Abstract
Blind hyperspectral unmixing involves jointly estimating endmembers and fractional abundances in hyperspectral images. An endmember is the spectral signature of a specific material in an image, while an abundance map specifies the amount of a material seen in each pixel in an image. In this paper, a new cyclic descent algorithm for blind hyperspectral unmixing using total variation (TV) and $\boldsymbol{\ell_q}$ sparse regularization is proposed. Abundance maps are both spatially smooth and sparse. Their sparsity derives from the fact that each material in the image is not represented in all pixels. The abundance maps are assumed to be piecewise smooth since adjacent pixels in natural images tend to be composed of similar material. The TV regularizer is used to encourage piecewise smooth images, and the $\boldsymbol{\ell_q}$ regularizer promotes sparsity. The dyadic expansion decouples the problem, making a cyclic descent procedure possible, where one abundance map is estimated, followed by the estimation of one endmember. A novel debiasing technique is also employed to reduce the bias of the algorithm. The algorithm is evaluated using both simulated and real hyperspectral images.
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