

The invention relates to a synthetic aperture radar image target recognition method based on noise independent component analysis, and belongs to the technical field of synthetic aperture radar image target recognition. First, preprocess the original training sample image of the input synthetic aperture radar, so that the image conforms to whitening and zero-mean, and the image noise probability density obeys the Gaussian distribution; then the training sample after preprocessing and the real-time measurement sample to be identified The independent component analysis of logarithmic noise is carried out to extract the independent component features of the image to be recognized; finally, the independent component analysis method is used to identify the sample to be recognized. The independent component features extracted by the method of the present invention are more suitable for classification; the image denoising process that must be carried out in the preprocessing stage in the ideal ICA algorithm is omitted, the robustness of the algorithm to abnormal data is improved, and the SAR image target recognition is improved. The real-time performance and reliability can be used for feature extraction and automatic target recognition of SAR images.

Description

Target Recognition Method in Synthetic Aperture Radar Image Based on Independent Component Analysis of Noise

technical field

The invention relates to a synthetic aperture radar image target recognition method based on noise independent component analysis, and belongs to the technical field of synthetic aperture radar image target recognition.

Background technique

Synthetic Aperture Radar (hereinafter referred to as SAR) forms SAR images according to the backward electromagnetic scattering of targets, which can overcome the shortcomings of optical imaging limited by distance, climate and other conditions. , image matching guidance and other fields play a vital role. However, in the process of SAR imaging, there are usually many scatterers distributed in the same resolution unit, and the phases of the echo signals of these scatterers are randomly distributed, and the mutual interference leads to the inherent multiplicative speckle noise of the SAR image. Compared with ordinary electron optical images, general SAR images have the characteristics of low resolution, sensitivity to operating conditions, and high multiplicative noise.

SAR image target recognition technology is to use the characteristics of the scattering field (such as the amplitude, phase, frequency and polarization information of the echo signal) generated by a single target or target group in the far zone of the radar to determine the shape, type, The technology of location and other attributes has been widely used in military and civilian fields; especially in complex battlefield environments, accurate and fast SAR image target recognition technology can provide a strong guarantee for improving battlefield perception and response capabilities.

In SAR image target recognition, the noise of SAR images often also includes the interference of various natural clutter (grassland, river, forest, etc.) and man-made clutter (buildings, etc.), and these noises are usually non-Gaussian . Therefore, in order to effectively overcome the influence of a large amount of noise in SAR images on target recognition and improve the accuracy of SAR image target recognition as much as possible, people have proposed many SAR image noise removal and feature extraction methods, such as Wavelet filtering, directional diffusion filtering, target detection method based on Markov random field, principal component analysis (Principle Component Analysis: hereinafter referred to as PCA), kernel PCA (Kernel PCA: KPCA), Fisher linearity based on multivariate statistical analysis and kernel criteria Discriminant Analysis (FLDA), Kernel Fisher Discriminant Analysis (KFDA), Independent Component Analysis (hereinafter referred to as ICA), etc., involve many fields of image processing and pattern recognition.

In the SAR image target recognition system, it is hoped that the following goals can be achieved through feature extraction: 1) Make similar SAR images with different orientations and great differences have the same description method; 2) Eliminate or reduce the high noise characteristics of SAR images. 3) Compress the huge amount of data in SAR images; then provide effective and easy-to-recognize secondary features to the classifier, and the classifier can identify the structure, type and other attributes of the target to complete the process of SAR image target recognition. Among the methods for feature extraction of SAR images, the widely used and more effective ones are feature extraction methods based on multivariate statistical analysis, which mainly involve PCA and ICA. Among them, PCA is a feature extraction method that seeks a set of orthogonal projection directions that can maximize the sample variance in the sense of the minimum mean square error to remove redundant information and retain components with the largest energy. What is extracted is the second-order statistic of the data, that is, the variance feature. As an extension of PCA, ICA extracts the high-order statistical features of the data, that is, seeks a set of independent source data in a high-order sense from the observation data, and linearly superimposes this set of source data into observation data.

A lot of information of the SAR image is contained in the high-order statistics of the image, and the noise is usually non-Gaussian, so for the SAR image, the ICA feature extraction method is more robust than the PCA, and contains high-order statistical information The ICA features are also more separable.

At present, the general ICA technology usually idealizes the observed data as zero noise, but this is often quite different from the actual situation, especially in the field of SAR image target recognition with high multiplicative non-Gaussian noise. The impact of ICA features is an open question. At present, the methods of dealing with noise can be generally divided into three types: ① Treat noise as an independent component; ② Denoise in the preprocessing stage; ③ Noise ICA model. Almost all noise-free ICA models adopt the first method by default, that is, the noise is regarded as one of the original independent components, but in SAR image target recognition, a larger noise component will weaken the contribution of the normal component to the classification , leading to a decrease in classification accuracy. The image denoising in the preprocessing stage can make the denoising process more targeted, so that the features extracted by ICA can achieve higher classification accuracy. For example, Shanghai Jiaotong University's patent ZL 200710046928.3 (Synthetic Aperture Radar image denoising method based on independent component analysis base image) uses wavelet index to smooth and enhance the image of SAR image, so as to achieve denoising effect; US Patent US 7508334 (Method and apparatus for processing SAR images based on an anisotropic diffusion filtering algorithm, March 24, 2009) proposed a directional diffusion filtering algorithm for SAR image speckle noise to achieve SAR image denoising. However, image denoising in the preprocessing stage will naturally increase a lot of calculations, resulting in too long time for image feature extraction, so it cannot meet the battlefield needs of SAR image target recognition that emphasizes real-time.

