CN101908138A

CN101908138A - Identification method of image target of synthetic aperture radar based on noise independent component analysis

Info

Publication number: CN101908138A
Application number: CN 201010212877
Authority: CN
Inventors: 赵巍; 丁卓姝; 马浩然
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2010-06-30
Filing date: 2010-06-30
Publication date: 2010-12-08
Anticipated expiration: 2030-06-30
Also published as: CN101908138B

Abstract

The invention relates to an identification method of image targets of a synthetic aperture radar based on noise independent component analysis, belonging to the technical filed of synthetic aperture radar image target identification. The method comprises the following steps: firstly, preprocessing input images of an original training sample of the synthetic aperture radar to ensure that the images conform to whitening and zero mean normalization and the probability density of image noise complies with Gaussian distribution; secondly, performing logarithm noise independent component analysis on the preprocessed training sample and a real-time measurement sample to be identified, extracting the independent component characteristics of the images to be identified; and finally, identifying the sample to be identified by an independent component analysis method. The independent component characteristics extracted by the method of the invention are more suitable for classification, thus eliminating the image denoising process necessarily to be carried out in the preprocessing stage in an ideal ICA algorithm, improving the robustness of the algorithm on abnormal data, improving the instantaneity and reliability of SAR image target identification, and being suitable for SAR image characteristic extraction and automatic target identification.

Description

Synthetic aperture radar image target identification method based on noise independent component analysis

Technical Field

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

Background

Synthetic Aperture Radar (SAR) forms an SAR image according to backward electromagnetic scattering of a target, can overcome the defect that optical imaging is limited by conditions such as distance and climate, and plays a vital role in the fields of aeronautical survey, aerial remote sensing, satellite marine observation, aerospace reconnaissance, image matching guidance and the like. However, in the SAR imaging process, many scatterers are generally distributed in the same resolution unit, the phases of echo signals of the scatterers are randomly distributed, and mutual interference causes inherent multiplicative speckle noise of the SAR image, so that the general SAR image has the characteristics of low resolution, sensitivity to operating conditions, high multiplicative noise and the like compared with a common electronic optical image.

The SAR image target identification technology is a technology for determining the attributes of a target such as shape, type, position and the like by utilizing the characteristics (such as amplitude, phase, frequency, polarization information and the like) of a scattered field generated by a single target or a target group in a radar far area, and is widely applied to the military and civil fields; especially, under a complex battlefield environment, the accurate and fast SAR image target recognition technology can provide a strong guarantee for improving the battlefield perception capability and the response capability.

In the target recognition of the SAR image, the noise of the SAR image often includes interference of various natural clutter (grass, river, forest, etc.) and artificial clutter (buildings, etc.), and the noise is usually non-gaussian. Therefore, aiming at overcoming the influence of a large amount of noise on target recognition in SAR images effectively and improving the accuracy of the SAR image target recognition as much as possible, people provide a plurality of SAR image noise removal and feature extraction methods, which apply wide methods such as wavelet filtering, directional diffusion filtering, a target detection method based on a Markov random field, a Principal Component Analysis (PCA) based on multivariate statistical Analysis and Kernel criterion, a Kernel PCA (Kernel PCA: KPCA), a Fisher Linear Discriminant Analysis (FLDA), a Kernel Fisher Discriminant Analysis (KFDA), an Independent Component Analysis (Independent Component Analysis: ICA) and the like, and relate to the fields of image processing and mode recognition.

In an SAR image target recognition system, the following objectives are expected to be achieved by feature extraction: 1) the similar SAR images in different directions and with large differences have the same description mode; 2) eliminating or reducing the influence of the high noise characteristic of the SAR image on the classification result; 3) the huge data volume of the SAR image is compressed; and further providing effective and easily-recognized secondary features for the classifier, and judging the attributes such as the structure, the type and the like of the target by the classifier to complete the process of SAR image target recognition. In the method for extracting the SAR image features, the method is widely applied and is more effective, and the method is a feature extraction method based on multivariate statistical analysis and mainly relates to PCA and ICA. The PCA is a feature extraction method which is used for removing redundant information and reserving components containing maximum energy by finding a group of orthogonal projection directions capable of maximizing sample variance in the sense of minimum mean square error, and the method actually extracts second-order statistics of data, namely variance features. And ICA is popularized as PCA, and the high-order statistic characteristics of data are extracted, namely a group of independent source data in a high-order meaning is sought from observation data, and the group of source data is linearly superposed to form the observation data.

