CN104408478A

CN104408478A - Hyperspectral image classification method based on hierarchical sparse discriminant feature learning

Info

Publication number: CN104408478A
Application number: CN201410647211.4A
Authority: CN
Inventors: 张向荣; 焦李成; 梁云龙; 马文萍; 侯彪; 刘若辰; 马晶晶; 白静
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2014-11-14
Filing date: 2014-11-14
Publication date: 2015-03-11
Anticipated expiration: 2034-11-14
Also published as: CN104408478B

Abstract

The invention specifically discloses a hyperspectral image classification method based on hierarchical sparse discriminant feature learning, which is mainly used to solve the problem that the prior art cannot learn the feature representation of hyperspectral data neighborhood blocks well. The implementation steps are as follows: input a sample set of hyperspectral image data, select a training set and a test set from it; based on the selected training set and sample set, use a layered discriminant feature learning method based on sparse coding to obtain the first layer of discriminant features and The second-level discriminant feature; combine the first-level discriminant feature and the second-level discriminant feature to obtain a hierarchical discriminant feature; based on the hierarchical discriminant feature, use the support vector machine to classify and output the classification result. On the basis of the spatial pyramid sparse coding model, the present invention adds the discriminant dictionary learning of class label supervision information, and adopts two-layer discriminant feature learning based on the spatial pyramid sparse model, which enhances the discriminability of features and improves the classification accuracy. Hyperspectral data classification is more accurate.

Description

A Hyperspectral Image Classification Method Based on Hierarchical Sparse Discriminative Feature Learning

技术领域 technical field

本发明属于图像处理技术领域，涉及机器学习和高光谱图像处理，具体是一种基于分层稀疏判别特征学习的高光谱图像分类方法，本发明可以通过对高光谱数据进行判别特征学习，恰当的表征出高光谱图像不同地物的特征，从而在此基础上实现计算机自主的对于高光谱图像不同地物进行分类识别。 The invention belongs to the technical field of image processing, relates to machine learning and hyperspectral image processing, and specifically relates to a hyperspectral image classification method based on layered and sparse discriminant feature learning. The characteristics of different ground objects in hyperspectral images are characterized, and on this basis, the computer can independently classify and recognize different ground objects in hyperspectral images. the

背景技术 Background technique

高光谱图像的地物分类是目前高光谱图像处理领域的研究热点，其研究主要致力于寻找使计算机智能地学习和识别不同图像目标的技术方法。高光谱图像具有比较高的光谱分辨率，通常能达到10^-2λ数量级，同时波段多，光谱通道数多达数十甚至数百个以上，而且各通道间往往是连续的。高光谱图像的地物分类在地质调查、农作物灾害监测、大气污染和军事目标打击等领域均有良好应用前景。最为普遍的高光谱图像地物分类方法通常是：(1)输入一幅高光谱图像；(2)从中选取训练样本和测试样本；(3)通过特征学习的方法分别对训练样本和测试样本学习特征；(4)将所学的特征通过分类器进行分类；(5)得到分类结果。其中的一个关键问题就是如何从大量带有冗余的高光谱数据中提取有用信息，使用合适的特征学习方法表征出不同地物的表示，因为表示的合理与否决定了后续分类的性能上限。另外，由于高光谱具有数据量大、冗余信息多、波段多等不利因素，因此要求对高光谱数据特征学习时用到的技术方法高效、简单且有一定抗噪声干扰能力。 The object classification of hyperspectral images is currently a research hotspot in the field of hyperspectral image processing, and its research is mainly devoted to finding technical methods to enable computers to intelligently learn and recognize different image targets. Hyperspectral images have relatively high spectral resolution, usually on the order of 10 ^-2λ , with multiple bands and dozens or even hundreds of spectral channels, and the channels are often continuous. The ground object classification of hyperspectral images has good application prospects in geological surveys, crop disaster monitoring, air pollution, and military target strikes. The most common hyperspectral image classification method is usually: (1) input a hyperspectral image; (2) select training samples and test samples from it; (3) learn training samples and test samples through feature learning method (4) Classify the learned features through the classifier; (5) Get the classification result. One of the key issues is how to extract useful information from a large amount of redundant hyperspectral data, and use appropriate feature learning methods to characterize the representation of different ground objects, because the reasonableness of the representation determines the performance upper limit of subsequent classification. In addition, due to the disadvantages of hyperspectral data such as large amount of data, redundant information, and multiple bands, it is required that the technical methods used in the learning of hyperspectral data features are efficient, simple, and have a certain ability to resist noise interference.

Jianchao Yang等人在论文“Linear Spatial Pyramid Matching Using Sparse Coding for Image Classification”(CVPR，2009)中利用基于Sparse Coding的方法对原始高光谱图像数据进行空间金字塔最大池化特征编码，最后结合分类器进行分类。该方法的具体步骤为第1步：提取样本SIFT特征；第2步：训练字典；第3步：根据字典对SIFT特征进行编码得到稀疏编码向量，对稀疏编码向量做最大池化算法得到每个样本的最终特征；第4步：对最终特征用线性支持矢量机方法进行分类。这种方法虽然对特征编码相对准确，但是，仍然存在的不足之处是，该方法比较依赖于稀疏编码的好坏。 In the paper "Linear Spatial Pyramid Matching Using Sparse Coding for Image Classification" (CVPR, 2009), Jianchao Yang et al. used the method based on Sparse Coding to encode the spatial pyramid maximum pooling feature of the original hyperspectral image data, and finally combined with the classifier Classification. The specific steps of the method are as follows: step 1: extract sample SIFT features; step 2: train dictionary; step 3: encode SIFT features according to the dictionary to obtain sparse coded vectors, and perform maximum pooling algorithm on sparse coded vectors to obtain each The final features of samples; Step 4: Classify the final features with a linear support vector machine method. Although this method is relatively accurate for feature encoding, it still has the disadvantage that this method is more dependent on the quality of sparse encoding. the

发明内容 Contents of the invention

本发明针对上述现有技术的不足，提出一种新的基于稀疏编码的分层判别特征学习方法，在对高光谱图像数据进行稀疏编码时加入了类标信息，在分层特征学习的过程中加入了结构信息，使得地物分类特征更具判别性，从而进一步提高对高光谱数据图像不同地物的智能识别能力。 Aiming at the deficiencies in the prior art above, the present invention proposes a new layered discriminant feature learning method based on sparse coding, adding class label information when performing sparse coding on hyperspectral image data, and in the process of layered feature learning The structural information is added to make the classification features of ground objects more discriminative, thereby further improving the intelligent recognition ability of different ground objects in hyperspectral data images. the

本发明的技术方案是：一种基于分层稀疏判别特征学习的高光谱图像分类方法，包括以下步骤： The technical solution of the present invention is: a hyperspectral image classification method based on hierarchical sparse discriminant feature learning, comprising the following steps:

(1)输入包含C类地物的高光谱遥感图像数据，每个像素即为样本，将样本用光谱特征向量表示，样本的特征维数为h，所有样本构成样本集其中y_i为第i个样本，N为样本总个数，R表示实数域； (1) Input hyperspectral remote sensing image data containing C-type ground objects, each pixel is a sample, and the sample is represented by a spectral feature vector, the feature dimension of the sample is h, and all samples constitute a sample set Where y _i is the i-th sample, N is the total number of samples, and R represents the real field;

(2)随机从每类样本集中选出10％的样本作为训练集n₁表示训练集样本数目，剩余的90％样本作为测试集n₂表示测试集样本数目； (2) Randomly select 10% samples from each type of sample set as the training set n ₁ represents the number of samples in the training set, and the remaining 90% samples are used as the test set n ₂ represents the number of samples in the test set;

