ℓP minimization for sparse vector reconstruction

In this paper we present a new technique for minimizing a class of nonconvex functions for solving the problem of under-determined systems of linear equations. The proposed technique is based on locally replacing the nonconvex objective function by a convex objective function. The main property of the utilized convex function is that it is minimized at a point that reduces the original concave function. The resulting algorithm is iterative and outperforms some previous algorithms that have been applied to the same problem.