Classification method combining gaussian regression mixture model and mrf hyperspectral function data

Abstract

In order to explore the effectiveness of the functional data analysis method in the hyperspectral image processing, the application proposes a classification method combining the Gaussian regression mixture model and the MRF hyperspectral function data; first, the polynomial regression is used to fit the hyperspectral image pixel spectrum curve, so as to express the pixel spectrum information in the form of function; then, the neighborhood relationship is introduced to establish the Markov random field model, and the neighborhood Gaussian regression mixture model is established in combination with the Gaussian regression mixture model; finally, according to the maximum posterior probability criterion, the final hyperspectral image classification result is obtained. Since the spatial-spectral information of the hyperspectral image is fully combined, the algorithm has high-precision classification result, and effectively improves the classification performance of the hyperspectral image.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of hyperspectral image classification, and particularly relates to a classification method combining a Gaussian regression mixture model and MRF hyperspectral function data. BACKGROUND

[0002] With the development of hyperspectral remote sensing technology, hyperspectral images are widely used in many fields such as ocean, agriculture, medical treatment and the like. The hyperspectral image has the characteristics of high data dimension, high correlation between bands, spectral mixing and the like, effectively reflects the subtle differences in spectral characteristics of different ground objects, and also brings great challenges to data processing. At present, there are two main ways for analyzing and processing high-dimensional data: one way is dimension reduction, that is, dimension reduction. The method reduces the dimension by appropriately transforming the original high-dimensional data, and then interprets the data in the low-dimensional space by using multivariate statistical analysis and the like; the other way is functional data analysis method, which converts the original discrete data into functional data form, so as to analyze by using the unique characteristics of functions, and can extend some classic analysis methods in traditional multivariate statistics, such as smoothing method, interpolation method, regression analysis, principal component analysis and linear model, to functional data analysis.

[0003] In functional data analysis, the Gaussian regression model plays a crucial role and can easily process classification and regression problems in machine learning. Zhang et al. compared the Gaussian process regression method for classification of high-dimensional data with limited samples with extended nearest neighbor, classic K-nearest neighbor, naive Bayes, linear discriminant analysis and classic multilayer perceptron neural network, and the results showed that the Gaussian process regression can learn from the global distribution, thereby improving the pattern recognition ability. In the face of functional processing of high-dimensional data, Chamroukhi and Nguyen expressed the conditional dependency of observation data by regression modeling, constructed a function data (Gaussian Regression Mixture Model, GRMM) for functional data analysis. Therefore, in the processing of hyperspectral images, expressing the spectral measurements of each band of the hyperspectral image pixels as functional data has more advantages, which not only makes full use of the rich spectral information contained in the hyperspectral data, but also effectively avoids the "Hughes" phenomenon caused by analysis of high-dimensional discrete data.

[0004] At present, hyperspectral image classification is mainly based on spectral information and spatial-spectral information. The method based on spectral information is mainly to use the spectral characteristics of hyperspectral image as the basis for classification, and the commonly used classification methods include support vector machine (SVM), decision tree, Bayesian classification, etc. Fauvel et al. used Gaussian mixture classifier, based on cross-validation estimation of classification rate, iteratively extracted spectral variables, thereby completing the classification of hyperspectral image. However, this method does not consider spatial information, resulting in insufficient information utilization. The classification method based on spatial-spectral information combines the spectral information and spatial information of hyperspectral image. Compared with the method based on spectral information, the classification method based on spatial-spectral information effectively improves the classification accuracy. In the face of spatial information processing problem of function data, Carlo et al. simulated the spatial dependence between sites through Markov random field (MRF), completed the classification of marine chlorophyll A concentration, and illustrated the importance of introducing spatial information. Therefore, it is necessary to propose a method for classifying hyperspectral function data by simultaneously introducing spatial correlation information using a polynomial regression model. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application designs a classification method of hyperspectral function data combining Gaussian regression mixture model and MRF. The band spectral measure of hyperspectral image is converted into function data by using a polynomial regression model, and an MRF model is established on the neighborhood of pixels for introducing spatial correlation information, and a neighborhood Gaussian regression mixture model (NGRMM) model is established by combining the GRMM model. The present application not only utilizes the advantages of function data, establishes the dependence between band spectral measure and band information, maximizes the utilization of spectral information, but also fully integrates spatial-spectral information, further improves the classification accuracy.