The noise ICA model is based on the aforementioned ideal noise-free ICA model, and takes noise interference as a non-negligible influencing factor. On this basis, Aapo Hyvarinen from the University of Helsinki in Finland and others proposed an ICA algorithm combined with noise removal technology - Noisy Fast ICA (Noisy FastICA: NFastICA) algorithm. This algorithm introduces the concept of Gaussian moments, successfully estimates the potential random variables directly from the observed data polluted by Gaussian noise, and has good robustness to the outliers sampled. However, the two important prerequisites of the NFastICA algorithm are that the data noise is Gaussian distribution (that is, normal distribution) and the noise covariance matrix is known, but the noise in the SAR image is mostly multiplicative noise, and except for the In addition to non-target echoes in the relevant area, it also includes natural and man-made clutter, which is almost impossible to fit with a Gaussian distribution. Therefore, the NFastICA algorithm cannot be directly applied to the field of SAR image target recognition.

Contents of the invention

The purpose of the present invention is to propose a synthetic aperture radar image target recognition method based on noise independent component analysis, based on the noise ICA model, to improve the existing ICA-based SAR image target recognition method to slow down or eliminate the use of ICA The method classifies and recognizes the influence of a large number of non-Gaussian multiplicative noises on feature extraction when classifying and recognizing SAR images, reduces the amount of calculation in the preprocessing stage, improves the robustness of the recognition algorithm, and finally improves the recognition accuracy of SAR image target recognition technology and identification efficiency purposes.

The synthetic aperture radar image target recognition method based on noise independent component analysis proposed by the present invention comprises the following steps:

(1) Preprocessing the original training sample image X _train of the input synthetic aperture radar, the specific process is as follows:

(1-1) Perform logarithmic transformation on the training sample image X _train to obtain X _ln = 20ln(1+X _Orig ), where X _Orig represents the input original training sample single image, and X _ln represents the noise after logarithmic transformation An image whose distribution conforms to a Gaussian distribution;

(1-2) above-mentioned X _ln is carried out de-average processing, obtains zero-mean image X _t , X _t =X _ln -E(X _ln ), wherein the expectation function E represents image averaging;

(1-3) Divide the above zero-mean image X _t into the target area X _o and the noise area n _o , and satisfy {X _t }={n _o }∪{X _o }, the two-dimensional of the target area and the noise area The image data are straightened into one-dimensional row vectors respectively, where the target area X _o contains echoes of targets, shadows and clutter related to the identified target, and the noise area n _o is the background clutter;

(1-4) Steps (1-1), (1-2) and (1-3) are repeated to obtain the one-dimensional target area data X _o of N training images in the training sample, forming N rows of training matrix X _O ;

其中的对角元素 

为每幅训练图像的噪声方差估计值， 

表示第i幅训练图像的噪声区域；(1-5) According to all the noise regions n _o of the N training images obtained above, construct the noise covariance diagonal matrix of the training samples

where the diagonal elements

is the noise variance estimate for each training image,

Indicates the noise area of the i-th training image;

(1-6) According to the noise covariance matrix Σ _O of the above-mentioned training samples, the above-mentioned training matrix X _O is subjected to dimensionality reduction and whitening processing, and the SAR training sample image subspace matrix X after dimensionality reduction and whitening is obtained;

(2) Obtain the synthetic aperture radar real-time measurement image X _test , and use the independent component analysis method to extract the independent component features of the above synthetic aperture radar training sample image X _train and the independent component features of the synthetic aperture radar real-time measurement image X _test respectively. The specific process is as follows :

(2-1) Using the fast independent component analysis method of noise to process the above SAR training sample image subspace matrix X, a set of base image estimation matrix S _e composed of base image estimation vectors is obtained, expressed as:

X＝c _train1 ·s ₁ +c _train2 ·s ₂ +...+c _trainm ·s _L ＝S _e ^T ·c _train .

Among them, s ₁ , s ₂ ,..., s _L represent the estimated column vectors of L base images in the base image estimation matrix _Se , c _train =(c _train1 , c _train2 ,..., c _trainL ) ^T represents the above training The projection coefficient of the sample image subspace matrix X in the base image subspace formed by the above base image estimation matrix _Se , c _train is the independent component feature of the synthetic aperture radar training sample X _train ;

(2-2) Project the image data to be recognized in the synthetic aperture radar real-time measurement image X _test to the base image subspace composed of the above-mentioned base image estimation matrix _Se , so that the real-time measurement image X _test uses the base image estimation vector The linear combination is expressed as:

X _test ＝c _test1 · s ₁ +c _test2 · s ₂ +...+c _testL · s _L = S _e ^T · c _test

Among them, c _test = (c _test1 , c _test2 , ..., c _testL ) ^T represents the projection coefficient of the above-mentioned real-time measurement image X _test in the base image subspace formed by the above-mentioned base image estimation matrix _Se , c _test = piv(S _e ^T ) X _test , where piv(S _e ^T ) represents the generalized inverse of matrix S _e transpose, and c _test is the independent component feature of the real-time synthetic aperture radar measurement image X _test to be identified;

(3) According _to the independent component feature c _{train of the synthetic aperture radar training sample image X train} obtained in the above step (2) and the independent component feature c _test of the real-time synthetic aperture radar measurement image X _test to be identified, the real-time measurement of the synthetic aperture radar The image X _test performs recognition and classification to determine the category of the target to be tested.