Much information of the SAR image is contained in high-order statistics of the image, and noise is usually non-Gaussian, so that the method for extracting the ICA features is more robust than PCA for the SAR image, and the ICA features containing the high-order statistics are more separable.

At present, the observation data is generally idealized to be zero noise by a general ICA technology, but the ideal is often different from the actual situation, and particularly in the field of SAR image target identification with high multiplicative non-Gaussian noise, how to eliminate or reduce the influence of the noise on the ICA characteristics is an urgent problem to be solved. Current methods of dealing with noise can be generally classified into three types: firstly, regarding noise as an independent component; denoising in a preprocessing stage; and thirdly, a noise ICA model. Almost all noise-free ICA models adopt the first method by default, namely, noise is regarded as one of original independent components, but in SAR image target recognition, the contribution effect of normal components on classification is weakened by larger noise components, and the classification precision is reduced. And the image denoising in the preprocessing stage can make the denoising process more specific, so that the characteristic extracted by the ICA achieves higher classification precision. For example, patent ZL 200710046928.3 of shanghai transportation university (synthetic aperture radar image denoising method based on independent component analysis base image) smoothly enhances the image of SAR by using wavelet index, thereby achieving denoising effect; US patent US 7508334(Method and apparatus for processing SAR images based on an anisotropic diffusion filtering algorithm, March 24, 2009) proposes a directional diffusion filtering algorithm for SAR image speckle noise to achieve SAR image denoising. However, in the preprocessing stage, the image denoising naturally increases a large amount of calculation, which results in too long time for extracting image features, and thus the battlefield requirement for SAR image target identification emphasizing real-time performance cannot be satisfied.

Noise ICA model based on the ideal noise-free ICA model, noise interference is regarded as a non-negligible influence factor, and on this basis, Aapo Hyvarinen et al, helsinki university, finland, proposed an ICA algorithm, the noise fast ICA (noise fast ICA: NFastICA) algorithm, combined with noise removal techniques. The algorithm introduces the concept of Gaussian moment, successfully and directly estimates potential random variables from observation data polluted by Gaussian noise, and has better robustness on sampling abnormal values. However, two important preconditions of the NFastICA algorithm are that the data noise is gaussian distributed (i.e., normal distributed) and the noise covariance matrix is known, but most of the noise in the SAR image is multiplicative noise and includes natural clutter and artificial clutter in addition to non-target echoes in the region associated with the target to be identified, and it is almost impossible to fit with gaussian distribution. Therefore, the NFastICA algorithm cannot be directly applied to the field of SAR image target recognition.

Disclosure of Invention

The invention aims to provide a synthetic aperture radar image target identification method based on noise independent component analysis, which is based on a noise ICA model and improves the existing SAR image target identification method based on ICA to slow down or eliminate the influence of a large amount of non-Gaussian multiplicative noise on feature extraction when the ICA method is used for carrying out classification identification on SAR images, reduce the calculated amount in a preprocessing stage, improve the robustness of an identification algorithm and finally achieve the purposes of improving the identification accuracy and the identification efficiency of the SAR image target identification technology.

The invention provides a synthetic aperture radar image target identification method based on noise independent component analysis, which comprises the following steps:

(1) raw training of input synthetic aperture radarTraining sample image X_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 an image in which the noise distribution conforms to a gaussian distribution after logarithmic transformation;

(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 image X of synthetic aperture radar_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.

The synthetic aperture radar image target identification method based on the noise independent component analysis has the advantages that:

1. the invention provides a synthetic aperture radar image target identification method based on noise independent component analysis, which relates to a new Log-normal noise independent component analysis (Log-normal noise ICA: LnICA) method, omits the image denoising process which is necessary to be carried out in the preprocessing stage by the existing noise-free independent component analysis algorithm, effectively overcomes the influence of a large amount of multiplicative non-Gaussian noise in a synthetic aperture radar image on the characteristic extraction, enables the extracted independent component characteristics to be more suitable for classification, thereby reducing the calculated amount, improving the reliability of the synthetic aperture radar image target identification and the robustness of abnormal data, and can greatly improve the identification accuracy and the identification efficiency of the synthetic aperture radar target identification, particularly the real-time automatic target identification.