[0006] The classification method of hyperspectral function data combining Gaussian regression mixture model and MRF includes the following steps:

[0007] Step 1, expressing the pixel spectral curve of hyperspectral image as a polynomial function;

[0008] Step 1-1, given a hyperspectral image g = {g i ,i = 1, …, n}, where i is the pixel index, g i =(g ij ,j = 1, …, m) T is the spectral measure vector of pixel i, n is the total number of pixels, j is the band index, and m is the number of bands; let x = {x j,..., m} are the sampling frequency sets of each band of the hyperspectral image, where x j is the electromagnetic wave frequency corresponding to band j; let the spectral curve of pixel i be g i = Y i (x); since the hyperspectral image has a large number of bands and narrow band intervals, g i = Y i (x) is sampled at high density to obtain (y i , x) = {(y ij , x j ), j = 1,..., m}; in order to realize hyperspectral image classification based on function data analysis, the hyperspectral image is represented as (y, x) = {(y i , x), i = 1,..., n}, that is, the spectral sampling (y i , x) is used instead of the spectral vector g i to express the spectral characteristics of the pixel;

[0009] Step 1-2, in order to express the conditional dependency in the spectral measure vector, a regression modeling method is used; given a k-class cluster, the spectral measure vector of the i-th pixel Y i is regarded as a regression function observed with noise, and E i is an independent and identically distributed standard Gaussian; a polynomial function representation of the pixel spectral curve is obtained;

[0010]

[0011] where T is matrix transposition, β k = (β k0 , β k1 ,..., β k(p-1) ) T is the mean regression coefficient vector of the k-class cluster, p is the polynomial degree, is the polynomial regression vector constructed from the input x, σ k is the noise standard deviation of the k-class cluster;

[0012] Step 2, the probability density distribution of the polynomial function obtained in step 1 is modeled using a Gaussian regression mixture model, and the spatial dependency existing between pixels is simulated using an MRF, and the Pott model is used to redefine the weight of the Gaussian regression mixture model; a neighborhood Gaussian regression mixture model is obtained;

[0013] Step 2-1, in the hyperspectral remote sensing image, in addition to the measured spectral observation (y i , x) of each pixel at each frequency, there is also an implicit variable representing the class attribute of each pixel, denoted as z i ∈ {1,..., K}, which is called the class label of pixel i, z i= k indicates that pixel i belongs to class k; define z i = k, the probability density function of pixel i belonging to class k is denoted as f(z i = k), and z = {z i , i = 1, …, n} is regarded as a random field representing the class attribute of the hyperspectral image, which is called a label field, and each realization of the label field corresponds to a classification of the hyperspectral image; the observed value and the hidden variable of the hyperspectral image form its complete data, that is, {(y, x), z}; in the model-based functional data clustering process, it is necessary to define the likelihood model of the spectral curve Y i (x); the conditional probability model of y i |x is constructed by using a mixture model, that is:

[0014]

[0015] where k is the index of the mixture component, and in the classification of the hyperspectral image, k is also the index of the class, K is the number of mixture components, that is, the number of classes, f k (y i |x; ψ k ) is the probability density function of the mixture component k, where ψ k represents the parameter set corresponding to the mixture component k, α ik = f(z i = k) is the probability of pixel i belonging to class k, and is also the weight coefficient of the mixture component k, α k = {α ik , i = 1, …, n}, and satisfies In practical applications, α ik is estimated in the Pott model solution as a variable;

[0016] Step 2-2, in order to fully utilize the spatial information of the hyperspectral image, considering the correlation of the labels of the neighboring pixels in the Gaussian regression mixture model, the NGRMM is constructed, and the MRF is used on the neighborhood of the pixel, and the static Potts model defining the relationship between the pixel and its neighborhood is used to define the prior probability of pixel i belonging to class k, and thus the weight coefficient α ik is defined as:

[0017]

[0018] where η is the spatial correlation coefficient of the neighboring pixels, N i represents the index set of the neighborhood of pixel i, k' represents the class to which the neighboring pixel belongs, and t(z i , z i' ) is an indicator function, that is, t(z i , z i' ) = 1 if z i ≠ z i' , and 0 otherwise.