The synthetic aperture radar image target recognition method based on noise independent component analysis that the present invention proposes has the advantages of:

1. The synthetic aperture radar image target recognition method based on noise independent component analysis proposed by the present invention relates to a new log-normal noise independent component analysis (Log-normal noise ICA: LnnICA) method, which saves the existing noise-free The image denoising process that the independent component analysis algorithm must carry out in the preprocessing stage effectively overcomes the influence of a large number of multiplicative non-Gaussian noises in the synthetic aperture radar image on feature extraction, making the extracted independent component features more suitable for classification, thereby reducing It reduces the amount of calculation, improves the reliability of SAR image target recognition and the robustness to abnormal data, and can greatly improve the recognition accuracy and recognition efficiency of SAR target recognition, especially real-time automatic target recognition.

2, the synthetic aperture radar image target recognition method of the present invention, in the process of dimensionality reduction and whitening, has improved the selection standard of principal component feature in the PCA algorithm, has proposed the most divisible component (Most DiscriminableComponent, hereinafter referred to as from the angle of noise reduction) MDC) selection criteria, that is, to use category separability to measure the degree to which a feature component can represent the category attributes of the original pattern, and select multiple MDC components with the strongest separability to represent the original image. Using the principle of separability of feature components to perform dimension reduction and whitening in the preprocessing stage can simultaneously improve the denoising effect of SAR images for the purpose of classification, and improve the accuracy and reliability of SAR image target recognition based on independent component analysis.

Description of drawings

FIG. 1 is a general process of the ICA-based SAR image target recognition technology in the prior art.

Fig. 2 is a comparison of noise distribution characteristics before and after logarithmic transformation of the SAR image in the method of the present invention.

Fig. 3 is a schematic diagram of extracting noise regions and target regions from a single training sample image in the method of the present invention.

FIG. 4 is a flow chart of a target recognition method in a synthetic aperture radar image based on noise independent component analysis proposed by the present invention.

specific implementation plan

The synthetic aperture radar image target recognition method based on noise independent component analysis proposed by the present invention comprises the following steps:

(1) Preprocessing the original training sample image X _train of the input synthetic aperture radar, the specific process is as follows:

(1-1) Perform logarithmic transformation on the training sample image X _train to obtain X _ln = 20ln(1+X _Orig ), where X _Orig represents the input original training sample single image, and X _ln represents the noise after logarithmic transformation An image whose distribution conforms to a Gaussian distribution;

(1-2) above-mentioned X _ln is carried out de-average processing, obtains zero-mean image X _t , X _t =X _ln -E(X _ln ), wherein the expectation function E represents image averaging;

(1-3) Divide the above zero-mean image X _t into the target area X _o and the noise area n _o , and satisfy {X _t }={n _o }∪{X _o }, the two-dimensional of the target area and the noise area The image data are straightened into one-dimensional row vectors respectively, where the target area X _o contains echoes of targets, shadows and clutter related to the identified target, and the noise area n _o is the background clutter;

(1-4) Steps (1-1), (1-2) and (1-3) are repeated to obtain the one-dimensional target area data X _o of N training images in the training sample, forming N rows of training matrix X _O ;

(1-5) According to all the noise regions n _o of the N training images obtained above, construct the noise coherence of the training samples

其中的对角元素 

为每幅训练图像的噪声方差估计值， 

表示第i幅训练图像的噪声区域；Variance Diagonal Matrix

where the diagonal elements

is the noise variance estimate for each training image,

Indicates the noise area of the i-th training image;

(1-6) According to the noise covariance matrix Σ _O of the above-mentioned training samples, the above-mentioned training matrix X _O is subjected to dimensionality reduction and whitening processing, and the SAR training sample image subspace matrix X after dimensionality reduction and whitening is obtained;

(2) Obtain the synthetic aperture radar real-time measurement image X _test , and use the independent component analysis method to extract the independent component features of the above synthetic aperture radar training sample image X _train and the independent component features of the synthetic aperture radar real-time measurement image X _test respectively. The specific process is as follows :

(2-1) Using the fast independent component analysis method of noise to process the above SAR training sample image subspace matrix X, a set of base image estimation matrix S _e composed of base image estimation vectors is obtained, expressed as:

X＝c _train1 ·s ₁ +c _train2 ·s ₂ +...+c _trainm ·s _L ＝S _e ^T ·c _train .

Among them, s ₁ , s ₂ ,..., s _L represent the estimated column vectors of L base images in the base image estimation matrix _Se , c _train =(c _train1 , c _train2 ,..., c _trainL ) ^T represents the above training The projection coefficient of the sample image subspace matrix X in the base image subspace formed by the above base image estimation matrix _Se , c _train is the independent component feature of the synthetic aperture radar training sample X _train ;

(2-2) Project the image data to be recognized in the synthetic aperture radar real-time measurement image X _test to the base image subspace composed of the above-mentioned base image estimation matrix _Se , so that the real-time measurement image X _test uses the base image estimation vector The linear combination is expressed as:

X _test ＝c _test1 · s ₁ +c _test2 · s ₂ +...+c _testL · s _L = S _e ^T · c _test

Among them, c _test = (c _test1 , c _test2 , ..., c _testL ) ^T represents the projection coefficient of the above-mentioned real-time measurement image X _test in the base image subspace formed by the above-mentioned base image estimation matrix _Se , c _test = piv(S _e ^T ) X _test , where piv(S _e ^T ) represents the generalized inverse of matrix S _e transpose, and c _test is the independent component feature of the real-time synthetic aperture radar measurement image X _test to be identified;

(3) According _to the independent component feature c _{train of the synthetic aperture radar training sample image X train} obtained in the above step (2) and the independent component feature c _test of the real-time synthetic aperture radar measurement image X _test to be identified, the real-time measurement of the synthetic aperture radar The image X _test performs recognition and classification to determine the category of the target to be tested.

Below in conjunction with accompanying drawing, introduce the content of the present invention in detail.

