A split Bregman method for non-negative sparsity penalized least squares with applications to hyperspectral demixing

We will describe an alternating direction (aka split Bregman) method for solving problems of the form min_u ∥Au - f∥² + η∥u∥₁ such that u ≥ 0, where A is an m×n matrix, and η is a nonnegative parameter. The algorithm works especially well for solving large numbers of small to medium overdetermined problems (i.e. m > n) with a fixed A. We will demonstrate applications in the analysis of hyperspectral images.