(3)基于训练集Y_train和样本集Y，利用基于稀疏编码的分层判别特征学习方法，得到第一层判别特征集及第二层判别特征集其中，为对应于样本集Y第i个样本的第一层判别特征，为对应于样本集Y第i个样本的第二层判别特征： (3) Based on the training set Y _train and the sample set Y, use the layered discriminant feature learning method based on sparse coding to obtain the first layer discriminant feature set and the second layer discriminative feature set in, is the discriminative feature of the first layer corresponding to the i-th sample of the sample set Y, is the discriminative feature of the second layer corresponding to the i-th sample of the sample set Y:

3a)从训练集中随机选取K₁个训练样本作为第一层判别字典的初始化字典利用判别K-SVD字典学习方法，得到第一层判别字典D； 3a) Randomly select K ₁ training samples from the training set as the initialization dictionary of the first layer of discriminant dictionary Using the discriminant K-SVD dictionary learning method, the first layer of discriminant dictionary D is obtained;

3b)基于第一层判别字典D，利用正交匹配追踪算法得到所有样本的第一层稀疏编码特征 $z = [z_{1}, z_{2}, . . ., z_{N}] &Element; R^{K_{1} \times N};$ 3b) Based on the first-level discriminant dictionary D, use the orthogonal matching pursuit algorithm to obtain the first-level sparse coding features of all samples $z = [z_{1}, z_{2}, . . ., z_{N}] &Element; R^{K_{1} \times N};$

3c)根据所有样本的第一层稀疏编码特征，利用第一层判别特征学习方法，得到第一层判别特征集 $\hat{F} = {{\hat{F}}_{i}}_{i = 1}^{N} &Element; R^{20 K_{1} \times N}$ 及第二层输入特征集 ${\hat{D}}_{i} &Element; R^{5 K_{1} \times 4}, i = 1,2, . . ., N;$ 3c) According to the first-level sparse coding features of all samples, use the first-level discriminative feature learning method to obtain the first-level discriminative feature set $\hat{f} = {{\hat{f}}_{i}}_{i = 1}^{N} &Element; R^{20 K_{1} \times N}$ and the second layer input feature set ${\hat{D.}}_{i} &Element; R^{5 K_{1} \times 4}, i = 1,2, . . ., N;$

3d)从训练集对应的第二层输入特征集中随机选取K₂个作为第二层判别字典的初始化字典D′₂，结合对应的类标矩阵和判别矩阵，类似于第一层判别字典学习方法优化判别字典目标函数，得到第二层判别字典 3d) Randomly select K ₂ from the second-layer input feature set corresponding to the training set as the initialization dictionary D′ ₂ of the second-layer discriminant dictionary, and combine the corresponding class label matrix and discriminant matrix, similar to the first-tier discriminant dictionary learning method Optimize the objective function of the discriminant dictionary to obtain the second layer of discriminant dictionary

3e)基于样本集Y的第二层输入特征集和第二层判别字典，利用正交匹配追踪算法得到每个样本的第二层稀疏编码特征i＝1,2,…,N，对所有样本的第二层稀疏编码特征利用最大池化算法，得到第二层判别特征集 3e) Based on the second-layer input feature set and the second-layer discriminant dictionary of the sample set Y, use the orthogonal matching pursuit algorithm to obtain the second-layer sparse coding features of each sample i=1,2,...,N, use the maximum pooling algorithm for the second-layer sparse coding features of all samples to obtain the second-layer discriminative feature set

(4)合并第一层判别特征集和第二层判别特征集得到样本集Y的分层判别特征集F， $F = [\hat{F}; \hat{\hat{F}}];$ (4) Merge the first layer discriminant feature set and the second layer discriminative feature set Obtain the hierarchical discriminant feature set F of the sample set Y, $f = [\hat{f}; \hat{\hat{f}}];$

(5)将训练集和测试集对应的分层判别特征集输入到支撑矢量机，得到测试集的分类标签向量，该类标签向量即为该高光谱图像的分类结果。 (5) Input the hierarchical discriminant feature set corresponding to the training set and the test set into the support vector machine to obtain the classification label vector of the test set, which is the classification result of the hyperspectral image. the

上述步骤3a)中判别K-SVD字典学习方法的具体步骤为： The concrete steps of discriminating K-SVD dictionary learning method in above-mentioned steps 3a) are:

第1步，基于训练集Y_train，判别K-SVD字典学习方法的目标函数如下： In the first step, based on the training set Y _train , the objective function of the discriminant K-SVD dictionary learning method is as follows:

$\begin{matrix} arg arg \underset{D D.,, W W,, A A,, X x}{min min} {| | | | {Y Y}_{train train} - - DX DX | | | |}_{22}^{22} + + α α {| | | | Q Q - - AX AX | | | |}_{22}^{22} + + β β {| | | | H h - - WX WX | | | |}_{22}^{22} \\ s the s . . t t . . &ForAll; &ForAll; i i,, {| | | | {x x}_{i i} | | | |}_{11} \leq \leq ϵ ϵ \end{matrix}$

其中，上述式子第一项为重构误差项，第二项为判别稀疏编码约束项，第三项为分类误差项，D表示第一层判别字典，包含K₁个字典原子，每个原子维数为d，W表示分类变换矩阵，A表示线性变换矩阵，X表示稀疏编码系数矩阵，表示l₂范数的平方和，α和β表示平衡类标判别项和分类误差项的正则参数，取值范围是1～5，表示理想状况下的判别稀疏编码系数矩阵，若D中第k个字典原子与训练样本集Y_train中第i个样本属于同一类时，则Qki值为1，不同类时为0，表示训练样本的类标矩阵，若Y_train中第i个样本属于第c(c＝1,2,…,C)类，H_ci为1，否则为0，x_i表示稀疏编码系数矩阵X的第i列向量，||·||₁表示l₁范数，ε为定义的10^-6； Among them, the first item of the above formula is the reconstruction error item, the second item is the discriminant sparse coding constraint item, and the third item is the classification error item, D represents the first layer of discriminant dictionary, including K ₁ dictionary atoms, each atom The dimension is d, W represents the classification transformation matrix, A represents the linear transformation matrix, X represents the sparse coding coefficient matrix, Indicates the sum of squares of the l ₂ norm, α and β represent the regular parameters of the balanced class label discriminant item and classification error item, and the value range is 1 to 5, Represents the discriminative sparse coding coefficient matrix under ideal conditions. If the kth dictionary atom in D and the i-th sample in the training sample set Y _train belong to the same class, then the Qki value is 1, and it is 0 when they are different classes. Indicates the class label matrix of the training sample, if the i-th sample in Y _train belongs to the c (c=1,2,...,C) class, H _ci is 1, otherwise it is 0, x _i represents the sparse coding coefficient matrix X The i-th column vector, ||·|| ₁ represents the l ₁ norm, and ε is the defined 10 ^-6 ;

第2步，为了求解判别K-SVD字典学习方法的目标函数，改写为： In the second step, in order to solve the objective function of the discriminative K-SVD dictionary learning method, it is rewritten as:

$\begin{matrix} arg arg \underset{{D D.}_{nwe nwe},, X x}{min min} {{{| | | | {Y Y}_{new new} - - {D D.}_{new new} X x | | | |}_{22}^{22}}} \\ s the s . . t t . . &ForAll; &ForAll; i i,, {| | | | {x x}_{i i} | | | |}_{11} \leq \leq ϵ ϵ \end{matrix}$

其中， $Y_{new} = {(Y_{train}^{T}, \sqrt{α} Q^{T}, \sqrt{β} H^{T})}^{T}, D_{new} = {(D^{T}, \sqrt{α} A^{T}, \sqrt{β} W^{T})}^{T},$ (·)^T表示矩阵的转置，对该目标函数利用K-SVD字典学习方法进行求解，从而得到第一层判别字典D。 in, $Y_{new} = {(Y_{train}^{T}, \sqrt{α} Q^{T}, \sqrt{β} h^{T})}^{T}, {D.}_{new} = {({D.}^{T}, \sqrt{α} A^{T}, \sqrt{β} W^{T})}^{T},$ (·) ^T represents the transposition of the matrix, and the objective function is solved using the K-SVD dictionary learning method to obtain the first layer of discriminant dictionary D.

