Sparsity and Total Variation Constrained Multilayer Linear Unmixing for Hyperspectral Imagery

Hyperspectral unmixing aims at estimating material signatures (known as endmembers) and the corresponding proportions (referred to abundances), which is a critical preprocessing step in various hyperspectral imagery applications. This study develops a novel approach called sparsity and total variation (TV) constrained multilayer linear unmixing (STVMLU) for hyperspectral imagery. Specifically, based on a multilayer matrix factorization model, to improve the accuracy of unmixing, a TV constraint is incorporated to consider adjacent spatial similarity. Additionally, a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{1 / 2}$</tex>-norm sparse constraint is adopted to effectively characterize the sparsity of the abundance matrix. For optimizing the STVMLU model, the method of alternating direction method of multipliers (ADMM) is employed, which allows for the simultaneous extraction of endmembers and their corresponding abundance matrix. Experimental results illustrate the enhanced performance of the proposed STVMLU when compared to other algorithms.