Hyperspectral Classification Using Low Rank and Sparsity Matrices Decomposition

Abstract

Classification is a major task in hyperspectral image (HSI) processing. This paper develops an approach by taking advantage of low rank matrix derived from the low rank and sparse matrix decomposition (LRSMD) model which decomposes a hyperspectral data matrix X as X = L+S+n where L, S and n are referred to low rank, sparse and noise matrices respectively. The hyperspectral image classification (HSIC) is then performed on the low rank matrix L rather than the original data matrix X where the well-known go decomposition (GoDec) is used to produce such LRSMD model. To determine the two key parameters used in GoDec, the rank of L, m, and the cardinality of the sparse matrix, $k$ the well-known virtual dimensionality (VD) and minimax-singular value decomposition (MX-SVD) methods are used for this purpose. Finally, to demonstrate advantages of using the low rank matrix L, support vector machine (SVM) and an edge-preserving filters (EPF)-based classifiers are implemented to evaluate classification performance.