上述步骤3b)中正交匹配追踪算法的具体步骤为： The specific steps of the orthogonal matching pursuit algorithm in the above step 3b) are:

第1步，基于第一层判别字典D，正交匹配追踪算法的目标优化函数如下： Step 1, based on the first layer of discriminant dictionary D, the objective optimization function of the orthogonal matching pursuit algorithm is as follows:

$\begin{matrix} \underset{{z z}_{i i}}{min min} {| | | | {y the y}_{i i} - - D D. {z z}_{i i} | | | |}_{22}^{22} & s the s . . t t . . {| | | | {z z}_{i i} | | | |}_{11} \leq \leq δ δ,, i i = = 1,2 1,2,, . . . . . .,, N N \end{matrix}$

其中，y_i表示样本集Y的第i个样本，z_i表示y_i的稀疏编码系数，δ为定义的10^-6； Among them, y _i represents the i-th sample of the sample set Y, z _i represents the sparse coding coefficient of y _i , and δ is the defined 10 ^-6 ;

第2步，构造残差项，残差项构造为r⁽⁰⁾＝y_i,i＝1,2…N，索引集Λ⁰为K维零向量，初始化变量J＝1； The second step is to construct the residual term. The residual term is constructed as r ⁽⁰⁾ =y _i , i=1, 2...N, the index set Λ ⁰ is a K-dimensional zero vector, and the initialization variable J=1;

第3步，找出残差r^(J-1)与字典D中的第j列d_j内积最大所对应的下标λ，即 $λ = \arg \max_{j = 1,2, . . ., T_{0}} | &lang; r^{(J - 1)}, d_{j} &rang; |;$ The third step is to find the subscript λ corresponding to the largest inner product between the residual r ^(J-1) and the jth column d _j in the dictionary D, that is $λ = \arg \max_{j = 1,2, . . ., T_{0}} | &lang; r^{(J - 1)}, d_{j} &rang; |;$

第4步，更新索引集Λ^(J)，Λ^(J)(J)＝λ；更新所选择的字典原子列构成的集合D^(J)＝D(:,Λ^(J)(1:J))，用最小二乘法得到J阶逼近的新残差 r^(J)＝y_i-D^(J)z_i,J＝J+1； Step 4, update the index set Λ ^(J) , Λ ^(J) (J) = λ; update the set D ^(J) = D(:,Λ ^(J) (1:J) composed of the selected dictionary atomic columns ), using the least squares method to obtain the J-order approximation New residual r ^(J) = y _i -D ^(J) z _i , J = J+1;

第5步，判断是否迭代结束：如果J≤K且仍有y_i未作为残差项，则返回第2步，否则，若J≤K且y_i,i＝1,2…N都作为残差项则程序结束，若J＞K，则返回到第3步继续执行。 Step 5, judge whether the iteration is over: if J≤K and there are still y _i not used as residual items, return to step 2, otherwise, if J≤K and y _i , i=1, 2...N are all used as residuals If the difference is the difference, the program ends. If J>K, return to step 3 and continue to execute.

上述步骤3c)中第一层判别特征学习方法的具体步骤为： The specific steps of the first layer of discriminative feature learning method in the above step 3c) are:

第1步，以每个样本的稀疏编码特征z_i,i＝1,2,...,N为中心，取邻域窗口大小为(2m+1)×(2m+1)内所有样本的稀疏编码特征构成稀疏编码块Z_i,i＝1,2,...,N，Z_i为(2m+1)×(2m+1)×K₁的一个三维矩阵； Step 1, take the sparse coding feature z _i ,i=1,2,...,N of each sample as the center, and take the neighborhood window size of all samples in (2m+1)×(2m+1) Sparse coding features constitute a sparse coding block Z _i , i=1, 2,..., N, Z _i is a three-dimensional matrix of (2m+1)×(2m+1)×K ₁ ;

第2步，对每个样本的稀疏编码块Z_i进行分块，利用(m+1)×(m+1)的滑动窗口，划窗步长为m，从上到下，从左到右遍历Z_i，依次提取稀疏编码表示子块Z_i ⁽¹⁾、Z_i ⁽²⁾、Z_i ⁽³⁾和Z_i ⁽⁴⁾，总共4个子块，每个子块的规模为(m+1)×(m+1)×K₁； Step 2: _Divide the sparse coding block Zi of each sample into blocks, using a sliding window of (m+1)×(m+1), with a window step size of m, from top to bottom, from left to right Traversing Z _i , sequentially extracting sparse coding representation sub-blocks Z _i ⁽¹⁾ , Z _i ⁽²⁾ , Z _i ⁽³⁾ and Z _i ⁽⁴⁾ , a total of 4 sub-blocks, the size of each sub-block is (m+1 )×(m+1)×K ₁ ;

第3步，依次对得到的4个子块进行空间金字塔最大池化算法 The third step is to perform the spatial pyramid maximum pooling algorithm on the obtained 4 sub-blocks in turn

$SM SM (({Z Z}_{i i}^{((j j))})) = = [[M m (({(({Z Z}_{i i}^{((j j))}))}_{11}^{11})),, . . . . . .,, M m (({(({Z Z}_{i i}^{((j j))}))}_{11}^{{V V}_{11}})),, . . . . . .,, M m (({(({Z Z}_{i i}^{((j j))}))}_{u u}^{{V V}_{u u}})),, . . . . . .,, M m (({(({Z Z}_{i i}^{((j j))}))}_{U u}^{{V V}_{U u}}))]],, j j = = 1,2,3,4 1,2,3,4$

其中，SM(·)表示进行空间金字塔最大池化操作，U代表空间金字塔分解层数，V_u是位于空间金字塔第u层的所有块的总数目，M(·)表示最大池化算法， $M ({(Z_{i}^{(j)})}_{u}^{V_{u}}) = [\max_{t &Element; Z_{i}^{(j)}} | z_{1 t} |, . . ., \max_{t &Element; Z_{i}^{(j)}} | z_{K_{1} t} |];$ Among them, SM( ) represents the maximum pooling operation of the spatial pyramid, U represents the number of spatial pyramid decomposition layers, V _u is the total number of all blocks located in the uth layer of the spatial pyramid, M( ) represents the maximum pooling algorithm, $m ({(Z_{i}^{(j)})}_{u}^{V_{u}}) = [\max_{t &Element; Z_{i}^{(j)}} | z_{1 t} |, . . ., \max_{t &Element; Z_{i}^{(j)}} | z_{K_{1} t} |];$

第4步，按矩阵行组合的方式 ${\hat{F}}_{i} = [SM (Z_{i}^{(1)}); SM (Z_{i}^{(2)}); SM (Z_{i}^{(3)}); SM (Z_{i}^{(4)})]$ 得到第i个样本的第一层判别特征按矩阵列组合的方式 ${\hat{D}}_{i} = [SM (Z_{i}^{(1)}), SM (Z_{i}^{(2)}), SM (Z_{i}^{(3)}), SM (Z_{i}^{(4)})]$ 得到第i个样本的第二层输入特征。 Step 4, according to the way of matrix row combination ${\hat{f}}_{i} = [SM (Z_{i}^{(1)}); SM (Z_{i}^{(2)}); SM (Z_{i}^{(3)}); SM (Z_{i}^{(4)})]$ Get the first layer of discriminative features of the i-th sample Combining by matrix column ${\hat{D.}}_{i} = [SM (Z_{i}^{(1)}), SM (Z_{i}^{(2)}), SM (Z_{i}^{(3)}), SM (Z_{i}^{(4)})]$ Get the second layer input features of the i-th sample.

