Pointwise Mutual Information-Based Graph Laplacian Regularized Sparse Unmixing

Abstract

Sparse unmixing (SU) aims to express the observed image signatures as a linear combination of pure spectra known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> and has become a very popular technique with promising results in analyzing hyperspectral images (HSIs) over the past ten years. In SU, utilizing the spatial–contextual information allows for more realistic abundance estimation. To make full use of the spatial–spectral information, in this letter, we propose a pointwise mutual information (PMI)-based graph Laplacian (GL) regularization for SU. Specifically, we construct the affinity matrices via PMI by modeling the association between neighboring image features through a statistical framework and then we use them in the GL regularizer. We also adopt a double reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm minimization scheme to promote the sparsity of fractional abundances. Experimental results on simulated and real datasets prove the effectiveness of the proposed method and its superiority over competing algorithms in the literature.