Convex hyperspectral unmixing algorithm using parameterized non-convex penalty function

Abstract

Unmixing of hyperspectral data is an area of major research because the information it provides is utilized in plethora of fields. The year of 2006 witnessed the emergence of Compressed Sensing algorithm which was later used to spearhead research in umixing problems. Later, the notion of lp norms 0 < p < 1 and other non-smooth and non-convex penalty function were used in place of the traditional convex l1 penalty. Dealing with optimization problems with non-convex objective function is rather difficult as most methodologies often get stuck at local optima. In this paper, a parameterised non-convex penalty function is used to induce sparsity in the unknown.The parameters of penalty function can be adjusted so as to make the objective function convex, thus resulting in the possibility of finding a global optimal solution. Here ADMM algorithm is utilized to arrive at the final iterative algorithm for the unmixing problem. The algorithm is tested on synthetic data set, generated from the spectral library provided by US geological survey. Different parametric penalty functions like log and arctan are used in the algorithm and is compared with the traditional l1 penalties, in terms of the performance measures RSNR and PoS. It was observed that the non-convex penalty functions out-performs the l1 penalty in terms of the aforementioned measures.