本发明的有益效果：本发明输入高光谱图像数据，利用随机选取的一部分的训练样本作为一层初始判别字典，经过判别字典学习得到一层判别字典，根据得到的一层判别字典求解出每个高光谱数据的邻域块的稀疏编码表示系数，经过金字塔最大池化方法，得到二层初始判别字典和一层编码特征，再利用二层初始判别字典经过判别字典学习算法得到二层判别字典，根据得到的二层判别字典求解出第二层特征编码对应区域块的稀疏编码表示系数，经过金字塔最大池化方法，得到二层编码特征，将一层编码特征跟二层编码特征进行结合，作为最终学习得到的特征，对这个特征利用分类器进行分类，从而达到高光谱地物分类的目的，并且取得了较高的地物分类精度。本发明与现有技术相比，具有以下优点： Beneficial effects of the present invention: the present invention inputs hyperspectral image data, uses a part of the training sample randomly selected as a layer of initial discrimination dictionary, obtains a layer of discrimination dictionary through discrimination dictionary learning, and solves each The sparse coding representation coefficients of the neighborhood blocks of hyperspectral data are obtained through the pyramid maximum pooling method to obtain the two-layer initial discriminant dictionary and one-layer coding features, and then use the two-layer initial discriminant dictionary to obtain the two-layer discriminant dictionary through the discriminant dictionary learning algorithm. According to the obtained two-layer discriminant dictionary, the sparse code representation coefficient of the corresponding area block of the second-layer feature code is solved, and the two-layer code feature is obtained through the pyramid maximum pooling method, and the one-layer code feature is combined with the two-layer code feature, as Finally, the feature learned is used to classify this feature, so as to achieve the purpose of hyperspectral object classification, and achieve a high accuracy of object classification. Compared with the prior art, the present invention has the following advantages:

第一，本发明利用判别字典学习的方法，在第一层字典学习和第二层字典学习时，考虑了类标信息，克服了传统的K-SVD字典学习没有充分利用类标信息的不足，使得本发明学习得到的字典以及通过该字典学习得到的稀疏编码系数更具有判别性的优点。 First, the present invention utilizes the method for discriminating dictionary learning, considers class label information when first-level dictionary learning and second-level dictionary learning, overcomes the deficiency that traditional K-SVD dictionary learning does not make full use of class-mark information, The dictionary learned by the present invention and the sparse coding coefficients learned by the dictionary are more discriminative. the

第二，本发明利用多层稀疏编码特征学习的方法，克服了传统使用单层稀疏编码系数直接进行分类而分类精度较低的缺点，使得本发明具有分类精度高的优点。 Second, the present invention utilizes a multi-layer sparse coding feature learning method, which overcomes the traditional disadvantage of using single-layer sparse coding coefficients for direct classification and low classification accuracy, so that the present invention has the advantage of high classification accuracy. the

第三，本发明利用空谱域结合的特征学习方法，克服了以一个像素点进行特征学习的算法的没有考虑周围邻域信息的不足，使得本发明具有对学习得到的特征鲁棒性更好的优点。 Thirdly, the present invention utilizes the feature learning method combined with the spatial spectrum domain to overcome the lack of consideration of the surrounding neighborhood information in the algorithm for feature learning with one pixel, so that the present invention has better robustness to the learned features The advantages. the

以下将结合附图对本发明做进一步详细说明。 The present invention will be described in further detail below in conjunction with the accompanying drawings. the

附图说明 Description of drawings

图1为本发明方法的流程图； Fig. 1 is the flowchart of the inventive method;

图2为本发明仿真实验中Indianan Pine的图像。 Fig. 2 is the image of Indianan Pine in the simulation experiment of the present invention. the

具体实施措施 Specific implementation measures

下面结合附图对发明做进一步描述。 The invention will be further described below in conjunction with the accompanying drawings. the

结合附图1对本发明的具体步骤描述如下： Concrete steps of the present invention are described as follows in conjunction with accompanying drawing 1:

步骤1，输入包含C类地物的高光谱遥感图像数据，每个像素即样本用光谱特征向量表示，样本的特征维数为h，所有样本构成样本集其中y_i为第i个样本，N为样本总个数，R表示实数域； Step 1, input hyperspectral remote sensing image data containing C-type ground objects, each pixel or sample is represented by a spectral feature vector, the feature dimension of the sample is h, and all samples constitute a sample set Where y _i is the i-th sample, N is the total number of samples, and R represents the real field;

步骤2，在这N个样本中，去除掉背景样本点，随机从每类样本集中选出10％的样本作为训练集n1表示训练集样本数目，剩余的90％样本作为测试集 n₂表示测试集样本数目； Step 2, in these N samples, remove the background sample points, and randomly select 10% samples from each type of sample set as the training set n1 represents the number of samples in the training set, and the remaining 90% samples are used as the test set n ₂ represents the number of samples in the test set;

步骤3，基于训练集和样本集，利用基于稀疏编码的分层判别特征学习方法，得到第一层判别特征集及第二层判别特征集其中，为对应于样本集第i个样本的第一层判别特征，为对应于样本集第i个样本的第i个第二层判别特征： Step 3, based on the training set and sample set, use the layered discriminant feature learning method based on sparse coding to obtain the first layer discriminant feature set and the second layer discriminative feature set in, is the discriminative feature of the first layer corresponding to the i-th sample in the sample set, is the i-th second-layer discriminant feature corresponding to the i-th sample in the sample set:

第一步，从各类训练集中随机选择一部分，总共选取K₁个训练样本作为第一层判别字典的初始化字典利用判别K-SVD字典学习方法，得到第一层判别字典D，判别K-SVD字典学习方法的目标函数如下： In the first step, a part is randomly selected from various training sets, and a total of K ₁ training samples are selected as the initialization dictionary of the first layer of discriminant dictionary Using the discriminative K-SVD dictionary learning method, the first layer of discriminative dictionary D is obtained. The objective function of the discriminative K-SVD dictionary learning method is as follows:

其中，第一项为重构误差项，第二项为判别稀疏编码约束项，第三项为分类误差项，D表示第一层判别字典，包含K₁个字典原子，每个原子维数为d，W表示分类变换矩阵，A表示线性变换矩阵，X表示稀疏编码系数矩阵，表示l₂范数的平方和，α和β表示平衡类标判别项和分类误差项的正则参数，取值范围是1～5，表示理想状况下的判别稀疏编码系数矩阵，若D中第k个字典原子与训练样本集Y_train中第i个样本属于同一类时，则Q_ki值为1，不同类时为0，表示训练样本的类标矩阵，若Y_train中第i个样本属于第c(c＝1,2,…,C)类，H_ci为1，否则为0，xi表示稀疏编码系数矩阵X的第i列向量，||·||₁表示l₁范数，ε为定义的10^-6； Among them, the first item is the reconstruction error item, the second item is the discriminant sparse coding constraint item, and the third item is the classification error item. D represents the first layer of discriminative dictionary, which contains K ₁ dictionary atoms, and the dimension of each atom is d, W represents the classification transformation matrix, A represents the linear transformation matrix, X represents the sparse coding coefficient matrix, Indicates the sum of squares of the l ₂ norm, α and β represent the regular parameters of the balanced class label discriminant item and classification error item, and the value range is 1 to 5, Represents the discriminative sparse coding coefficient matrix under ideal conditions. If the kth dictionary atom in D and the i-th sample in the training sample set Y _train belong to the same class, then the value of Q _ki is 1, and it is 0 when they are different classes. Indicates the class label matrix of the training samples. If the i-th sample in Y _train belongs to the c (c=1,2,...,C) class, H _ci is 1, otherwise it is 0, and xi represents the sparse coding coefficient matrix X. i column vector, ||·|| ₁ means l ₁ norm, ε is the defined 10 ^-6 ;

为了求解判别K-SVD字典学习方法的目标函数，改写为： In order to solve the objective function of the discriminant K-SVD dictionary learning method, it is rewritten as:

其中， $Y_{new} = {(Y_{train}^{T}, \sqrt{α} Q^{T}, \sqrt{β} H^{T})}^{T}, D_{new} = {(D^{T}, \sqrt{α} A^{T}, \sqrt{β} W^{T})}^{T},$ (·)^T表示矩阵的转置，对该目标函数利用K-SVD字典学习方法进行求解，从而得到第一层判别字典D； in, $Y_{new} = {(Y_{train}^{T}, \sqrt{α} Q^{T}, \sqrt{β} h^{T})}^{T}, {D.}_{new} = {({D.}^{T}, \sqrt{α} A^{T}, \sqrt{β} W^{T})}^{T},$ (·) ^T represents the transposition of the matrix, and the K-SVD dictionary learning method is used to solve the objective function, so as to obtain the first layer of discriminant dictionary D;

${| | | | {Y Y}_{new new} - - {D D.}_{new new} X x | | | |}_{22}^{22} = = | | | | {Y Y}_{new new} - - {Σ Σ}_{j j = = 11}^{L L} {d d}_{j j} {x x}_{j j}^{T T} | | | | = = {| | | | (({Y Y}_{new new} - - {Σ Σ}_{j j &NotEqual; &NotEqual; k k}^{L L} {d d}_{j j} {x x}_{j j}^{T T})) - - {d d}_{k k} {x x}_{k k}^{T T} | | | |}_{22}^{22} = = {| | | | {E E.}_{k k} - - {d d}_{k k} {x x}_{k k}^{T T} | | | |}_{22}^{22}$

其中，d_j表示D_new的第j列原子，表示X的第j行，L表示D_new的总列数，d_k表示D_new的第k列原子，表示X的第k行，E_k表示不使用D_new的第k列原子d_k进行稀疏分解所产生的误差矩阵； Among them, d _j represents the jth column atom of D _new , Indicates the jth row of X, L indicates the total number of columns of D _new , d _k indicates the kth column atom of D _new , Indicates the k-th row of X, and E _k represents the error matrix generated by sparse decomposition without using the k-th column atom d _k of D _new ;

其中K-SVD字典学习方法如下： The K-SVD dictionary learning method is as follows:

1.对判别字典目标函数进行变形，即将Y_new使用向量形式E_k表示，将D_new使用向量形式d_k表示，将X使用向量形式表示，对变形后所得的公式乘以Ω_k，得到目标分解公式： 1. For the discriminant dictionary objective function Transformation, that is, Y _new is expressed in vector form E _k , D _new is expressed in vector form d _k , and X is expressed in vector form Indicates that for the formula obtained after deformation Multiply by Ω _k to get the target decomposition formula:

${| | | | {E E.}_{k k} {Ω Ω}_{k k} - - {d d}_{x x} {x x}_{k k}^{T T} {Ω Ω}_{k k} | | | |}_{22}^{22} = = {| | | | {E E.}_{k k}^{R R} - - {d d}_{k k} {x x}_{k k}^{R R} | | | |}_{22}^{22}$

其中变形误差矩阵表示误差矩阵E_k的变形，Ω_k的大小为P×|ω_k|，P表示训练样本集Y_new的列数，|ω_k|表示ω_k的模值，且Ω_k在(ω_k(j),j)处为1，其他地方全为0，其中1≤j≤|ω_k|，ω_k(j)表示ω_k的第j个数； where the deformation error matrix Denotes the deformation of the error matrix _Ek , The size of Ω _k is P×|ω _k |, P represents the number of columns of the training sample set Y _new , |ω _k | represents the modulus value of ω _k , and Ω _k is 1 at (ω _k (j), j), and all other places are 0, where 1≤j≤|ω _k |, ω _k (j) represents The jth number of ω _k ;

2.对所得目标分解公式中的变形误差矩阵进行SVD分解得到其中U表示左奇异矩阵，V^Τ表示右奇异矩阵，Δ表示奇异值矩阵； 2. Decompose the formula for the obtained target The deformation error matrix in Perform SVD decomposition to get Wherein U represents the left singular matrix, V ^Τ represents the right singular matrix, and Δ represents the singular value matrix;

3.用所得左奇异矩阵U的第一列去更新目标训练字典D_new的第k列原子d_k； 3. Use the first column of the resulting left singular matrix U to update the kth column atom d _k of the target training dictionary D _new ;

4.重复步骤1到步骤3对D_new中所有原子进行更新处理，得到K个新的字典D₁′,D₂′…D_K′。 4. Repeat steps 1 to 3 to update all atoms in D _new to obtain K new dictionaries D ₁ ′, D ₂ ′…D _K ′.

第二步，基于第一层判别字典D，利用正交匹配追踪算法求解如下目标函数，得到所有样本的第一层编码特征 In the second step, based on the first-level discriminant dictionary D, use the orthogonal matching pursuit algorithm to solve the following objective function, and obtain the first-level coding features of all samples

其中，y_i表示样本集Y的第i个样本，z_i表示y_i的稀疏编码系数，δ为定义的10^-6，正交匹配追踪算法如下： Among them, y _i represents the i-th sample of the sample set Y, z _i represents the sparse coding coefficient of y _i , and δ is the defined 10 ^-6 , the orthogonal matching pursuit algorithm is as follows:

首先构造残差项，残差项构造为r⁽⁰⁾＝y_i，索引集Λ⁰为K维零向量，初始化变量J＝1； First construct the residual term, the residual term is constructed as r ⁽⁰⁾ = y _i , the index set Λ ⁰ is a K-dimensional zero vector, and the initialization variable J=1;

然后循环执行如下步骤1-5 Then perform the following steps 1-5 in a loop

1.找出残差r^(J-1)与字典D中的第j列d_j内积最大所对应的下标λ，即 $λ = \arg \max_{j = 1,2, . . ., T_{0}} | &lang; r^{(J - 1)}, d_{j} &rang; |;$ 1. Find the subscript λ corresponding to the largest inner product between the residual r ^(J-1) and the jth column d _j in the dictionary D, namely $λ = \arg \max_{j = 1,2, . . ., T_{0}} | &lang; r^{(J - 1)}, d_{j} &rang; |;$

2.更新索引集Λ^(J)，Λ^(J)(J)＝λ。更新所选择的字典原子列构成的集合D^(J)＝D(:,Λ^(J)(1:J))； 2. Update the index set Λ ^(J) , Λ ^(J) (J) = λ. Update the set D ^(J) =D(:, Λ ^(J) (1:J)) formed by the selected dictionary atomic columns;

3.利用最小二乘法得到J阶逼近的 3. Use the least squares method to get the J-order approximation

4.更新残差r^(J)＝y_i-D^(J)z_i,J＝J+1； 4. Update residual r ^(J) =y _i -D ^(J) z _i , J=J+1;

5.判断是否迭代结束。如果J＞K,则结束，否则继续1。 5. Determine whether the iteration is over. If J>K, then end, otherwise continue to 1. the

第三步，根据所有样本的第一层稀疏编码特征，利用第一层判别特征学习方法，得到第一层判别特征集 $\hat{F} = {{\hat{F}}_{i}}_{i = 1}^{N} &Element; R^{20 K_{1} \times N}$ 及第二层输入特征集 ${\hat{D}}_{i} &Element; R^{5 K_{1} \times 4}, i = 1,2, . . ., N;$ 其中第一层判别特征学习方法如下： In the third step, according to the first-level sparse coding features of all samples, the first-level discriminative feature set is obtained by using the first-level discriminative feature learning method $\hat{f} = {{\hat{f}}_{i}}_{i = 1}^{N} &Element; R^{20 K_{1} \times N}$ and the second layer input feature set ${\hat{D.}}_{i} &Element; R^{5 K_{1} \times 4}, i = 1,2, . . ., N;$ The first layer of discriminative feature learning method is as follows:

1.以每个样本的稀疏编码特征z_i为中心，取邻域窗口大小为(2m+1)×(2m+1)，m＝1,2,…，将每个样本的稀疏编码特征构建成为稀疏编码表示块 Z_i,i＝1,2,...,N，即一个规模为(2m+1)×(2m+1)×K₁的三维矩阵； 1. Take the sparse coding feature z _i of each sample as the center, take the neighborhood window size as (2m+1)×(2m+1), m=1, 2,..., construct the sparse coding feature of each sample Become a sparse coding representation block Z _i , i=1,2,...,N, that is, a three-dimensional matrix with a size of (2m+1)×(2m+1)×K ₁ ;

2.对每个样本的稀疏编码表示块Z_i进行分块，利用(m+1)×(m+1)的滑动窗口，划窗步长为m，从上到下，从左到右遍历每个样本的稀疏编码表示块，依次提取稀疏编码表示子块Z_i ⁽¹⁾、Z_i ⁽²⁾、Z_i ⁽³⁾和Z_i ⁽⁴⁾，总共4个子块，每个子块的规模为(m+1)×(m+1)×K₁； 2. Divide the sparse coded representation block Z _i of each sample into blocks, using a sliding window of (m+1)×(m+1), with a window step size of m, traversing from top to bottom and from left to right The sparse coded representation block of each sample is extracted sequentially to represent the sparse coded sub-blocks Z _i ⁽¹⁾ , Z _i ⁽²⁾ , Z _i ⁽³⁾ and Z _i ⁽⁴⁾ , a total of 4 sub-blocks, the size of each sub-block is (m+1)×(m+1)×K ₁ ;

3.依次对得到的4个子块进行空间金字塔最大池化算法 3. Carry out the spatial pyramid maximum pooling algorithm on the obtained 4 sub-blocks in turn

其中，SM(·)表示进行空间金字塔最大池化操作，U代表空间金字塔分解层数，V_u是位于空间金字塔第u层的所有块的总数目，M(·)代表最大池化算法， $M ({(Z_{i}^{(j)})}_{u}^{V_{u}}) = [\max_{t &Element; Z_{i}^{(j)}} | z_{1 t} |, . . ., \max_{t &Element; Z_{i}^{(j)}} | z_{K_{1} t} |];$ Among them, SM( ) represents the maximum pooling operation of the spatial pyramid, U represents the number of decomposition layers of the spatial pyramid, V _u is the total number of all blocks located in the uth layer of the spatial pyramid, M(·) represents the maximum pooling algorithm, $m ({(Z_{i}^{(j)})}_{u}^{V_{u}}) = [\max_{t &Element; Z_{i}^{(j)}} | z_{1 t} |, . . ., \max_{t &Element; Z_{i}^{(j)}} | z_{K_{1} t} |];$

4.按矩阵行组合的方式 ${\hat{F}}_{i} = [SM (Z_{i}^{(1)}); SM (Z_{i}^{(2)}); SM (Z_{i}^{(3)}); SM (Z_{i}^{(4)})]$ 得到第i个样本的第一层判别特征按矩阵列组合的方式 ${\hat{D}}_{i} = [SM (Z_{i}^{(1)}), SM (Z_{i}^{(2)}), SM (Z_{i}^{(3)}), SM (Z_{i}^{(4)})]$ 得到第i个样本的第二层输入特征。 4. Combining by matrix row ${\hat{f}}_{i} = [SM (Z_{i}^{(1)}); SM (Z_{i}^{(2)}); SM (Z_{i}^{(3)}); SM (Z_{i}^{(4)})]$ Get the first layer of discriminative features of the i-th sample Combining by matrix column ${\hat{D.}}_{i} = [SM (Z_{i}^{(1)}), SM (Z_{i}^{(2)}), SM (Z_{i}^{(3)}), SM (Z_{i}^{(4)})]$ Get the second layer input features of the i-th sample.

第四步，从训练集得到第二层的输入特征集中随机选出一部分，总共选取K₂个作为第二层判别字典的初始化字典D′₂，结合对应的类标矩阵和判别矩阵，类似于第一层判别字典构造方法通过判别字典目标函数可得二层判别字典 The fourth step is to randomly select a part of the input feature set of the second layer from the training set, select K ₂ in total as the initialization dictionary D′ ₂ of the second layer discriminant dictionary, and combine the corresponding class label matrix and discriminant matrix, similar to The first-level discriminant dictionary construction method can obtain the second-level discriminant dictionary through the discriminant dictionary objective function

第五步，基于第二层的输入特征和第二层判别字典，利用正交匹配追踪算法得到每个样本的第二层稀疏编码特征其中j＝1,2,3,4对应于第i个第二层的输入特征得到的第j列第二层稀疏编码特征，对所有样本的第二层稀疏编码特征利用最大池化算法，得到第二层判别特征集 In the fifth step, based on the input features of the second layer and the discriminant dictionary of the second layer, the second layer sparse coding feature of each sample is obtained by using the orthogonal matching pursuit algorithm in j=1,2,3,4 corresponds to the input features of the i-th second layer The second layer sparse coding feature of the jth column is obtained, and the maximum pooling algorithm is used for the second layer sparse coding feature of all samples to obtain the second layer discriminant feature set

步骤4，将所有样本的第一层判别特征集及第二层判别特征集结合，得到分层判别特征集F Step 4, the first layer discriminant feature set of all samples and the second layer discriminative feature set combined to obtain a hierarchical discriminative feature set F

$F f = = [[\overset{^^}{F f};; \overset{^^}{\overset{^^}{F f}}]]$

步骤5，将训练集和测试集对应的分层判别特征集输入到支撑矢量机，得到测试集的分类标签向量，该类标签向量即为该高光谱图像的分类结果。 Step 5: Input the hierarchical discriminant feature sets corresponding to the training set and the test set into the support vector machine to obtain the classification label vector of the test set, which is the classification result of the hyperspectral image. the

下面结合附图2对本发明的效果做进一步描述。 The effect of the present invention will be further described below in conjunction with accompanying drawing 2 . the

本发明的仿真是在具有代表性的美国国家宇航局NASA的AVIRIS于1992年6月在印第安纳西北部获取的高光谱图像Indiana Pine上进行的，Indiana Pine图像大小为145×145像素，图像中包含220个波段，移除被水域吸收的20个波段剩余200个波段，该图像共包含如表1所示的16类地物。 The simulation of the present invention is carried out on the hyperspectral image Indiana Pine obtained by AVIRIS of representative American National Aeronautics and Space Administration NASA in northwestern Indiana in June, 1992. The size of the Indiana Pine image is 145×145 pixels, and the image contains 220 bands, remove the 20 bands absorbed by the water and the remaining 200 bands, the image contains a total of 16 types of ground objects as shown in Table 1. the

本发明的仿真实验是在AMDA4-3400APU、主频2.69GHz，内存4G，Windows732位平台上的MATLAB2011a上实现的。 The simulation experiment of the present invention is realized on the MATLAB2011a on the AMDA4-3400APU, main frequency 2.69GHz, internal memory 4G, Windows732 bit platform. the

表1 Indiana Pine图像中的16类数据 Table 1 16 types of data in Indiana Pine image

类别 category 类别名称 classification name 样本个数 Sample size 训练样本个数 Number of training samples 1 1 苜蓿 Alfalfa 46 46 4 4 2 2 玉米-未耕犁 Corn - Unploughed 1428 1428 142 142 3 3 玉米-灌溉 Corn - Irrigation 830 830 83 83 4 4 玉米 corn 237 237 23 twenty three 5 5 牧草 grass 483 483 48 48 6 6 树木 the trees 730 730 73 73 7 7 切割的牧草 cut grass 28 28 2 2 8 8 干草料堆 Haystack 478 478 47 47 9 9 荞麦 buckwheat 20 20 2 2 10 10 大豆-未耕犁 Soybeans - Unploughed 972 972 97 97 11 11 大豆-灌溉 soybeans - irrigation 2455 2455 245 245 12 12 黄豆 soybeans 593 593 59 59 13 13 小麦 wheat 205 205 20 20 14 14 树林 the woods 1265 1265 126 126 15 15 建筑物-草-树 buildings-grass-trees 386 386 38 38 16 16 石头-钢筋 stone-rebar 93 93 9 9

