Research Of Dimensionality Reduction For Hyperspectral Image Based On Tensor Theory

Hyperspectral image(HSI)is obtained by the imaging spectrometer using hundreds of narrow electromagnetic spectral bands to image the region-of-interest,which can not only capture two-dimensional spatial information of ground objects,but also obtain the continuous spectral information of ground objects.Comparing with traditional remote sensing images,HSI has a further improvement on both spatial and spectral resolutions,especially,the spectral resolution is high enough for distinguishing different ground objects by subtle spectral feature changes.Therefore,HSI has been successfully applied in many fields,such as resource investigation,atmospheric monitoring,mapping,agricultural management,etc.However,the development of hyperspectral image processing technology lags behind that of imaging technology,which limits the further application of HSI.In particular,as one of the key technologies of HSI processing,dimensionality reduction(DR)technique has attracted extensive attention and become a hot topic in the field of HSI processing.DR can reduce the dimensionality of features without loss of useful information,which is an effective way to deal with the curse of dimensionality and prevent the occurrence of Hughes phenomenon.Actually,most of the current DR methods for HSI are developed on vector space,which ignore the intrinsic high-order structure of HSI.Therefore,this thesis combines the latest tensor theory with the inherent 3D data structure and low-rank characteristics of HSI to develop novel tensor subspace learning methods for DR of HSI.Meanwhile,theoretical analysis and simulation experiments are utilized to verify the effectiveness of the proposed methods.The main research work of this thesis is as follows:1.The DR of HSI based on tensor locality preserving projection(TLPP)and its improved algorithm is studied.In order to overcome the shortage that the existing methods cannot directly process multidimensional data,we first introduce the multiple projections-based TLPP algorithm for the DR of HSI,which can take full use of the intrinsic 3D data structure in HSI by using the tensor representation of HSI.For HSI,TLPP performs DR with data in the original data form that also can avoid the loss of local spatial information.Furthermore,in order to improve the robustness of TLPP,the region covariance descriptor is exploited to characterize a region of interest around each hyperspectral pixel and a modified TLPP(MTLPP)method is proposed for DR of HSI.Specifically,MTLPP constructs the intrinsic graph on a dual feature space that composed by region covariance descriptors rather than the original space.The resulting covariances are the symmetric positive definite matrices lying on a Riemannian manifold such that the Log-Euclidean metric is utilized as the similarity measure for the search of the nearest neighbors.2.A tensor low-rank discriminant embedding(TLRDE)model is constructed for DR of HSI.Although the low-rank representation(LRR)theory has been widely applied to the dimensionality reduction of HSI,the existing LRR-based DR methods usually only consider the spectral information and ignore the important spatial information.To this end,considering the fact that hyperspectral data is a data cube and has potential low-rank characteristics,this thesis builds a novel model named tensor low-rank discriminant embedding by integrating tensor representation of HSI,LRR theory,and tensor margin maximization criterion(MMC)together.Specifically,this model can effectively retain the intrinsic structural information of hyperspectral data by tensor representation,reveal the potential relationship between samples by using LRR,and enhance the separability of low-dimensional features by with make use of the priori label information.3.A patch tensor-based multi-graph embedding(PTMGE)framework is proposed for HSI DR.The graph embedding(GE)framework is one of the most widely used DR methods for HSI.However,most the existing GE methods focus on employing a single graph to describe the structure of data,which fails to consider the informations from other aspects.For example,the vector-based single graph do not take spatial information into consideration,while tensorbased graph methods assume that the pixels in each patch tensor belong to the same class,which is not exactly correct in practice.Considering the differences and correlations between pixels in each patch tensor,this thesis proposed a patch tensor-based multi-graph embedding(PTMGE)framework for the DR of HSI.Firstly,three different types of subgraphs are constructed to intrinsic geometrical structure of hyperspectral data from different aspects.Then,a novel subgraph fusion strategy is designed for computing the final weight matrix,which comprehensively characterizes the potential relationships among data.Finally,a projection matrix is learned for DR by using the objective function of classical GE framework.4.A tensor low-rank sparse preserving projection(TLRSPP)model is established,which integrates de-noising and dimensionality reduction together into one model.In order to compensate for the shortage of matrix projection method in processing high-order tensor data and enhance the robustness of DR model to noise,this thesis proposes a tensor low rank sparse preserving projection model based on tensor -product by integrating the tensor projection learning into the additive low-rank and sparse tensor decomposition.Firstly,this model regards the whole HSI as 3(9-order tensor,which avoids the loss of structure information caused by segmentation.Secondly,the map obtained by the proposed model also is a 3(9-order tensor that can directly transform the high-order data into a low subspace with informations from all directions used.Finally,the proposed model integrates the two independent steps de-noising and DR into one model,which simultaneously improves the efficiency of HSI processing and enhances the robustness of low-dimensional features.In general,this thesis mainly carry out the research of tensor-based HSI DR.By using tensor representation of HSI,GE,LRR,linear projection learning,and tensor -product,this thesis constructs the framework of tensor subspace learning-based DR for HSI step by step,and performs simulation experiments on real hyperspectral data to demonstrate the effectiveness of the proposed methods.