Firstly, the related concepts and basic principles of target recognition in Synthetic Aperture Radar (SAR) images are briefly explained using Independent Component Analysis (ICA) method.

The basic principle of ICA can be simply expressed by the following two formulas:

X=AS

S=WX

In the prior art, the basic process of using ICA to perform target recognition on SAR images is shown in FIG. 1 .

In order to improve the accuracy of SAR image target recognition, it is necessary to preprocess the image before using ICA to extract the features of SAR image. The preprocessing methods mainly include: ① transform the original SAR image or use another measurement method to represent the source data; ② normalize the transformed image; The target area, also known as the region of interest (Region of Interest: ROI), may contain one or more targets in these areas; among them, the target area basically contains all echoes related to target identification, including target echo, Shadow echoes and other clutter, etc., while the noise area is almost entirely composed of background clutter, so the target area is usually used to extract ICA features for the target to be recognized, and the noise area is only used for noise recognition. Estimate the variance.

ICA is suitable for processing one-dimensional data. After preprocessing, two-dimensional image samples need to be straightened into one-dimensional row vectors. And each row vector can be regarded as a mixed signal composed of multiple vectors linearly superimposed, that is, each observed SAR image can be considered to be a linear combination of a set of potential mutually independent base images. Let x be a SAR image, let S be the base image matrix composed of base image vectors, and the column vector s _i be the ith base image vector, then x can be expressed by S as

x=b ₁ ·s ₁ +b ₂ ·s ₂ +...+b _n ·s _n =b·S

Wherein, the coefficient vector b=(b ₁ , b ₂ , . . . , b _n ) is the ICA feature of the image sample x.

Most of the data processed by ICA requires zero-mean whitening data, that is, satisfying E{X}=0, E{XX ^T }=I. Let X _O be the training data, and subtract X _O from its mean value vector m=E{X _O } to realize centralization. After using the centered data to obtain the confusion matrix A, the mean vector of the source signal s is added back to the estimated value of s after centering to complete the estimation of the source signal s. Among them, the mean vector of s can be obtained by A ^-1 m.

)。可采用如下方法对X_O进行白化。It is assumed here that X _O is already zero mean. The whitening process of X _O is to make the components of X _O independent of each other, which is equivalent to the covariance matrix of X _O being an identity matrix (ie

). The following methods can be used to whiten X _O.

X＝W _Z X _O

${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}$

The ICA method requires that all independent components of multivariate data must be non-Gaussian distributed, or at most one independent component can be Gaussian distributed. The key to evaluating an ICA model is the non-Gaussianity of the independent components of the data. The central limit theorem shows that the distribution of the sum of a group of independent random variables usually approaches the Gaussian distribution, from which the following inferences can be obtained:

Corollary 1: The sum of n independent random variables is closer to a Gaussian distribution than any of the original variables.

According to the noise-free ICA model X=AS, let y be an independent component in S, namely

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

Where w is the undetermined column vector corresponding to y in the de-confusion matrix W, w _i is its i-th element, and x _i is the i-th observation signal. Adopt the conclusion of Corollary 1 to make w equal to the corresponding columns of the inverse matrix of matrix A. Let the column vector z= ^AT w, then

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; AS</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

According to Corollary 1, y is more Gaussian than the original independent variable _si . If the Gaussianity of y is minimized, then y will be equal to a certain component s _k in S. The greater the non-Gaussianity of y, the greater the independence between y and other components, and vice versa; if the non-Gaussianity of y reaches the maximum, an independent component can be obtained. Therefore, in ICA theory, non-Gaussianity is equivalent to independence.

The overall flow of the present invention based on the noise independent component analysis synthetic aperture radar image target recognition method is as shown in Figure 4, and its specific content is as follows:

(1) The inventive method first carries out preprocessing to the original training sample image X _train of the synthetic aperture radar of input, and its process is:

(1-1) Perform logarithmic transformation on the training sample image X _train to obtain X _ln = 20ln(1+X _Orig ), where X _Orig represents the input original training sample single image, and X _ln represents the noise after logarithmic transformation An image whose distribution conforms to a Gaussian distribution.

The purpose of this step is to make the SAR noise probability density obey Gaussian distribution, which is commonly called normal distribution. As can be seen from the background technology section, one of the basic characteristics of SAR images is that they contain a large amount of multiplicative speckle noise. In the field of target classification and recognition, the noise of SAR images also includes a large amount of natural or artificial clutter interference, so it is almost impossible to simply use A Gaussian distribution is fitted to these noises.

The lognormal distribution model is a SAR image clutter statistical model suitable for ground scenes proposed by S.F.George. It is a commonly used statistical model to describe non-Rayleigh envelope data. The main idea is to use homomorphic filtering The multiplicative noise of the SAR image is converted into additive Gaussian white noise by the filter. The probability density expression for the lognormal distribution is

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; nx</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

Where x is the gray value of the pixel, μ is the mean of lnx (scale parameter), and σ is the standard deviation of lnx (ie shape parameter). And the expression of parameter moment estimation is

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>$ ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Therefore, after the logarithmic transformation of the SAR image data, its noise probability density approximately obeys the Gaussian distribution, as shown in Figure 2.

(1-2) De-average processing is performed on the above X _ln to obtain a zero-mean image X _t , X _t =X _ln -E(X _ln ), where the expectation function E represents the mean value of the image.

(1-3) Divide the above zero-mean image X _t into target area X _o and noise area n _o , and satisfy {X _l }={n _o }∪{X _o }, divide the two-dimensional The image data are straightened into one-dimensional row vectors respectively, where the target area X _o contains echoes of targets, shadows and clutter related to the identified target, and the noise area n _o is the background clutter;

Since the ICA algorithm adopted in the present invention can only process one-dimensional signals, it is necessary to expand the target area and noise area matrixes of each image data into one-dimensional row vectors in this step.

