Title: Total variation regularized non-negative matrix factorization for smooth hyperspectral unmixing,
Abstract: Hyperspectral analysis has gained popularity over recent years as a way to
infer what materials are displayed on a picture whose pixels consist of a
mixture of spectral signatures. Computing both signatures and mixture
coefficients is known as unsupervised unmixing, a set of techniques usually
based on non-negative matrix factorization. Unmixing is a difficult non-convex
problem, and algorithms may converge to one out of many local minima, which may
be far removed from the true global minimum. Computing this true minimum is
NP-hard and seems therefore out of reach. Aiming for interesting local minima,
we investigate the addition of total variation regularization terms. Advantages
of these regularizers are two-fold. Their computation is typically rather
light, and they are deemed to preserve sharp edges in pictures. This paper
describes an algorithm for regularized hyperspectral unmixing based on the
Alternating Direction Method of Multipliers.