2. The synthetic aperture radar image target identification method improves the selection standard of the principal component characteristics in the PCA algorithm in the process of dimensionality reduction and whitening, and provides a Most separable component (MDC) selection criterion from the viewpoint of noise reduction, namely, the degree that a certain characteristic component can represent the attribute of the original mode category is measured by using category separability, and a plurality of MDC components with the strongest separability are selected from the characteristic components to represent the original image. Dimension reduction and whitening are carried out in a preprocessing stage by adopting the separability principle of the characteristic components, the SAR image denoising effect aiming at classification can be improved simultaneously, and the accuracy and reliability of SAR image target identification based on an independent component analysis method are improved.

Drawings

Fig. 1 is a general flow of an ICA-based SAR image target recognition technique in the prior art.

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

FIG. 3 is a schematic diagram of extracting a noise region and a target region from a single training sample image according to the method of the present invention.

Fig. 4 is a flow of a synthetic aperture radar image target identification method based on noise independent component analysis according to the present invention.

Detailed description of the preferred embodiments

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

(1-5) all noise regions N of the N training images obtained as described above_oNoise covariance for constructing training samples

Variance diagonal matrix

Wherein the diagonal elements

For the noise variance estimate for each training image,

representing the i-th training imageA noise area;

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

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

The following describes the present invention in detail with reference to the accompanying drawings.

First, the related concepts and basic principles of Synthetic Aperture Radar (SAR) image target recognition using an Independent Component Analysis (ICA) method will be briefly explained.

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

X＝AS

S＝WX

the basic flow of the prior art for target recognition of SAR images by using ICA is shown in fig. 1.

In order to improve the accuracy of the target identification of the SAR image, the image needs to be preprocessed before the ICA is used for extracting the features of the SAR image. The pretreatment method mainly comprises the following steps: carrying out certain transformation on an original SAR image or using another measurement mode to represent source data; normalizing the transformed image; cutting out target areas (also called ROI) related to the identified target from the original image, wherein the areas may contain one or more targets; the target region basically contains all echoes related to target identification, including target echoes, shadow echoes and other clutter, and the noise region almost completely consists of background clutter, so the target region is usually used for ICA feature extraction of a target to be identified and used for classification identification of the target, and the noise region is only used for variance estimation of noise.

ICA is suitable for processing one-dimensional data, and after preprocessing, two-dimensional image samples need to be straightened into one-dimensional row vectors. Each row vector can be regarded as a mixed signal formed by linearly superimposing a plurality of vectors, that is, each observed SAR image can be considered to be linearly combined by a group of potential mutually independent base images. Let x be an SAR image, let S be a base image matrix composed of base image vectors, and column vectors S_iFor the ith base image vector, x can be represented by S

x＝b₁·s₁+b₂·s₂+...+b_n·s_n＝b·S

Wherein the coefficient vector b ═ b (b)₁，b₂，...，b_n) I.e. the ICA feature of the image sample x.

Most ICA processes require zero mean whitening data, i.e., E { X } -, 0, E { XX }, as satisfied^TI. Let X_OTo train the data, X_OSubtracting the mean vector m ═ E { X }_OThe centralization can be realized. After the confusion matrix a is solved using the centered data, 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. Wherein the mean vector of s can pass through A^-1m is obtained.

It is assumed here that X_OIs already zeroAnd (4) average value. To X_OThe whitening process of (A) is letting X_OAre not related to each other and are equivalent to X_OThe covariance matrix of (a) is an identity matrix (i.e., an identity matrix)

). The following method can be adopted for X_OWhitening is performed.

X＝W_ZX_O

The ICA approach requires that all individual components of the multivariate data must be non-gaussian distributed, or at most one individual component may be gaussian distributed. The key to evaluating an ICA model is the non-Gaussian nature of the independent components of the data. The central limit theorem states that the distribution of the sum of a set of mutually independent random variables generally approaches a gaussian distribution, from which the following can be deduced:

inference 1: the sum of the n independent random variables is closer to a gaussian distribution than either of the original variables.