2.仿真内容及分析 2. Simulation content and analysis

使用本发明与现有三种方法对高光谱图像进行分类，现有三种方法分别是：支撑矢量机SVM，基于稀疏表示的分类方法SRC，基于稀疏表示的空间金字塔匹配分类方法SCSPM，其中SVM方法的惩罚因子核参数通过5倍交叉验证确定，SRC方法的正则项参数λ设置为0.1，SRC方法和SCSPM方法的稀疏参数设置为20，SCSPM方法和本发明的空域尺度参数设置为7×7，从16类数据中每类随机取10％的像素点作为训练样本，其余的90％作为测试，进行5次实验取平均，则三种方法实验精度和本方法的实验精度如下表所示： Use the present invention and existing three methods to classify hyperspectral images, existing three methods are respectively: support vector machine SVM, classification method SRC based on sparse representation, spatial pyramid matching classification method SCSPM based on sparse representation, wherein the SVM method penalty factor Kernel parameters Determined by 5-fold cross-validation, the regular term parameter λ of the SRC method is set to 0.1, the sparse parameter of the SRC method and the SCSPM method is set to 20, the SCSPM method and the space scale parameter of the present invention are set to 7×7, from 16 types of data Randomly take 10% of the pixels of each category as training samples, and the remaining 90% as testing, and take the average of 5 experiments. The experimental accuracy of the three methods and the experimental accuracy of this method are shown in the following table:

表2 现有的三种方法与本发明实验精度结果 Existing three kinds of methods of table 2 and the experimental precision result of the present invention

方法 method 分类精度 classification accuracy SVM SVM 89.23％ 89.23% SRC SRC 83.70％ 83.70% SCSPM SCSPM 92.34％ 92.34% 本发明的方法 Method of the invention 96.54％ 96.54%

从表2可以看出，本发明的方法在分类精度上表现最优，本发明的方法学习得到的特征经过SVM分类器得到的分类精度比SVM直接对原始数据分类得到的精度高，说明本发明学习得到的特征更适合SVM分类器，从侧面反映出学习得到的特征有效；本发明的方法经过两层字典学习和稀疏编码得到的特征比SCSPM学习得到的特征更加有效，更加适合SVM分类器，从而说明了本发明与现有的方法相比具有明显的优势。 As can be seen from Table 2, the method of the present invention performs optimally on the classification accuracy, and the classification accuracy obtained by the feature learned by the method of the present invention is higher than that obtained by the SVM classifier directly on the original data classification, indicating that the classification accuracy of the present invention is The learned feature is more suitable for the SVM classifier, which reflects that the learned feature is effective; the method of the present invention is more effective than the SCSPM learned feature obtained through two-layer dictionary learning and sparse coding, and is more suitable for the SVM classifier. Thereby it is illustrated that the present invention has obvious advantages compared with the existing methods. the

综上，本发明基于稀疏编码的分层判别特征学习方法进行高光谱图像分类，充分利用高光谱图像的稀疏特性和空域上下文信息，能够对原始高光谱图像更准确地分类，在与现有三种图像分类方法的对比后，说明了本发明的准确性和有效性。与现有技术相比，具有以下优点： In summary, the present invention classifies hyperspectral images based on the sparse coding layered discriminant feature learning method, fully utilizes the sparse characteristics of hyperspectral images and spatial context information, and can classify original hyperspectral images more accurately. Compared with the existing three After the comparison of the image classification methods, the accuracy and effectiveness of the present invention are illustrated. Compared with the prior art, it has the following advantages:

第一，本发明利用判别字典学习的方法，在第一层字典学习和第二层字典学习时，考虑了类标信息，克服了传统的KSVD字典学习没有充分利用类标信息的不足，使得本发明学习得到的字典以及通过该字典学习得到的稀疏编码系数更具有判别性的优点。 First, the present invention utilizes the method for discriminating dictionary learning, considers class label information when first-level dictionary learning and second-level dictionary learning, overcomes the deficiency that traditional KSVD dictionary learning does not make full use of class-mark information, making The dictionary learned by the present invention and the sparse coding coefficients learned by the dictionary have more discriminative advantages. the

第二，本发明利用多层稀疏编码特征学习的方法，克服了传统使用单层稀疏编码系数直接进行分类而分类精度较低的缺点，使得本发明具有分类精度高的优点。 Second, the present invention utilizes a multi-layer sparse coding feature learning method, which overcomes the disadvantage of low classification accuracy of traditional single-layer sparse coding coefficients for direct classification, making the present invention have the advantage of high classification accuracy. the

第三，本发明利用空谱域结合的特征学习方法，克服了以一个像素点进行特征学习的算法的没有考虑周围邻域信息的不足，使得本发明具有对学习得到的特征鲁棒性更好的优点。 Thirdly, the present invention utilizes the feature learning method combined with the spatial spectrum domain, which overcomes the disadvantage of not considering the surrounding neighborhood information in the algorithm of feature learning with one pixel point, so that the present invention has better robustness to the learned features The advantages. the

本实施方式中没有详细叙述的部分属本行业的公知的常用手段，这里不一一叙述。以上例举仅仅是对本发明的举例说明，并不构成对本发明的保护范围的限制，凡是与本发明相同或相似的设计均属于本发明的保护范围之内。 The parts that are not described in detail in this embodiment are commonly known and commonly used means in this industry, and will not be described here one by one. The above examples are only illustrations of the present invention, and do not constitute a limitation to the protection scope of the present invention. All designs that are the same as or similar to the present invention fall within the protection scope of the present invention. the

Claims

1. A hyperspectral image classification method based on hierarchical sparse discriminant feature learning, characterized in that, comprising the following steps:

(1) Input hyperspectral remote sensing image data containing C-type ground objects, each pixel is a sample, and the sample is represented by a spectral feature vector, the feature dimension of the sample is h, and all samples constitute a sample set Where y _i is the i-th sample, N is the total number of samples, and R represents the real field;

(2) Randomly select 10% samples from each type of sample set as the training set n ₁ represents the number of samples in the training set, and the remaining 90% samples are used as the test set n ₂ represents the number of samples in the test set;

(3) Based on the training set Y _train and the sample set Y, use the layered discriminant feature learning method based on sparse coding to obtain the first layer discriminant feature set and the second layer discriminative feature set in, is the discriminative feature of the first layer corresponding to the i-th sample of the sample set Y, is the discriminative feature of the second layer corresponding to the i-th sample of the sample set Y:

3a) Randomly select K ₁ training samples from the training set as the initialization dictionary of the first layer of discriminant dictionary Using the discriminant K-SVD dictionary learning method, the first layer of discriminant dictionary D is obtained;

3b) Based on the first-level discriminant dictionary D, use the orthogonal matching pursuit algorithm to obtain the first-level sparse coding features of all samples

z = [z_{1}, z_{2}, &Center Dot; \cdot &Center Dot;, z_{N}] &Element; R^{K_{1} \times N};

3c) According to the first-level sparse coding features of all samples, use the first-level discriminative feature learning method to obtain the first-level discriminative feature set and the second layer input feature set

{\hat{D.}}_{i} &Element; R^{5 K_{1} \times 4}, i = 1,2, &Center Dot; &Center Dot; \cdot, N;

3d) Randomly select K ₂ from the second-layer input feature set corresponding to the training set as the initialization dictionary D′ ₂ of the second-layer discriminant dictionary, and combine the corresponding class label matrix and discriminant matrix, similar to the first-tier discriminant dictionary learning method Optimize the objective function of the discriminant dictionary to obtain the second layer of discriminant dictionary

3e) Based on the second-layer input feature set and the second-layer discriminant dictionary of the sample set Y, use the orthogonal matching pursuit algorithm to obtain the second-layer sparse coding features of each sample i=1,2,...,N, use the maximum pooling algorithm for the second-layer sparse coding features of all samples to obtain the second-layer discriminative feature set

(4) Merge the first layer discriminant feature set and the second layer discriminative feature set Obtain the hierarchical discriminant feature set F of the sample set Y,

(5) Input the hierarchical discriminant feature set corresponding to the training set and the test set into the support vector machine to obtain the classification label vector of the test set, which is the classification result of the hyperspectral image.

