Multidimensional Low-Rank Representation for Sparse Hyperspectral Unmixing

Abstract

Hyperspectral unmixing is aimed at identifying pure materials in hyperspectral images as well as their relative proportions within each pixel. In light of the high similarity of spectral signatures among neighboring pixels, a low-rank property is proposed as a prior to enhance the abundance estimation results. In the previous studies, however, the low-rank prior is only reflected in the low-rank constraint on the abundance matrix. In this letter, we present a multidimensional low-rank model for the hyperspectral unmixing problem. We first reshape the abundance matrix to a 3-D abundance tensor. Then we simultaneously impose low-rank constraints on different modes of the abundance tensor to maximize the use of latent spatial information. Moreover, we incorporate the bilateral joint-sparse structure and derive a new algorithm, named as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multidimensional low-rank representation based sparse unmixing</i> . Experiments on both synthetic and real data demonstrate the effectiveness of the proposed algorithm.