Hyperspectral Remote Sensing Image Classification Via Sparse Graph Embedding

Hyperspectral remote sensing is one of the most important research lines in geoscience and remote sensing society. Hyperspectral remote sensing can simultaneously obtain land cover images in spatial domain and dense spectra in spectral domain. The characteristics of unified spectral-spatial information make hyperspectral remote sensing superior to other remote sensing techniques, which also pose great challenges for hyperspectral image processing. The generally limited availability of training samples relative to the usually high data dimension make hyperspectral image classification an ill-posed problem. In this context, traditional parametric models are usually unavailable or inaccurate. Researchers have dedicated to ill-posed problems from two perspectives. On the one hand, reducing high-dimensional spectral domain to low-dimensional feature domain by using feature extraction (or feature selection). Hyperspectral data exhibits complex nonlinear characteristics. Manifold learning is capable of considering the nonlinear characteristics in feature extraction. However, current studies of manifold learning mainly focus on single graph embedding, which cannot sufficiently represent the complex manifolds hidden in hyperspectral data. On the other hand, semi-supervised (or active learning based) classification models can improve the generalization performance. Graph-based semi-supervised learning belongs to non-parametric method, which is discriminative and capable of modeling nonlinear characteristics of hyperspectral data, emerging as a promising semi-supervised classification method. However, most of graph-based semi-supervised learning methods scale poorly with data size for hyperspectral image, and the generalization performance also need to be improved. Exploring robust and accurate classification methods for hyperspectral image under the condition of high data dimension and very limited labeled data has become an important scientific problem with urgent need to solve in this community.On the basis of theoretical analysis and improvements of sparse representation and graph techniques, this dissertation systematically studies hyperspectral image feature extraction and classification via sparse graph embedding, with particular emphasize on designing two feature extraction methods including collaborative sparse graph embedding and sparse multi-manifold learning, and designing a sparse graph regularization based active semi-supervised classification method. Two widely used data sets including ROSIS and AVIRIS were adopted for evaluating the performance of the proposed methods. In order to accurately discriminate different crops in Heihe watershed, CASI/SASI data set was also used for validating the proposed methods.The main research contents and the conclusions are given as follows:1) The logic relationships between sparse representation and graph construction were uncovered. Then, two modified sparse graph construction methods were proposed. Theory foundations and physical significances can be found in sparsely representing hyperspectral image, and the obtained sparse coefficients represent the similarity between image and dictionary. By using matrix computation, the correlations of image-to-dictionary were extended to image-to-image, thus designing an efficient sparse graph construction method via SUnSAL, and designing a shape-adaptive sparse graph construction method via SOMP. The built sparse graph is data-adaptive, and it inherits the merits of sparse representation, namely, good discriminative power, sparsity, and robustness to noise. Those characteristics were certified by analyzing the results of sparse representation and graph construction for some typical objects, where we also found that SA-based-CSR graph construction method can significantly improve the representative power for image spatial information.2) With the built sparse graph at hand, graph embedding was adopted to extract features, aiming at improving the separability power. Then, collaborative sparse graph embedding and sparse multi-manifold learning methods were proposed. Firstly, sparse graph embedding (SGE) and its kernerlization were exploited. Secondly, collaborative sparse graph embedding (CSGE) was proposed by employing collaborative sparse graph construction. Thirdly, by using view generation and SGE for multiple manifolds representation and coupling, the sparse multi-manifold learning (SMML) method was proposed. Finally, the performance of feature extraction for the proposed methods was evaluated by using eigenvalue analysis, correlation analysis, K-ary neighborhood preservation, separability analysis, etc. The experimental results demonstrated that the proposed methods outperform traditional methods in terms of representing data structure, decorrelation, feature separability, robustness to noise, and computational complexity. Spatial information is beneficial to CSGE in modeling neighborhood data structures. Spectral discriminant information is beneficial to SMML, which enhances the feature separability power.3) Hyperspectral remote sensing image classification was achieved by using sparse multinomial logistic regression (SMLR) model based on the extracted low-dimensional features. Sparse graph regularization based active semi-supervised classification method was designed by using a fully constrained sparse representation model to construct the sparse graph. Firstly, SGE, CSGE and SMML methods were evaluated by using SMLR. Secondly, SGE-based methods were kernalized to enhance the feature separability, thus reducing "Hughes" phenomena. Graph cuts was used to introduce spatial information, leading to more homogenous classification maps, which greatly relieves the "salt-and-paper" phenomena. Finally, SGR was designed by using fully constrained sparse representation to build the sparse graph. The experimental results with very limited training samples demonstrated that, SGR is insensitive to parameters, and it outperforms other traditional supervised methods (e.g., SVM and LORSAL) and semi-supervised methods (e.g., AGR and SSMLR) in terms of robustness to noise, generalization performance, and computational complexity. The overall classification accuracy reaches to 85% for the CASI/SASI data set with very limited training samples (i.e.,40 labeled samples in total), which meets the needs of object identification and information extraction for hyperspectral image.This dissertation focused on ill-posed classification problems of hyperspectral image by following the research line of "sparse representation—sparse graph construction—feature extraction—image classification". The involved theoretical and technical issues in sparse graph embedding were discussed, and a new solution for ill-posed hyperspectral image classification problems was provided.