Feature Extraction And Classification For Hyperspectral Images Based On Sparse And Low-rank Representation

The hyperspectral image(HSI)is consisted of hundreds of spectral bands that contain the spectral characteristic of the land covers,which shows high spectral resolution as well as good spatial resolution.To date,the HSI has been widely used in lots of fields,such as agricultural management,atmospheric monitoring,urban planning,and mineral exploration.The main pro-cessing technologies include unmixing,feature extraction and classification,object detection,fusion and so on,among which feature extraction and classification have been the research fronts and hot topics in hyperspectral image processing until now.In the research fields of HSI,the "curse of dimensionality" is one common and difficult issue that needs to be overcome.As the imaging sensors are more and more advanced,the dimensionality becomes much higher.Feature extraction can effectively address this problem,which is able to preserve the discriminative information for subsequent application.Classifi-cation can provide the decision basis by labeling the land covers in the interesting area.Some drawbacks make the existing feature extraction and classification methods not very effective,such as old algorithmic theory,high complexity,and low performance.As a result,by combin-ing new research progress from the fields of pattern recognition and computer vision,this the-sis mainly makes a study on feature extraction and classification based on sparse and low-rank representation for hyperspectral images,and proposes some new models.Moreover,theoreti-cal analysis and experiments are adopted to demonstrate the effectiveness and usability of the proposed methods.The main work of this thesis can be summarized as follows:1.A kernel sparse and low-rank graph-based discriminant analysis method for feature extraction of hyperspectral images is proposed.Due to the nonlinear characteristic of HSI,the existing linear feature extraction methods fail to extract the most discriminative informa-tion from the original data.To address this problem,classical kernel sparse and low-rank graph-based discriminant analysis model and fast kernel sparse and low-rank graph-based dis-criminant analysis model are proposed in this thesis.The classical kernel sparse and low-rank graph-based discriminant analysis model introduces classical kernel transformation to implic-itly project original data information into high dimensional kernel space to improve the sepa-rability through the kernel trick.Then,a kernel sparse and low-rank graph can be constructed.After the optimization,the weight matrix can preserve the local and global structures well by imposing the sparse and low-rank constraints.Finally,the projection matrix can be obtained by kernel locality preserving projection.Although this model can overcome the problem of nonlinear feature extraction,it needs to compute the whole kernel matrix,leading to the heavy computational burden.To improve the computational efficiency,a fast kernel sparse and low-rank graph-based discriminant analysis method is proposed,which can explicitly project the original data into the virtual kernel space by exploiting the Nystrom theory.According to this theory,only part of representative samples are adopted to construct the virtual kernel space,in which the virtual samples with the same dimensionality can be obtained.This proposed model can not only effectively reduce the computational cost,especially for large scale data,but also improve the discriminative ability of the extracted features.2.A tensor sparse and low-rank graph-based discriminant analysis method for spatial-spectral feature extraction of hyperspectral images is developed.The land covers in HSI usu-ally present block areas and show local similarities that is known as spatial information.Some researches have demonstrated that spatial information is useful for improving the performance.However,deep exploration for the intrinsic data structure is not enough.To overcome this problem,a tensor sparse and low-rank graph-based discriminant analysis model is proposed in this thesis,which tries to preserve the intrinsic data structure with the help of tensor represen-tation.First of all,some 3-order tensor patches with an appropriate spatial size centering at each training sample are extracted and then exploited to construct one 4-order tensor.Then,a tensor sparse and low-rank graph model is presented,which can be optimized by the alternating direction method.The coefficient matrix obtained from the objective function is just the weight matrix of this tensor graph.Finally,the factor matrices are obtained by tensor locality preserv-ing projection.With the factor matrices in hand,the original tensor samples can be projected into the low-dimensional subspaces,leading to both the reduction of redundant information and great improvement of the discriminative ability for the extracted features.3.A tensor robust projection learning method for unsupervised spatial-spectral feature extraction of hyperspectral images is proposed for the first time.Due to the noise and corruption contained in HSI,the performance of some processing methods is greatly degraded.To address this problem,a new tensor robust principal component analysis model is first proposed in this thesis to improve the robustness for processing the hyperspectral data.By considering the low robustness to noise and the independence of the graph construction and projection of the existing graph embedding-based feature extraction methods,this thesis introduces the required projection into the new tensor robust principal component analysis model,finally generating unsupervised tensor robust projection learning method.This new method can remove the noise and corruption of the original data and simultaneously learn the required projection matrix for the following feature extraction,presenting double benefits in one model.Compared to those graph embedding-based methods,the proposed robust projection learning model can not only show good robustness but also further transmit this robustness to the projection matrix,resulting in more separable and discriminative low dimensional features.4.A joint sparse and low-rank representation classification method is proposed for hyper-spectral images.Only the local structure,i.e.,single subspace structure,of the hyperspectral data is preserved in the existing sparse representation-based classifiers.However,the fact is that the hyperspectral data usually shows multiple subspace structures.According to some recent researches,the low-rank representation can exactly capture the global structure of the hyper-spectral data.As such,a joint sparse and low-rank representation model is proposed to capture both the local and global structures.In addition,a spectral consistency constraint matrix is designed and imposed on sparse term and low-rank term simultaneously,which can constrain that samples from the same class will have the same representation coefficients while samples from different class will have different representation coefficients as much as possible.By us-ing this kind of constraint,the coding matrix will present a sparse and low-rank structure,and even more importantly,it may be a favorite block structure,which can further improve the dis-criminative ability.In the case where the singular value thresholding method fails to provide a solution for the subproblem that needs to optimize a low-rank term with a locality constraint,a closed-from solution can be obtained by introducing the rank equivalence of a matrix.This new optimization method can also reduce the computational cost of the algorithm effectively.In conclusion,this thesis mainly develops the study work on the feature extraction and classification for HSI.On the basis of sparse representation,low-rank representation,graph embedding,kernel technology,and tensor,this thesis constructs the framework of feature ex-traction and classification for HSI step by step,and demonstrates the effectiveness of the pro-posed methods by conducting the experiments on the real hyperspectral data.