According to the noise-free ICA model, X is equal to AS, and y is an independent component in S, namely

Wherein w is defrobulatedThe undetermined column vector, W, of matrix W corresponding to y_iIs its i-th element, x_iIs the ith observed signal. Employing the conclusion of inference 1 makes w equal to the corresponding column of the inverse of matrix a. Let column vector z equal to A^Tw, then

According to the inference 1, y is compared with the original independent variable s_iIs more gaussian. If we minimize the Gaussian of y, then y will equal some component S in S_k. The higher the non-gaussian property of y, the higher the independence of y from other components, and vice versa; if the non-Gaussian nature of y is maximized, a separate component is obtained. Thus, in ICA theory, non-gaussian is equivalent to independence.

The general flow of the synthetic aperture radar image target identification method based on the noise independent component analysis is shown in fig. 4, and the specific content is as follows:

(1) the method firstly inputs original training sample image X of the synthetic aperture radar_trainThe pretreatment is carried out, and the process comprises the following steps:

(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 an image in which the noise distribution after logarithmic transformation conforms to a gaussian distribution.

The purpose of this step is to make the synthetic aperture radar noise probability density follow a gaussian distribution, known as a normal distribution. As can be seen from the background section, a basic feature of the SAR image is that it contains a lot of multiplicative speckle noise, and in the field of object classification and identification, the noise of the SAR image also includes a lot of interference of natural or artificial noise, so it is almost impossible to simply fit the noise by using gaussian distribution.

The lognormal distribution model is an SAR image clutter statistical model suitable for ground scenes and proposed by S.F.George, is a commonly used statistical model for describing non-Rayleigh envelope data, and has the main idea that multiplicative noise of an SAR image is converted into additive white Gaussian noise by adopting a homomorphic filter. The probability density expression of the lognormal distribution is

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

Therefore, after the SAR image data is subjected to logarithmic transformation, its noise probability density approximately follows a gaussian distribution, as shown in fig. 2.

(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) Where 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_l}＝{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;

since the ICA algorithm adopted by the present invention can only process one-dimensional signals, the target region and noise region matrix of each image data need to be respectively stretched into one-dimensional row vectors in this step.

(1-4) repeating the steps (1-1), (1-2) and (1-3) to obtain a one-dimensional straightening vector X of the target area of the N training images in the training sample_oForming an N-row training matrix X_OI.e. the input matrix X in the ICA algorithm;

(1-5) in general, each SAR image is independently imaged, and therefore the noise contained therein should be statistically independent from each other, so that the data (i.e., X in the previous step) is observed_O) The noise covariance matrix of (2) is a diagonal matrix. All noise regions N of the N training images obtained by the method_oThe noise covariance diagonal matrix of the training sample can be constructed

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

It can be observed from fig. 2 that in the SAR image after logarithmic transformation, the shape of the probability distribution of the noise approximately follows the gaussian model, and the noise region n_oCentered, the diagonal elements of the noise covariance matrix can be directly estimated by

Wherein,

representing the noisy region of the i-th training image.

(1-6) data X in the above step_OHas been centered with a covariance matrix ofAnd, the image noise n has been estimated_OIs the noise covariance matrix sigma_O. For the above training matrix X_OAnd performing dimensionality reduction and whitening treatment to obtain a synthetic aperture radar training sample image subspace matrix X after dimensionality reduction and whitening.

This step can be implemented by means of Principal Component Analysis (PCA) or best-separable component (MDC) criteria to simultaneously whiten and reduce the dimensions of the data, as described in detail below.

First, take the PCA method as an example: firstly, the covariance matrix C-sigma of the non-noise data_OGo on speciallyEigenvalue Decomposition (EVD) of

C-∑_O＝EDE^T

Thus X_OWhitening can be achieved by the following formula:

X＝ED^-1/2E^TX_O

it is easy to prove that the data X thus obtained satisfy E { XX^T}＝I。

Since the whitening process does not combine X with X_OThus re-estimating the covariance matrix of noise n in X as

∑＝E{nn^T}＝(ED^-1/2E^T)∑_O(ED^-1/2E^T)

In general, the raw data X_OIs very high, resulting in huge computation and redundancy, and even an over-learning phenomenon. Therefore, removing too small components in D according to the PDC method, selecting L (L is less than or equal to M) components with the largest energy, and finally obtaining a new characteristic value matrix D of the image_LThis process is also referred to as subspace selection. Wherein D is_LFor a diagonal matrix of the first L largest eigenvalues selected from D, E_LAnd forming a matrix by the eigenvectors corresponding to the L eigenvalues. Thus, data X will be reduced to L dimension, and ∑ is L × L size, and with E_LD_L ^-1/2E_L ^TReplaces ED in the original formula^-1/2E^T. Therefore, the PCA method is adopted to simultaneously realize the whitening and noise reduction processes of the input data, and a more meaningful subspace image data is input for the next ICA characteristic extraction process

