Robust Hyperspectral Unmixing Using Total Variation Regularized Low-Rank Approximation

Abstract

Hyperspectral unmixing is the process of finding the fractional abundances and corresponding spectral signatures of a mixed pixel in a hyperspectral image. However, several types of noise such as dead pixels, stripes, impulse noise and Gaussian noise called as mixed noise are introduced in the hyperspectral images due to imperfect imaging sensors and atmospheric conditions, which degrades the performance of the unmixing algorithms. We propose a robust semi-supervised unmixing method to obtain the fractional abundances of the spectral signatures based on low-rank representation (LRR)and total variation (TV)using a a priori available spectral library. LRR estimates the global lowest rank representation of the abundance matrix whose columns are the abundance vectors of each pixel and TV regularization promotes the spatial piecewise smoothness of the abundance map. The sparse noise components are suppressed using an $l_{1}$ norm regularization term. Extensive simulation results on synthetic and real hyperspectral data sets show that the proposed method is effective in obtaining the abundance maps under mixed noise.