(1-4) Repeat steps (1-1), (1-2) and (1-3) to obtain the one-dimensional straightening vector X _o of the target area of N training images in the training sample, and form N rows of training matrix X _O , which is the input matrix X in the ICA algorithm;

并且其对角元素值分别对应为每幅图像各自的噪声方差。(1-5) In general, each SAR image is independently imaged, so the noise contained in it should also be statistically independent from each other, so the noise covariance matrix of the observed data (that is, X _O in the previous step) is a diagonal matrix. According to all the noise regions n _o of the N training images obtained above, the noise covariance diagonal matrix of the training samples can be constructed

And its diagonal element values correspond to the respective noise variance of each image.

It can be observed from Figure 2 that the shape of the probability distribution of the noise in the logarithmically transformed SAR image approximately obeys the Gaussian model, and since the noise area n _o has been centered, the diagonal elements of the noise covariance matrix can be directly estimated by the following formula

${\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

表示第i幅训练图像的噪声区域。in,

Indicates the noise region of the i-th training image.

(1-6) In the above steps, the data X _O has been centered, and its covariance matrix is Also, the noise covariance matrix Σ _O of the image noise n _O has been estimated. Dimensionality reduction and whitening are performed on the training matrix X _O above to obtain the SAR training sample image subspace matrix X after dimensionality reduction and whitening.

In this step, data whitening and dimensionality reduction can be realized simultaneously by means of principal component analysis (PCA) or the most divisible component (MDC) criterion, as detailed below.

First, take the PCA method as an example: first, perform eigenvalue decomposition (Eigenvalue Decomposition: EVD) on the non-noise data covariance matrix C-∑ _O , and there is

C-∑ _O ＝ EDE ^T

So X _O can be whitened by the following formula:

X＝ED ^-1/2 E ^T X _O

It is easy to prove that the data X obtained in this way satisfies E{XX ^T }=I.

Since the whitening process does not remove the noise in X _O , the covariance matrix of the noise n in X is re-estimated as

∑＝E{nn ^T }＝(ED ^-1/2 E ^T )∑ _O (ED ^-1/2 E ^T )

Usually, the dimensionality of the original data X _O is very high, resulting in huge calculation and redundancy, and even over-learning phenomenon. Therefore, according to the PDC method, the too small components in D are removed, and L(L≤M) components with the largest energy are selected, and finally a new eigenvalue matrix D _L of the image is obtained. This process is also called subspace selection. Among them, D _L is a diagonal matrix composed of the first L largest eigenvalues selected from D, and E _L is a matrix composed of eigenvectors corresponding to the L eigenvalues. In this way, the data X will be reduced to L dimension, and Σ is L×L size, and ED ^-1/2 E ^T in the original formula is replaced by E _L D _L ^-1/2 E _L ^T . Therefore, the PCA method is used to realize the whitening and noise reduction process of the input data at the same time, and a more meaningful subspace image data is input for the next step of the ICA feature extraction process.

X＝E _L D _L ^-1/2 E _L ^T X _O

∑＝E{nn ^T }＝(E _L D _L ^-1/2 E _L ^T )∑ _O (E _L D _L ^-1/2 E _L ^T )

As mentioned in the background art, there are certain defects in the method of dimensionality reduction and compression of SAR images by using PCA. PCA selects the first L principal components with the largest energy to represent the original image data, but the energy of the component (projection direction) is not directly related to the degree to which it can represent the image category attributes; therefore, in extreme cases, the current L principal components Both represent the energy of noise, and when the noises of different types of images are basically similar, the feature quantities that can be used for image classification will be completely lost, let alone the correct identification of SAR images.

The present invention improves the PCA method, and proposes the most discriminable component (Most discriminable Component: MDC) analysis method that uses class discriminability (Class Discriminability) to measure the display degree of a component to the image category attribute, and selects the first L The most separable components to represent the original image. The specific selection method of MDC is as follows:

设p_k为PCA变换矩阵P中的第k个投影方向(即第k个成分)，b_ij表示第i类第j个样本在该方向上的投影系数(1≤i≤C，1≤j≤N_i)，所有投影系数b_ij的平均为 第i类样本投影系数b_i·j的平均为 定义类间方差 

类内方差 

MDC方法采用两者之比作为样本成分可分性的度量，表示为Assuming that N image samples contain a total of C types of targets, let the number of samples belonging to the i-th type of targets be N _i , then

Let p _k be the kth projection direction (that is, the kth component) in the PCA transformation matrix P, b _ij represents the projection coefficient of the jth sample of the i-th class in this direction (1≤i≤C, 1≤j ≤N _i ), the average of all projection coefficients b _ij is The average of the i-th sample projection coefficient b _{i j} is Define between-class variance

Intra-class variance

The MDC method uses the ratio of the two as a measure of the separability of the sample components, expressed as

r＝ _σbetween / _σwithin

The larger the value of r, the higher the separability of the component of the sample.

Image noise can also be suppressed simultaneously with PCA or MDC methods. The extracted principal components are approximated by the aforementioned inverse transformation to obtain an approximation of the original SAR image, and the noise of the approximate image is significantly reduced and suppressed compared with the original image. The MDC method removes similar components (including main noise components) that are not separable or have very little separability in the principal components, and obtain higher separability with less energy of the image. Although the components removed by the MDC method are not all noise components, these components do not have much positive effect on the classification results, and they can all be regarded as noise components.

