Superpixel-Based Graph Laplacian Regularization for Sparse Hyperspectral Unmixing

Abstract

An efficient spatial regularization method using superpixel segmentation and graph Laplacian regularization is proposed for the sparse hyperspectral unmixing method. Since it is likely to find spectrally similar pixels in a homogeneous region, we use a superpixel segmentation algorithm to extract the homogeneous regions by considering the image boundaries. We first extract the homogeneous regions, which are called superpixels, and then, a weighted graph in each superpixel is constructed by selecting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -nearest pixels in each superpixel. Each node in the graph represents the spectrum of a pixel, and edges connect the similar pixels inside the superpixel. The spatial similarity is investigated using the graph Laplacian regularization. Sparsity regularization for an abundance matrix is provided using a weighted sparsity promoting norm. Experimental results on simulated and real data sets show the superiority of the proposed algorithm over the well-known algorithms in the literature.