X＝E_LD_L ^-1/2E_L ^TX_O

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

As described in the background art, the method of performing the dimensionality reduction compression on the SAR image by using the PCA has certain defects. PCA selects the first L principal components with the largest energy to represent original image data, but the energy of the components (projection direction) has no direct relation with the degree of representing the image category attribute; therefore, in an extreme case, when the current L principal components all represent the energy of noise and the noise of the images of different categories is basically similar, the feature quantity available for image classification is completely lost, and the SAR image cannot be correctly identified.

The invention improves the PCA method, proposes a Most separable component (MDC) analysis method which utilizes Class separability (Class separability) to measure the display degree of one component to the image Class attribute, and selects the first L Most separable components to represent the original image. The specific selection method of MDC is as follows:

let N image samples contain C-type target in total, and let the number of samples belonging to i-th type target be N_iThen, then

Let p_kFor the k-th projection direction (i.e. the k-th component), b, in the PCA transformation matrix P_ijRepresents the projection coefficient of the ith sample in the ith direction (1 ≦ i ≦ C, 1 ≦ j ≦ N_i) All projection coefficients b_ijIs on average ofProjection coefficient b of i-th sample_i·jIs on average ofDefining inter-class variance

Variance within class

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

r＝σ_between/σ_within

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

Image noise can also be suppressed simultaneously with the PCA or MDC methods. The extracted principal component is subjected to the inverse transformation to obtain the approximation of the original SAR image, and compared with the original image, the noise of the approximated image is obviously reduced and suppressed. The MDC method removes similar components (including main noise components) having no or little separability in the main component, and obtains higher separability with less energy of the image. Although the components removed by the MDC method are not all noise components, these components have no significant positive effect on the classification result and can also be regarded as noise components.

If the MDC method is adopted to realize the step, only the first L most separable components are selected as the selected subspace according to the MDC index in the subspace selection process, and the data input into the ICA still is

X＝E_LD_L ^-1/2E_L ^TX_O

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

In this step, a principal component having an energy content of the first 95% of the principal components (in the theory of image processing, the first 95% of the energy can substantially represent an image) is selected, the separability of the principal components is calculated using the MDC index, the components are arranged in the separability order, and the first L projection directions P 'are selected'_LThe next ICA feature extraction was performed.

(2) Obtaining real-time measurement image X of synthetic aperture radar_testUsing a stand-aloneRespectively extracting the synthetic aperture radar training sample images X by a component analysis method_trainIndependent component feature and synthetic aperture radar real-time measurement image X_testThe specific process comprises the following steps:

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

the noise ICA model adopted by the invention is a noise FastICA (NFastICA) model, and the NFastICA model is combined with the preprocessing step to form a novel lognormal noise independent component analysis (Log-normal noise ICA: LnnICA) method. The NFastICA algorithm can directly estimate potential random variables from observed image data contaminated by Gaussian noise through the characteristics of Gaussian Moments (Gaussian Moments), and a specific implementation of noise image independent component feature extraction using NFastICA based on the FastICA method is detailed below.

On the basis of the ideal ICA model, the noise ICA model can be expressed AS X ═ AS + n_OZero-averaged, covariance matrix

And noise n_oSatisfy the Gaussian distribution, and the covariance matrix is sigma_O. Whitening SAR image data and using covariance matrix C-sigma with noise removed_OInstead of C, the whitening operation should be

X＝(C-∑_O)^-1/2X_O

Where X is also the input to the noise ICA model and its covariance matrix of the noise is

∑＝E{nn^T}＝(C-∑_O)^-1/2∑_O(C-∑_O)^-1/2

It has been mentioned previously that in ICA theory, non-Gaussian is equivalent to independence. Among the various measurement methods of non-gaussian, one method for making robustness to outliers of random variables is to measure non-gaussian with approximately negative entropy. From information theory, it is known that the random variables with higher disorder have larger entropy, and for the gaussian variables, one basic property is that the entropy is the largest among all random variables with the same variance. Defining a measure of negative entropy

J(y)＝H(y_Gauss)-H(y)

Wherein, y_GaussRepresents a gaussian random variable with the same variance as the variable y, and H (·) is the entropy-finding function. Thus, the values of the negative entropy J (y) are all non-negative, while Gaussian-type variables have a negative entropy of zero.