If the MDC method is used to realize this step, it is only necessary to select the first L most divisible components as the selected subspace according to the aforementioned MDC index in the above subspace selection process, and the data input into ICA is still

X＝E _L D _L ^-1/2 E _L ^T X _O

∑＝E{nn ^T }＝(E _L D _L ^-1/2 E _L ^T )∑ _O (E _L D _L ^-1/2 E _L ^T )

When implementing this step, first select the principal components whose energy accounts for the first 95% of the principal components (in image processing theory, the first 95% of the energy can basically represent the image), and then use the MDC index to calculate the possible components of these principal components respectively. Separation, these components are arranged according to the size of the separability, and the first L projection directions P′ _L are selected for the next step of ICA feature extraction.

(2) Obtain the synthetic aperture radar real-time measurement image X _test , and use the independent component analysis method to extract the independent component features of the above synthetic aperture radar training sample image X _train and the independent component features of the synthetic aperture radar real-time measurement image X _test respectively. The specific process is as follows :

(2-1) Using the fast independent component analysis method of noise to process the above SAR training sample image subspace matrix X, a set of base image estimation matrix S _e composed of base image estimation vectors is obtained, expressed as:

X＝c _train1 ·s ₁ +c _train2 ·s ₂ +...+c _trainm ·s _L ＝S _e ^T ·c _train .

Among them, s ₁ , s ₂ ,..., s _L represent the estimated column vectors of L base images in the base image estimation matrix _Se , c _train =(c _train1 , c _train2 ,..., c _trainL ) ^T represents the above training The projection coefficient of the sample image subspace matrix X in the base image subspace formed by the above base image estimation matrix _Se , c _train is the independent component feature of the synthetic aperture radar training sample X _train ;

The noise ICA model that the present invention adopts is Noisy FastICA (NFastICA) model, and NFastICA model combines above-mentioned pretreatment step, has formed a kind of new Log-normal noise independent component analysis (Log-normal noise ICA: LnnICA) method. The NFastICA algorithm can directly estimate potential random variables from the observed image data polluted by Gaussian noise through the characteristics of Gaussian Moments. The following details the specific implementation of the independent component feature extraction of noise images using NFastICA based on the FastICA method. .

且噪声n_o满足高斯分布，其协方差矩阵为∑_O。对SAR图像数据进行白化处理，并用去除了噪声的协方差矩阵C-∑_O代替C，则白化操作应为On the basis of the aforementioned ideal ICA model, the noise ICA model can be expressed as X=AS+n. The training sample data X _O has been zero-meaned, and the covariance matrix

And the noise n _o satisfies the Gaussian distribution, and its covariance matrix is ∑ _O . Whiten the SAR image data, and replace C with the noise-removed covariance matrix C-∑ _O , then the whitening operation should be

X＝(C-∑ _O ) ^-1/2 X _O

Among them, X is also the input of the noise ICA model, and its noise covariance matrix is

∑＝E{nn ^T }＝(C-∑ _O ) ^-1/2 ∑ _O (C-∑ _O ) ^-1/2

As mentioned earlier, in ICA theory, non-Gaussianity is equivalent to independence. Among the various measures of non-Gaussianity, a method that is robust to outliers of random variables is to use approximate negative entropy to measure non-Gaussianity. It can be known from information theory that random variables with higher disorder have larger entropy values, and for Gaussian variables, a basic property is that their entropy values are the largest among all random variables with the same variance. Defining the measure of negentropy

J(y)＝H(y _Gauss )-H(y)

Among them, y _Gauss represents a Gaussian random variable with the same variance as the variable y, and H(·) is an entropy function. In this way, the values of the negentropy J(y) are all non-negative, and Gaussian variables have a negentropy of zero.

In order to simplify the calculation, an approximate method is usually used to estimate the negative entropy, namely

J(y)≈c[E{G(y)}-E{G(v)}] ²

$G_1\left(u\right)=\frac{1}{a_1}\log \cosh a_{1}u,\mathrm{where}1\&le;a_1\&le;2.$ or $G_2\left(u\right)=-\exp \left(\frac{{-\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000190440200012.png"\; state="\{\{state\}\}">u</figure-callout>}}^2}{2}\right)$

Among them, v is a standard normal variable with zero mean and unit variance, and G is a non-quadratic function. This method of approximate negative entropy is often easy to understand, fast to calculate, and has strong robustness. Therefore, it is also used in FastICA This non-Gaussian measurement method is adopted, and the optimal solution is searched by Newton's descent method (each component is most independent of each other).

The learning rule of FastICA is to find a direction vector w, so that the non-Gaussian property of the input data projected in this direction y=w ^T X is the largest, even if the approximate negative entropy function of the negative entropy measure is used

J(y)≈[E{G(y)}-E{G(v)}] ²

The value of is the largest. At the same time, it is also necessary to ensure that each independent component y _i does not repeat, that is, W is an orthogonal unit matrix.

A standard normally distributed variable v constrains the variance of y to be 1 as well. If the original data X is whitened data, then the restriction on the unit variance of y is equivalent to normalizing the second-order norm of w, that is

E{(w ^T x)} ² }＝||w|| ² ＝1.

Therefore, the FastICA algorithm can be described as the following steps:

1) Univariate search for the optimal w _i .

Step 1: Randomly select an initial weight vector w _i ;

其中，其中g为非二次函数G的二阶导函数，η为牛顿法参数；step 2: update wi, command

Wherein, wherein g is the second-order derivative function of non-quadratic function G, and n is the parameter of Newton's method;

Step 3: Normalize the w _i obtained in step 2, that is,

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$

Step 4: Determine whether w _i is convergent, if convergent, this step ends, otherwise return to step2.

2) Perform a global de-correlation search on the de-confusion matrix W to ensure that W is orthogonal.