2. a kind of hyperspectral image classification method based on hierarchical sparse discriminant feature learning according to claim 1, is characterized in that, the concrete steps of discriminating K-SVD dictionary learning method in described step 3a) are:

In the first step, based on the training set Y _train , the objective function of the discriminant K-SVD dictionary learning method is as follows:

arg arg \underset{D D.,, W W,, A A,, X x}{min min} {| | | | {Y Y}_{train train} - - DX DX | | | |}_{22}^{22} + + α α {| | | | Q Q - - AX AX | | | |}_{22}^{22} + + β β {| | | | H h - - WX WX | | | |}_{22}^{22}

s the s . . t t . . &ForAll; &ForAll; i i,, {| | | | {x x}_{i i} | | | |}_{11} \leq \leq ϵ ϵ

Among them, the first item of the above formula is the reconstruction error item, the second item is the discriminant sparse coding constraint item, and the third item is the classification error item, D represents the first layer of discriminant dictionary, including K ₁ dictionary atoms, each atom The dimension is d, W represents the classification transformation matrix, A represents the linear transformation matrix, X represents the sparse coding coefficient matrix, Indicates the sum of squares of the l ₂ norm, α and β represent the regular parameters of the balanced class label discriminant item and classification error item, and the value range is 1 to 5, Represents the discriminative sparse coding coefficient matrix under ideal conditions. If the kth dictionary atom in D and the i-th sample in the training sample set Y _train belong to the same class, then the value of Q _ki is 1, and it is 0 when they are different classes. Indicates the class label matrix of the training sample, if the i-th sample in Y _train belongs to the c (c=1,2,...,C) class, H _ci is 1, otherwise it is 0, x _i represents the sparse coding coefficient matrix X The i-th column vector, ||·|| ₁ represents the l ₁ norm, and ε is the defined 10 ^-6 ;

In the second step, in order to solve the objective function of the discriminant K-SVD dictionary learning method, rewrite it as:

arg arg \underset{{D D.}_{new new},, X x}{min min} {{{| | | | {Y Y}_{new new} - - {D D.}_{new new} X x | | | |}_{22}^{22}}}

s the s . . t t . . &ForAll; &ForAll; i i,, {| | | | {x x}_{i i} | | | |}_{11} \leq \leq ϵ ϵ

in,

Y_{new} = {(Y_{train}^{T}, \sqrt{α} Q^{T}, \sqrt{β} h^{T})}^{T},

{D.}_{new} = {({D.}^{T}, \sqrt{α} A^{T}, \sqrt{β} W^{T})}^{T},

(·) ^T represents the transposition of the matrix, and the objective function is solved using the K-SVD dictionary learning method to obtain the first layer of discriminant dictionary D.

3. a kind of hyperspectral image classification method based on layered sparse discriminant feature learning according to claim 1, is characterized in that, the specific steps of orthogonal matching pursuit algorithm in described step 3b) are:

In the first step, based on the first layer of discriminant dictionary D, the objective optimization function of the orthogonal matching pursuit algorithm is as follows:

\underset{{z z}_{i i}}{min min} {| | | | {y the y}_{i i} - - {Dz Z}_{i i} | | | |}_{22}^{22},, s the s . . t t . . {| | | | {z z}_{i i} | | | |}_{11} \leq \leq δ δ,, i i = = 1,2 1,2,, . . . . . .,, N N

Among them, y _i represents the i-th sample of the sample set Y, z _i represents the sparse coding coefficient of y _i , and δ is the defined 10 ^-6 ;

The second step is to construct the residual term. The residual term is constructed as r ⁽⁰⁾ =y _i , i=1, 2...N, the index set Λ ⁰ is a K-dimensional zero vector, and the initialization variable J=1;

The third step is to find the subscript λ corresponding to the largest inner product between the residual r ^(J-1) and the jth column d _j in the dictionary D, that is

λ = {\arg \max}_{j = 1,2, . . ., T_{0}} | < r^{(J - 1)}, d_{j} > |

Step 4, update the index set Λ ^(J) , Λ ^(J) (J) = λ; update the set D ^(J) = D(:,Λ ^(J) (1:J) composed of the selected dictionary atomic columns ), using the least squares method to obtain the J-order approximation New residual r ^(J) =y _i -D ^(J) z _i , J=J+1;

Step 5, judge whether the iteration is over: if J≤K and there are still y _i not used as residual items, return to step 2, otherwise, if J≤K and y _i , i=1, 2...N are all used as residuals If the difference is the difference, the program ends. If J>K, return to step 3 and continue to execute.

4. a kind of hyperspectral image classification method based on layered sparse discriminant feature learning according to claim 1, is characterized in that, the concrete steps of first layer discriminant feature learning method in described step 3c) are:

Step 1, take the sparse coding feature z _i ,i=1,2,...,N of each sample as the center, and take the sparse coding of all samples in the neighborhood window size (2m+1)×(2m+1) Features form a sparse coding block Z _i , i=1, 2,..., N, Z _i is a three-dimensional matrix of (2m+1)×(2m+1)×K ₁ ;

Step 2: _Divide the sparse coding block Zi of each sample into blocks, using a sliding window of (m+1)×(m+1), with a window step size of m, from top to bottom, from left to right Traversing Z _i , sequentially extracting sparse coded representation sub-blocks and A total of 4 sub-blocks, the size of each sub-block is (m+1)×(m+1)×K ₁ ;

Step 3: Carry out the spatial pyramid maximum pooling algorithm on the obtained 4 sub-blocks in turn

SM (Z_{i}^{(j)}) = [m ({(Z_{i}^{(j)})}_{1}^{1}), \cdot \cdot \cdot, m ({(Z_{i}^{(j)})}_{1}^{V_{1}}), &Center Dot; &Center Dot; &Center Dot;, m ({(Z_{i}^{(j)})}_{u}^{V_{u}}), &Center Dot; \cdot \cdot, m ({(Z_{i}^{(j)})}_{u}^{V_{u}})],

j=1,2,3,4

Among them, SM( ) represents the maximum pooling operation of the spatial pyramid, j=1,2,3,4, U represents the number of spatial pyramid decomposition layers, V _u is the total number of all blocks located in the uth layer of the spatial pyramid, M( ) represents the maximum pooling algorithm,

m ({(Z_{i}^{(j)})}_{u}^{V_{u}}) = [\max_{t &Element; Z_{i}^{(j)}} | z_{1 t} |, &Center Dot; &Center Dot; &Center Dot;, \max_{t &Element; Z_{i}^{(j)}} | z_{K_{1} t} |];

Step 4, according to the way of matrix row combination

{\hat{f}}_{i} = [SM (Z_{i}^{(1)}); SM (Z_{i}^{(2)}); SM (Z_{i}^{(3)}); SM (Z_{i}^{(4)})]

Get the first layer of discriminative features of the i-th sample Combining by matrix column

{\hat{D.}}_{i} = [SM (Z_{i}^{(1)}); SM (Z_{i}^{(2)}); SM (Z_{i}^{(3)}); SM (Z_{i}^{(4)})]

Get the second layer input features of the i-th sample.