Adaptive LASSO hyperspectral unmixing using ADMM

In this paper, a method of hyperspectral unmixing for the linear regression model is introduced. The proposed algorithm employs an adaptive lasso problem using the alternating direction method of multipliers (ADMM) for unmixing process. Indeed, we formulate a weighted l₁ norm problem under the reasonable given error to reconstruct the fractional abundances and to avoid inconsistent end member selection in a sparse semi-supervised hyperspectral imaging process. We show that this problem can be efficiently solved by appropriate selection of functions and parameters appearing in the ADMM approach. First, we enforce both non-negativity and full additivity constraints of the abundance fractions in the objective function. Then, we apply the ADMM algorithm to solve the acquired optimization problem. Our simulations show that the proposed algorithms outperform the state-of-the-art methods in terms of mean square error and reconstruction signal-to-noise-ratio with reasonably reduced computational costs.