  An efficient spatial regularization method using superpixel segmentation and
graph Laplacian regularization is proposed for 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, then a weighted graph in each superpixel
is constructed by selecting $K$-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
graph Laplacian regularization. Sparsity regularization for 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.