Here, the method of decorrelating directly on W is used: all the w _i obtained in step 1) are composed into a de-confusion matrix W, and the following search formula is iteratively calculated until W converges.

W＝3W/2-WW ^T W/2

So the base image matrix can be expressed as

S＝WX＝WW _Z X _O ＝W _I X _O

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; S</span>}$

而测试数据X_test的ICA特征为X_testS⁺(+表示广义逆)。Among them, W _I =WW _Z contains two meanings, that is, W _I not only removes the second-order correlation (W transformation), but also removes the high-order correlation of ICA (W _z transformation), so as to achieve the relationship between the components of the vector S mutual independence. Therefore, it is not difficult to obtain the ICA characteristic of X _O as

The ICA feature of the test data X _test is X _test S ⁺ (+ means generalized inverse).

After the PCA decomposition of the training sample data X _O before dimensionality reduction, it is expressed as follows:

X _O =RP ^T

Among them, P is the transformation matrix of PCA, each column represents a projection direction, and P ^T P = I; R is the projection of X _O on P. Let _PL be the first L projection axes (the first L principal components) of P, and _RL be the projection of X _O on it, that is, _RL = X _O P _L ; the minimum mean square error estimate of X is then

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

和 

且对应有In this way, ICA is performed on _PL , and L is less than N, which can achieve the effect of dimensionality reduction and reduce the amount of calculation, and similarly obtain a deconfusion matrix

and

and corresponding to

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}$

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}$

thus get

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}$

即为X_O的ICA特征。同样的，X_test的ICA特征向量为

That is, the ICA feature of X _O. Similarly, the ICA feature vector of X _test is

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; test</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; test</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

In fact, due to the existence of noise, E{G(y)}=E{G(w ^T X)} approximates the negative entropy function J _G (y)≈[E{G(y)}-E{G( v)}] ² no longer represents the statistics of independent components, but the statistics of the sum of independent components and noise components. A basic idea of NFastICA based on Gaussian moments is to choose G to be a zero-mean Gaussian random variable density function or a related functional form, so that _JG can be coherently and simply calculated from a series of observation data. If z is a zero-mean non-Gaussian variable, and n is Gaussian noise with a variance of σ ² , the relationship between E{G(z)} and E{G(z+n)} can be simply expressed algebraically. Similarly, when G is a density function or correlation function of a zero-mean Gaussian variable, E{G(w ^T X)} can directly estimate J _G (y) of the noise-free data based on the noise-containing data X .

According to the assumption, the noise of the SAR image obeys the Gaussian distribution (this situation is often not true in practice, and this is the main problem solved by the present invention). Define a Gaussian density function with variance c ²

表示 

的1(1＞0)阶导函数， 

表示 

本身， 

表示 

的1次积函数 

设 表示任意一个分布函数为 

的独立成分(非高斯)， 

表示方差为σ²的独立高斯噪声变量。由于 

函数由高斯函数衍生而来，因此称 

为 

的高斯矩，而对于任意c＞σ²，令 

得到make

express

The 1(1>0) derivative function of ,

express

itself,

express

Product function of degree 1

set up Indicates that any distribution function is

Independent components of (non-Gaussian),

Denotes independent Gaussian noise variables with variance ^σ2 . because

The function is derived from the Gaussian function, so it is called

for

Gaussian moments of , and for any c>σ ² , let

get

与其观测 

的高斯矩是等价的。另外还可以证明，用 

替代 

上式同样成立。因此，令 

从而可以使用随机变量的高斯矩从含噪声的观测中直接估计出无噪声的独立成分。令This explains

rather than observe

The Gaussian moments of are equivalent. In addition, it can be proved that with

replace

The above formula is also established. Therefore, let

The noise-free independent components can thus be directly estimated from noisy observations using the Gaussian moments of the random variables. make

应用牛顿法，在w归一化的条件下求上式的极大值，优化w得in

Apply Newton's method to find the maximum value of the above formula under the condition of normalization of w, and optimize w to get

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; xg</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; xg</span>}<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

Among them, g is the derivative of function G, which can be taken as g ₁ (x)=tanh(x), g ₂ (x)=x·exp(-x ² /2) or g ₃ (x)=x ³ .

为高斯累计分布函数。in,

is the Gaussian cumulative distribution function.

Using the concept of Gaussian moments, this step uses NFastICA in the case of Gaussian distribution of noise, which can easily extract the independent component features of the SAR training sample X _train from the noisy observation data, denoted by C _train .

(2-2) Project the image data to be recognized in the synthetic aperture radar real-time measurement image (denoted as X _test ) to the base image subspace spanned by the above-mentioned base image estimation matrix _Se , so that the real-time measurement image X _test The linear combination representation of the base image estimation vector is:

X _test ＝c _test1 · s ₁ +c _test2 · s ₂ +...+c _testL · s _L = S _e ^T · c _test

Among them, c _test = (c _test1 , c _test2 , ..., c _testL ) ^T represents the projection coefficient of the above-mentioned real-time measurement image X _test in the base image subspace spanned by the above-mentioned base image estimation matrix _Se , through c _test = piv(S _e ^T ) X _test , where piv(S _e ^T ) represents the generalized inverse of the matrix, and c _test is the independent component feature of the synthetic aperture radar real-time measurement image X _test ; (3) according to the above The independent component feature c _train of the synthetic aperture radar training sample image X _train obtained in step (2) and the independent component feature c _test of the real-time synthetic aperture radar measurement image X _test to be identified are identified for the real-time synthetic aperture radar measurement image X _test Classification, to determine the category of the target to be tested.