[0019] Step 2-3, the spectral measure of the k-th class of pixels is modeled by a Gaussian distribution, whose probability density is defined as:

[0020] f k (y i |x; ψ k ) = N(y i ; μ k (x), Σ k (x), ψ k ) (4)

[0021] where μ k (x) is the mean function defined by the p-1 order polynomial regression model, i.e.:

[0022]

[0023] Σ k is the covariance matrix of the k-th class of clusters, i.e.:

[0024]

[0025] where σ k = {σ k1 ,…, σ km}, I m is an m x m identity matrix; thus, the parameters of the k-th class of spectral measure model are represented as ψ k = {β k , σ k}; in combination with equations 1-6, the functional probability model of the hyperspectral image g is defined as,

[0026]

[0027] where ψ = {α1,…, α K-1 , ψ1,…, ψ K} is the parameter set of the model;

[0028] Step 3, the EM algorithm is applied to solve the neighborhood Gaussian regression mixture model, and the hyperspectral image is classified according to the maximum posterior criterion;

[0029] Step 3-1, the parameter ψ of the log-likelihood function is calculated;

[0030]

[0031] The EM algorithm is used to estimate the values of the parameters in ψ under the condition of equation 8; for this purpose, the log-likelihood model of the aforementioned complete data is constructed according to equation 8, i.e.:

[0032]

[0033] wherein z ik =1 if and only if z i =k.

[0034] Step 3-2, the EM algorithm for solving the parameter ψ includes two processes of E and M; the E process calculates the expected function of formula 9 according to the current value of ψ, with q as an iteration pointer, denoted as ψ (q) , that is, formula 10.

[0035]

[0036]

[0037] wherein τ ik (q) is the posterior probability of pixel i belonging to class k in the current state, that is, the qth iteration;

[0038] Step 3-3, the M process is to maximize formula 9 to obtain the parameter of the q+1th iteration, that is, formula 11.

[0039]

[0040] The specific parameter estimation value is ψ

[0041]

[0042]

[0043] Step 3-4, unlike the traditional mixture model which needs to estimate the component weight coefficient by using the EM algorithm, the neighborhood Gaussian regression mixture model of the application defines the weight coefficient by formula 3 so as to consider the spatial relationship of the neighborhood pixels; thus, formula 3 is rewritten as formula 12.

[0044]

[0045] wherein z i (q) (i=1,...,n) is the label of pixel i in the qth iteration.

[0046] The optimal estimation value of z i is formula 13.

[0047]

[0048] That is, the maximum posterior probability is taken as a criterion to complete the hyperspectral image classification.

[0049] The application has the beneficial technical effects that:

[0050] 1. This invention uses a function data analysis method to process hyperspectral images. It performs polynomial fitting on the hyperspectral images and transforms them into function-type data for analysis, which is more conducive to discovering their potential internal features.

[0051] 2. This invention applies MRF to simulate the spatial dependencies that may exist between pixels, uses the Pott model to redefine weights, and fully integrates the spatial-spectral information of hyperspectral images. Attached Figure Description

[0052] Figure 1 Flowchart of hyperspectral image functional data classification using Gaussian regression mixture model and MRF in this invention;

[0053] Figure 2 Comparison of hyperspectral image curve fitting before and after in an embodiment of the present invention; wherein Figure a is the original spectral mean curve, and Figure b is the mean function curve;

[0054] Figure 3 The classification results of hyperspectral image functional data using Gaussian regression mixture model and MRF in this embodiment of the invention are shown in the figure; where Figure a is the truth plot and Figure b is the experimental result. Detailed Implementation

[0055] An embodiment of the present invention will be further described below with reference to the accompanying drawings.

[0056] In this embodiment of the invention, a classification method combining a Gaussian regression mixture model and MRF hyperspectral function data is used, such as... Figure 1 As shown, it includes the following steps:

[0057] Step 1: Represent the pixel spectral curves of the hyperspectral image as a polynomial function;

[0058] Step 1-1: Given a hyperspectral image g = {g i Let g be a pixel index, i = 1, ..., n. i =(g ij (j=1,…,m) T Let x be the spectral measure vector of pixel i, n be the total number of pixels, j be the band index, and m be the number of bands; let x = {x j Let {x,j=1,…,m} be the set of sampling frequencies corresponding to each band of the hyperspectral image, where x j Let g be the electromagnetic wave frequency corresponding to band j; let g be the spectral curve of pixel i. i =Y i (x); Due to the numerous bands and narrow band spacing in hyperspectral imaging, therefore, for g i =Y i (x) is sampled at high density to obtain (y) i ,x)={(yij ,x j ),j = 1,...,m}, which can completely express the spectral curve; in order to realize the classification of hyperspectral image based on function data analysis, the hyperspectral image is expressed as (y, x) = {(y i ,x), i = 1,...,n}, that is, the spectral sampling (y i ,x) is used instead of the spectral vector g i to express the spectral characteristics of each pixel;