To simplify the calculation, the negative entropy is usually estimated by approximation, i.e.

J(y)≈c[E{G(y)}-E{G(v)}]²

<math><mrow><msub><mi>G</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><msub><mi>a</mi><mn>1</mn></msub></mfrac><mi>log</mi><mi>cosh</mi><msub><mi>a</mi><mn>1</mn></msub><mi>u</mi><mo>,</mo><mi>where</mi><mn>1</mn><mo>≤</mo><msub><mi>a</mi><mn>1</mn></msub><mo>≤</mo><mn>2</mn><mo>.</mo></mrow></math>

Or

G_{2} (u) = - \exp (\frac{{- u}^{2}}{2})

Wherein v is a standard normal variable with zero mean and unit variance, and G is a non-quadratic function, the method of commonly taking the approximate negative entropy is easy to understand, quick to calculate and strong in robustness, so that the FastICA also adopts the non-Gaussian measurement method, and the Newton descent method is adopted to search for an optimal solution (components are mutually most independent).

The learning rule of FastICA is to find a direction vector w such that the input data projects in this direction y-w^Tnon-Gaussian maximization of X, i.e. using an approximate negative entropy function using a negative entropy measure

J(y)≈[E{G(y)}-E{G(v)}]²

The value of (c) is maximum. At the same time, it is necessary to ensure that each independent component y_iAnd is not repeated, namely W is an orthogonal unit array.

The standard normal distribution variable v limits the variance of y to also have to be 1. If the raw data X is whitened data, then the constraint on the y unit variance is equivalent to normalizing the second order norm of w, i.e. the

E{(w^Tx)}²}＝||w||²＝1.

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

1) univariate search for the optimum w_i。

step 1: arbitrarily selecting an initial weight vector w_i；

step 2: update wi, command

Wherein G is a second derivative function of the non-quadratic function G, and η is a Newton method parameter;

step 3: for w obtained from step2_iNormalized, i.e. ordered

w_{i} = w_{i}^{+} / | | w_{i}^{+} | |

step 4: judgment of w_iIf so, the process ends, otherwise, step2 is returned.

2) And carrying out global decorrelation search on the confusion removal matrix W to ensure that W is orthogonal.

Here, a direct decorrelation on W is used: all w obtained in step 1)_iThe de-obfuscating matrix W is composed and the following search formula is iteratively computed until W converges.

W＝3W/2-WW^TW/2

Whereby the base image matrix can be represented as

S＝WX＝WW_ZX_O＝W_IX_O

Wherein W_I＝WW_ZMeaning two layers, i.e. W_IBoth the second order correlation (W transform) and the higher order correlation (W) of ICA are removed_zTransform) to achieve inter-component space between the components of the vector SAre independent of each other. Thus, it is not difficult to obtain X_OICA of (A) is characterized by

And test data X_testICA of (A) is characterized by X_testS⁺(+ represents a generalized inverse).

And training sample data X before dimensionality reduction_OAfter PCA decomposition, the results are shown below:

X_O＝RP^T

where P is the transformation matrix of PCA, each column represents a projection direction, and P^TP is I; r is X_OProjection onto P. Let P_LThe first L projection axes (first L principal components) of P, R_LIs X_OProjection thereon, i.e. R_L＝X_OP_L(ii) a The minimum mean square error estimate of X is

{\hat{X}}_{O} = R_{L} P_{L}^{T}

Thus, at P_LBy performing ICA in the above way, and taking L smaller than N, the effect of reducing the dimension and the calculation amount can be achieved, and a de-confusion matrix is obtained similarly

