Multiobjective-Based Sparse Representation Classifier for Hyperspectral Imagery Using Limited Samples

Bin Pan, Zhenwei Shi, Xia Xu

Abstract: Recent studies about hyperspectral imagery (HSI) classification usually focus on extracting more representative features or combining joint spectral-spatial information. However, besides feature extraction, developing more powerful classifiers can also contribute to the accuracies of HSI classification. In this paper, we propose a multiobjective-based sparse representation classifier (MSRC) for HSI data, which mainly tries to address two problems: 1) pixel mixing and 2) lacking abundant labeled samples. MSRC is motivated by the SRC, and further integrating the idea of hyperspectral unmixing. Different from the traditional SRC-based methods, the novelty of MSRC consists of the optimization process, i.e., we directly handle the L0-norm problem without any relaxation. The sparse term is not considered as a regularization operation. Instead, we transform the problem of weight vector estimation to subset selection, and propose a multiobjective-based method to optimize the L0-norm sparse problem. The residual term and sparse term are regarded as two parallel objective functions that are optimized simultaneously. We further utilize the linear mixing model to represent test pixels based on the selected atoms. The final class labels are determined according to the abundance estimation results by nonnegative least squares. Owing to the characteristics of the multiobjective method and the binary property of the sparse solution vector, MSRC does not require too many training samples to build the dictionary. Moreover, theoretically, MSRC can be easily improved to extended version such as combining spatial information.