[0059] Step 1-2, in order to express the conditional dependence in the spectral measure vector, the method of regression modeling is used; given the k-class cluster, the spectral measure vector of the i-th pixel Y i is regarded as a regression function observed with noise, and is a standard Gaussian E i independent and identically distributed; the polynomial function expression of the pixel spectral curve is obtained;

[0060]

[0061] wherein T is the matrix transpose, β k = (β k0 , β k1 ,..., β k(p-1) ) T is the mean regression coefficient vector of the k-class cluster, and p is the polynomial degree, is the polynomial regression vector constructed by the input x, and σ k is the noise standard deviation of the k-class cluster;

[0062] Step 2, the probability density distribution of the polynomial function obtained in step 1 is modeled by using the Gaussian regression mixture model, and the spatial dependence relationship existing between the pixels is simulated by using the MRF, and the weight of the Gaussian regression mixture model is redefined by using the Pott model; a neighborhood Gaussian regression mixture model is obtained;

[0063] Step 2-1, in the hyperspectral remote sensing image, in addition to the measured spectral observation (y i ,x) of each pixel at each frequency, there is also an implicit variable z i ∈ {1,...,K}, which is called the class label of the pixel i, z i =k indicates that the pixel i belongs to class k; define z i as a random variable, then the probability density function of the pixel i belonging to class k is denoted as f(z i =k), and in summary, z = {z iThe sequence {i=1,…,n} is considered a random field characterizing the class attributes of hyperspectral images, called the label field. Each implementation of the label field corresponds to a classification of the hyperspectral image. The observed values ​​and latent variables of the hyperspectral image constitute its complete data, i.e., {(y,x),z}. In the model-based function data clustering process, the spectral curve Y needs to be defined. i A probability model for (x) is constructed using a mixture model. i The conditional probability model for |x, i.e.:

[0064]

[0065] Where k is the mixed component index, and in hyperspectral image classification, k is also the category index, K is the number of mixed components (i.e., the number of categories), and f k (y i |x;ψ k Let ψ be the probability density function of the mixture component k, where ψ k Let α represent the parameter set corresponding to the mixed component k. ik =f(z) i =k) ​​is the probability that pixel i belongs to class k, which is also the weighting coefficient of the mixture component k, α k ={α ik Given a group of integers i = 1, ..., n, and satisfying the following conditions: In practical applications, α ik It is estimated as a variable in the solution of the Pott model;

[0066] Step 2-2: To fully utilize the spatial information of hyperspectral imagery and considering the correlation of neighboring pixel labels in the Gaussian regression mixture model, an NGRMM is constructed. MRF is used in the pixel neighborhood, and a static Potts model defining the relationship between pixels and their neighbors is employed to characterize the prior probability that pixel i belongs to class k. Based on this, the weighting coefficient α is defined. ik for:

[0067]

[0068] Where η is the spatial correlation coefficient of neighboring pixels, and N i Let t(z) represent the set of neighborhood indices of pixel i, k' represent the category of the neighboring pixels, and t(z) represent the set of neighborhood indices of pixel i. i ,z i' ) is an indicator function, if z i ≠z i' Then t(z) i ,z i' =1, otherwise 0;

[0069] Steps 2-3: Model the spectral measure of the k-th pixel using a Gaussian distribution, with its probability density defined as:

[0070] fk (y i |x;ψ k )=N(y i ;μ k (x),Σ k (x),ψ k ) (4)

[0071] where μ k (x) is the mean function defined by the p-1 order polynomial regression model, i.e.,

[0072]

[0073] Σ k is the covariance matrix of the kth cluster, i.e.,

[0074]

[0075] where σ k ={σ k1 ,…,σ km}, I m is the m x m identity matrix; thus, the parameters of the kth spectral measure model are denoted as ψ k ={β k ,σ k}; combining equations 1-6, the functional probability model of hyperspectral imagery g is defined as,

[0076]

[0077] where ψ = {α1,…,α K-1 ,ψ1,…,ψ K} is the parameter set of the model;

[0078] Step 3, applying the EM algorithm to solve the neighborhood Gaussian regression mixture model, according to the maximum a posteriori (MAP) criterion, the hyperspectral image is classified;