And

and is correspondingly provided with

{\hat{W}}_{I} P_{L}^{T} = \hat{S}

P_{L}^{T} = {\hat{W}}_{I}^{- 1} \hat{S}

Thereby obtaining

Is namely X_OThe ICA characteristic of (4). Likewise, X_testThe ICA feature vector of

b = R_{test} {\hat{W}}_{I}^{- 1} = X_{test} P_{L} {\hat{W}}_{I}^{- 1}

In fact, E { G (y) } ═ E { G (w) due to the presence of noise^TX) } in an approximate negative entropy function J_G(y)≈[E{G(y)}-E{G(v)}]²Is no longer representative of the statistics of the independent components, but of the sum of the independent components and the noise components. One basic idea of the Gaussian moment based NFastICA is to select G to be a zero mean Gaussian random variable density function or to be related to itIs a functional form of, such that J_GCan be simply calculated from a series of observations consecutively. If z is a zero-mean non-Gaussian variable, n is the variance σ²The Gaussian noise of (2) can be simply represented by an algebraic expression of the relationship between E { G (z) } and E { G (z + n) }. Similarly, when G is a density function or correlation function of a zero mean Gaussian variable, E { G (w)^TX) } the J of data without noise can be directly estimated from the data X with noise_G(y)。

It is assumed that the noise of SAR images follows a gaussian distribution (in practice this situation is often not true, and this is the main problem solved by the present invention). Defining variance as c²Gaussian density function of

Order to

To represent

1(1 > 0) order derivative function of (A),

to represent

As such, the first and second electrodes are,

to represent

1-order product function of

Is provided withRepresenting any one of the distribution functions as

The independent component of (non-gaussian),

representing variance as σ²Independent gaussian noise variance. Due to the fact that

The function being derived from a Gaussian function and hence being called

Is composed of

And for any c > σ²Let us order

To obtain

This illustrates

And observation thereof

Is equivalent. In addition, it can also prove that

Substitution

The same holds true for the above equation. Thus, let

So that the gaussian moment of the random variable can be used to directly estimate the noise-free independent components from noisy observations. Order to

Wherein

Using Newton method to calculate maximum value of the above formula under w normalization condition, and optimizing w to obtain

Where G is the derivative of the function G, G may be taken₁(x)＝tanh(x)，g₂(x)＝x·exp(-x²/2) or g₃(x)＝x³.

Wherein,

the distribution function is accumulated for gaussians.

By using the concept of Gaussian moment, the NFastICA is used in the step under the condition that the noise is in Gaussian distribution, and the synthetic aperture radar training sample X can be simply extracted from the observation data with the noise_trainIs characterized by the independent component C_trainAnd (4) showing.

(2-2) real-time measuring image (marked as X) of the synthetic aperture radar_test) In the image data to be identified is projected onto the estimation matrix S from the base image_eIn the spanned base image subspace, the real-time measurement image X_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 spanned base image subspace, by c_test＝piv(S_e ^T)·X_testObtaining piv (S) therein_e ^T) Representing the generalized inverse of the matrix, c_testNamely a real-time measurement image X of the synthetic aperture radar_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.

(3) The synthetic aperture radar training sample image X obtained according to the step (2)_trainCharacteristic of the independent componentc_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 identifying and classifying, and judging the category of the detected target by adopting a proper classifier.

The selection of the classifier needs to comprehensively consider various factors such as actual requirements and classification effects, for example, a simple and feasible minimum Mean Square Error (MSE) classifier or a Support Vector Machine (SVM) classifier with a high-dimensional kernel mapping and a better classification effect can be adopted.

The following specific steps of classifying and identifying the target of the synthetic aperture radar are described by taking an MSE classifier as an example, and the specific steps are as follows:

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

D_i＝||C_traini-C_tost||₂

Wherein the index i indicates the class of known training samples, C_testiICA features, C, representing class i training samples_testRepresenting the ICA characteristics of a single sample to be identified.

2) And respectively calculating the distance metric (ICA characteristic distance) between each test sample and each type of training sample according to the distance metric defined in the step 1). If there are N types of training samples, then N distances { D ] for each test sample can be obtained by this step₁，D₂...D_N}。

And for each test sample, solving the minimum value of the distance between the test sample and the N types of training samples, and classifying the test sample into the category to which the training sample with the minimum distance belongs. I.e. for a certain test sample, if it is the distance D from the ith class training sample_i＝min{D₁，D₂...D_NThen the MSE classifier will classify the test sample into the ith class, i.e., identify the target as the ith class.

Claims

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

(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;

Wherein the diagonal elements

For the noise variance estimate for each training image,

representing a noise region of the ith training image;

(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:

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

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