(3) According _to the independent component feature c _{train of the synthetic aperture radar training sample image X train} obtained in the above step (2) and the independent component feature c _test of the real-time synthetic aperture radar measurement image X _test to be identified, the real-time measurement of the synthetic aperture radar The image X _test is used for recognition and classification, and an appropriate classifier is used to determine the category of the target to be tested.

The selection of a classifier needs to comprehensively consider various factors such as actual needs and classification effects. For example, a simple and easy minimum mean square error (Mean Square Error: MSE) classifier or a high-dimensional kernel map with better classification effect can be used. Support Vector Machine (SVM) classifier.

The following takes the MSE classifier as an example to illustrate the specific steps of target classification and recognition for synthetic aperture radar, as follows:

1) The value of the vector 2-norm is used as the measurement function of the distance between the target to be tested and the ICA characteristic coefficient of the training sample (other distance measures can also be defined, such as Markov distance, etc.), that is, a single test sample and a certain The ICA feature distance between a class of training samples can be expressed as

D _i ＝||C _traini -C _tost || ₂

Among them, the subscript i represents the category of known training samples, C _testi represents the ICA feature of the i-th type of training sample, and C _test represents the ICA feature of a single sample to be identified.

2) According to the distance measure defined in step 1), for each test sample, obtain the distance measure (the above-mentioned ICA feature distance) between it and various types of training samples. If there are N types of training samples, N distances {D ₁ , D _{2 .} . . D _N } about each test sample can be obtained through this step.

For each test sample, find the minimum distance between it and the N-type training samples, and classify the test samples into the category to which the training sample with the smallest distance belongs. That is to say, for a test sample, if the distance D _i =min{D ₁ , D ₂ ... D _N } to the i-th training sample, then the MSE classifier will divide the test sample into the i-th class, that is, This target is identified as the i-th class.

Claims (1)

1. A synthetic aperture radar image target identification method based on noise independent component analysis is characterized by comprising the following steps:

(1) original training sample image X for input synthetic aperture radar_trainThe pretreatment is carried out, and the specific process is as follows:

(1-1) to training sample image X_trainPerforming logarithmic transformation to obtain X_ln＝20ln(1+X_Orig) Wherein X is_OrigRepresenting an input original training sample single image, X_lnRepresenting noise after logarithmic transformationDistributing the images according with Gaussian distribution;

(1-2) for the above X_lnCarrying out de-equalization processing to obtain a zero-mean image X_t，X_t＝X_ln-E(X_ln) Wherein the expectation function E represents averaging the image;

(1-3) subjecting the zero-mean image X to_tDivision into target areas X_oAnd noise region n_oAnd satisfy { X_t}＝{n_o}∪{X_oStraightening two-dimensional image data of a target area and a noise area into one-dimensional line vectors respectively, wherein the target area X is_oEchoes containing objects, shadows and clutter associated with the identified objects, noise regions n_oIs background clutter;

(1-4) repeating the steps (1-1), (1-2) and (1-3) to obtain one-dimensional target area data X of N training images in the training sample_oForming an N-row training matrix X_O；

(1-5) all noise regions N of the N training images obtained as described above_oAnd constructing a noise covariance diagonal matrix of the training sample

Wherein the diagonal elements

For the noise variance estimate for each training image,

representing a noise region of the ith training image;

(1-6) noise covariance matrix Σ based on the above training samples_OFor the above training matrix X_OPerforming dimensionality reduction and whitening processing to obtain a synthetic aperture radar training sample image subspace matrix X after dimensionality reduction and whitening;

(2) obtaining real-time measurement map of synthetic aperture radarImage X_testRespectively extracting the synthetic aperture radar training sample images X by using an independent component analysis method_trainIndependent component feature and synthetic aperture radar real-time measurement image X_testThe specific process comprises the following steps:

(2-1) processing the image subspace matrix X of the synthetic aperture radar training sample by adopting a noise fast independent component analysis method to obtain a group of base image estimation matrixes S consisting of base image estimation vectors_eExpressed as:

X＝c_train1·s₁+c_train2·s₂+...+c_trainm·s_L＝S_e ^T·c_train.

wherein s is₁，s₂，…，s_LRepresenting a base image estimation matrix S_eEstimated column vectors of the L base images in, c_train＝(c_train1，c_train2，...，c_trainL)^TRepresenting the subspace matrix X of the training sample image in the estimation matrix S from the base image_eProjection coefficients in the constructed base image subspace, c_trainIs a synthetic aperture radar training sample X_trainThe individual component characteristics of (a);

(2-2) real-time measurement of image X by synthetic aperture radar_testIn the image data to be identified is projected onto the estimation matrix S from the base image_eIn the constructed primary image subspace, measuring the image X in real time_testExpressed as a linear combination of the basis image estimate vectors, is:

X_test＝c_test1·s₁+c_test2·s₂+...+c_testL·s_L＝S_e ^T·c_test

wherein, c_test＝(c_test1，c_test2，...，c_testL)^TRepresenting the above-mentioned real-time measurement image X_testIn estimating the matrix S from the base image_eProjection coefficients in the constructed base image subspace, c_test＝piv(S_e ^T)·X_testWherein piv (S)_e ^T) Representation matrix S_eGeneralized inverse of transposition, c_testNamely, the real-time measurement image X of the synthetic aperture radar to be identified_testThe individual component characteristics of (a);

(3) the synthetic aperture radar training sample image X obtained according to the step (2)_trainCharacteristic of the independent component c_trainAnd real-time measurement image X of synthetic aperture radar to be identified_testCharacteristic of the independent component c_testSynthetic aperture radar real-time measurement image X_testAnd (5) carrying out identification and classification, and judging the category of the detected target.

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