[0079] Step 3-1, calculate the parameter ψ log-likelihood function;

[0080]

[0081] The EM algorithm is used to estimate the maximum value of each parameter in ψ under the condition of equation 8; for this purpose, the log-likelihood model of the aforementioned complete data is constructed according to equation 8, i.e.,

[0082]

[0083] where z ik = 1 if and only if z i = k;

[0084] Step 3-2, the EM algorithm solving parameter ψ includes two processes of E and M; the E process is based on the current value of ψ, with q as an iteration pointer, denoted as ψ (q) , the expected function of formula 9 is calculated, that is:

[0085]

[0086]

[0087] Wherein, τ ik (q) is the posterior probability of pixel i belonging to class k in the current state, that is, the qth iteration;

[0088] Step 3-3, the M process is to obtain the parameter of the q+1th iteration by maximizing formula 9, that is:

[0089]

[0090] The specific parameter estimation value is,

[0091]

[0092] Step 3-4, unlike the traditional mixture model which needs to estimate the component weight coefficient by using the EM algorithm, the neighborhood Gaussian regression mixture model of the application defines the weight coefficient by formula 3, so as to consider the neighborhood pixel class membership spatial relationship; thus, formula 3 is rewritten as:

[0093]

[0094] Wherein, z i (q) (i=1,…,n) is the label of pixel i in the qth iteration;

[0095] The optimal estimation value of z i is:

[0096]

[0097] That is, the maximum posterior probability (Maximum a Posteriori, MAP) is used as a criterion to complete the hyperspectral image classification.

[0098] In the examples of the application, the mean function curve obtained by the method described in the application is compared with the original mean spectrum curve, as shown in Figure 2As shown in the figure, the original spectrum mean curve fluctuates in a jagged manner, which is not conducive to the judgment and selection of spectral characteristics, while the fitted mean function curve has a high smoothness, which reflects the dependence between the wave band and the reflectivity and shows the reflectivity change trend with the change of the wave band. The fitting processing of the spectrum curve not only maintains the basic characteristics of the original spectrum curve, but also highlights the alternating state of the wave peak and the wave trough, and better reflects the spectral characteristics of the ground object.

[0099] In the examples of the present application, the results obtained by the method described in the present application are compared with the true value map, as shown in the figure, Figure 3 As shown in the figure, the experimental data of the present application is a hyperspectral image of tea trees in Changzhou, the tea tree image is obtained by an aerial pushbroom hyperspectral imager (PHI), the spectral coverage range is 417-855 nm, the image size is 348*512 pixels, the spatial resolution is 2.25 m, and there are 80 wave bands that can be used for classification, and 9 ground object categories of the image are applied to the classification of the present application. The overall accuracy of the experimental results is 86.97%, the average accuracy is 74.07%, and the Kappa coefficient is 0.8166. The experimental results show that the algorithm of the present application reasonably uses the advantages of function analysis and fully combines the space-spectrum information of the hyperspectral image.

