Spatial Group Sparsity Regularized Nonnegative Matrix Factorization for Hyperspectral Unmixing

In recent years, blind source separation (BSS) has received much attention in the hyperspectral unmixing field due to the fact that it allows the simultaneous estimation of both endmembers and fractional abundances. Although great performances can be obtained by the BSS-based unmixing methods, the decomposition results are still unstable and sensitive to noise. Motivated by the first law of geography, some recent studies have revealed that spatial information can lead to an improvement in the decomposition stability. In this paper, the group-structured prior information of hyperspectral images is incorporated into the nonnegative matrix factorization optimization, where the data are organized into spatial groups. Pixels within a local spatial group are expected to share the same sparse structure in the low-rank matrix (abundance). To fully exploit the group structure, image segmentation is introduced to generate the spatial groups. Instead of a predefined group with a regular shape (e.g., a cross or a square window), the spatial groups are adaptively represented by superpixels. Moreover, the spatial group structure and sparsity of the abundance are integrated as a modified mixed-norm regularization to exploit the shared sparse pattern, and to avoid the loss of spatial details within a spatial group. The experimental results obtained with both simulated and real hyperspectral data confirm the high efficiency and precision of the proposed algorithm.