Collaborative Representation and Sparsity are Both Indispensable for Hyperspectral Imagery Classification

Abstract

As a recently proposed technique, sparse representation based classifier (SRC) has been widely used for hyperspectral imagery classification and detection. The collaborative representation (CR) and the sparse coding are two key points in SRC scheme. More recently, the proposition that which one of them plays a dominant role in SRC scheme has attracted much attention from researchers in fields of image processing, computer vision, and pattern recognition. In this paper, we first discuss why CR or sparsity works and why one of them alone is not sufficient, and then analyze how CR and sparsity interact with each other. Although we focus on how sparsity augments CR, the necessity of CR for sparsity is also illustrated in both pixel-wise model and joint sparsity model. Inspired by the analysis, we indicate that CR is a powerful tool for solving the high-dimensional pattern recognition with small sample in SRC scheme; sparsity augments CR-based classification in stabilizing, making sure unique solution and rejecting outlying samples. In other words, CR and sparsity complement each other and are both indispensible for hyperspectral imagery classification. The experimental results on simulated data and real hyperspectral imagery confirm the conclusion.