Claims

1. A classification method combining Gaussian regression mixture model and MRF hyperspectral function data, characterized in that, The method comprises the following steps: Step 1, representing a pixel spectrum curve of a hyperspectral image as a polynomial function; Step 2, modeling a probability density distribution of the polynomial function obtained in step 1 by using a Gaussian regression mixture model, applying a MRF to simulate a spatial dependence relationship between pixels, and redefining a weight of the Gaussian regression mixture model by using a Pott model to obtain a neighborhood Gaussian regression mixture model; Step 2 is specifically as follows: Step 2-1: In the hyperspectral remote sensing image, in addition to the measured spectral observations of each pixel at each frequency ( , In addition to the above, it also contains implicit variables that express the class attributes of each pixel, denoted as... , called a pixel Category label, = Indicator Pixel Belongs to class ;definition If it is a random variable, then the pixel Belongs to class The probability density function is denoted as In conclusion, = { , =1, …, } is considered a random field characterizing the class attributes of hyperspectral images, called a label field. Each realization of the label field corresponds to a classification of the hyperspectral image. The observed values ​​and latent variables of the hyperspectral image constitute its complete data, i.e., {( , ), In model-based function-based data clustering, spectral curves need to be defined. Probability model; constructing a mixture model The conditional probability model, namely: (2)； wherein, is the index of the mixture component, in hyperspectral image classification, is also the index of the class, is the number of mixture components, i.e. the number of classes, is the mixture component , wherein denotes the mixture component corresponding parameter set, is the pixel belongs to class with probability is the weight coefficient of the mixture component = { , = 1, …, } and satisfies ; is estimated as a variable in the Pott model solution;​ Step 2-2, in order to make full use of the spatial information of hyperspectral image, considering the correlation of the neighborhood pixel labels in the Gaussian regression mixture model, the Gaussian regression mixture model is constructed, the MRF is used on the pixel neighborhood, and the static Potts model defining the pixel and its neighborhood relationship is used to mark the pixel The prior probability belongs to the class , and thus the weight coefficient is defined as: (3) ； wherein, is a spatial correlation coefficient of the neighborhood pixels, denotes a neighborhood index set of the pixel , denotes a class to which the neighborhood pixels belong, is an indicator function, if ≠ then = 1, otherwise 0. Step 2-3, Gaussian distribution is adopted to model the spectral measure of the class of pixels, whose probability density is defined as: The probability density of the spectral measure of the class of pixels is defined as: (4) ； wherein is a mean function defined by a quadratic polynomial regression model, i.e.: (5) ； For The covariance matrix of the cluster, i.e.: (6) ； where = { , …, }, is × the identity matrix; thus, the parameters of the parametric spectral measure model are represented as = { , } ; in combination with equation (6), the hyperspectral image function is defined as the probabilistic model. (7) ； wherein, = { , …, , , …, } is a set of model parameters; Step 3, solving the neighborhood Gaussian regression mixture model by using an EM algorithm, and classifying the hyperspectral image according to a maximum posterior criterion.

2. The classification method of combining Gaussian regression mixture model and MRF hyperspectral function data according to claim 1, characterized in that, Step 1 is specifically as follows: Step 1-1: Given a hyperspectral image = { , =1, …, },in For pixel index, = ( , = 1,…, ) T Let i be the spectral metric vector of pixel i. This represents the total number of pixels. For band indexing, Let x = { , =1, …, } represents the set of sampling frequencies corresponding to each band of the hyperspectral image, where For band Corresponding electromagnetic wave frequency; let pixel The spectral curve is = Because hyperspectral imaging has numerous bands and narrow band intervals, it is therefore difficult to... = High-density sampling was performed to obtain ( , )={ , = 1, …, }; In order to achieve hyperspectral image classification based on function data analysis, the hyperspectral image is represented as ( , )={ ( , ), = 1, …, }, that is, using spectral sampling ( , ) replace spectral vector Characterize the spectral features of pixels; Step 1-2, in order to express a conditional dependence in a spectral measure vector, a regression modeling method is adopted; Given the class cluster, the spectral measure vector of the pixel is considered as a regression function observed with noise, which is a standard Gaussian independent and identically distributed; a polynomial function representation of the pixel spectrum curve is obtained; (1) ； Where T is the matrix transpose. =( , , …, ) T Let be the mean regression coefficient vector of the k-class clusters. Let the degree be a polynomial. = (1, , , …, ) T For input The constructed polynomial regression vector, for Cluster noise standard deviation.

3. The classification method of combining Gaussian regression mixture model and MRF hyperspectral function data according to claim 1, characterized in that, Step 3 is specifically as follows: Step 3-1, calculating parameters Log-likelihood function; (8) ； The EM algorithm is used to estimate the values of the parameters in Equation 8 that maximize the conditional likelihood To do so, the log-likelihood model of the complete data is constructed according to Equation 8, i.e., (9) ； wherein = 1 if and only if = ; Step 3-2: Solve for parameters using the EM algorithm It includes two processes: E and M; the E process is based on... The current value, in For the iteration pointer, denoted as Calculate the expected function of Equation 9, that is: (10) ； (11) ； wherein, is the current state, i.e. the iteration, the pixel belongs to the class with posterior probability; Step 3-3, M process is to maximize the formula 9, the first +1 iteration of the parameters, namely: (12) ； a specific parameter estimation value is, (13) ； (14) ； Step 3-4, different from a traditional mixture model which needs to estimate a component weight coefficient by using an EM algorithm, the neighborhood Gaussian regression mixture model of the application defines the weight coefficient by using formula 3 so as to consider a neighborhood pixel class spatial relationship; thus, formula 3 is rewritten as follows: (15) ； wherein is the th iteration of the pixel with index = 1, …, ; The optimal estimate of is (16) ； that is, a maximum posterior probability is taken as a criterion to complete the hyperspectral image classification.

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