Substance Dependence Constrained Sparse NMF for Hyperspectral Unmixing

Abstract

Hyperspectral unmixing is one of the most important problems in analyzing remote sensing images, which aims to decompose a mixed pixel into a collection of constituent materials named endmembers and their corresponding fractional abundances. Recently, various methods have been proposed to incorporate sparse constraints into hyperspectral unmixing and achieve advanced performance. However, most of them ignore the complex distribution of substances in hyperspectral data so that they are only effective in limited cases. In this paper, the concept of substance dependence is introduced to help hyperspectral unmixing. Generally, substance dependence can be considered in a local region by $K$ - nearest neighbors method. However, since substances of hyperspectral images are complicatedly distributed, number $K$ of the most similar substances to each substance is difficult to decide. In this case, substance dependence should be considered in the whole data space, and the number of the $K$ most similar substances to each substance can be adaptively determined by searching from the whole space. Through maintaining the substance dependence during unmixing, the abundances resulted from the proposed method are closer to the real fractions, which lead to better unmixing performance. The following contributions can be summarized. 1) The concept of substance dependence is proposed to describe the complicated relationship between substances in the hyperspectral image. 2) We propose substance dependence constrained sparse nonnegative matrix factorization (SDSNMF) for hyperspectral unmixing. Using SDSNMF, we meet or exceed state-of-the-art unmixing performance. 3) Adequate experiments on both synthetic and real hyperspectral data have been tested. Compared with the state-of-the-art methods, the experimental results prove the superiority of the proposed method.