Improved Non Convex Optimization Algorithm for Reconstruction of Sparse Signals

It is now well understood that it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements. The form is solution to the optimization problem min ||s||₀ , subject to As = x. while this is an NP hard problem, i.e., a non convex problem, therefore researchers try to solve it by constrained l ¹-norm minimization and get near-optimal solution. In this paper, we study a novel method, called smoothed l ⁰-norm, for sparse signal recovery. Unlike previous methods, our algorithm tries to directly minimize the l ⁰-norm. It is experimented on synthetic and real image data and shows that the proposed algorithm outperforms the interiorpoint LP solvers, while providing the same even better accuracy.