Projection subspace based low-rank representation for sparse hyperspectral unmixing

With a known large spectral library, sparse hyperspectral unmixing has been taken as a hotspot in academia all these years. Its fundamental task is to estimate the abundance fractions of the spectral signatures in mixed pixels. Typically, the sparse and low-rank properties of the abundance matrix have been exploited simultaneously in the literature. Many studies only consider the low-rank property of the entire abundance matrix, however, pay less attention to the property of each abundance map. In this paper, we propose a new way to describe the low-rank prior. Firstly, an abundance cube is obtained by concatenating the abundance maps along the third dimension. We construct a lower-dimensional projection subspace of the abundance cube using a projection matrix, and the low-rankness of the abundance matrix is preserved during the projection process. Secondly, we consider the low-rank property by directly analyzing the abundance maps in the projection subspace. Finally, two algorithms, namely: projection subspace low-rank structure for sparse unmixing and projection subspace low-rank structure for bilateral sparse unmixing, are proposed based on different sparse structures of the abundance matrix. Both simulated and real-data experiments demonstrate that compared with classical sparse unmixing algorithms, the proposed ones obtain better unmixing results as well as cut down on calculation time.