Sparsity recovery by iterative orthogonal projections of nonlinear mappings

Abstract

This paper provides a new regularization method for sparse representation based on a fixed-point iteration schema which combines two Lipschitzian-type mappings, a nonlinear one aimed to uniformly enhance the sparseness level of a candidate solution and a linear one which projects back into the feasible space of solutions. It is shown that this strategy locally minimizes a problem whose objective function falls into the class of the ℓp-norm and represents an efficient approximation of the intractable problem focusing on the ℓ0-norm. Numerical experiments on randomly generated signals using classical stochastic models show better performances of the proposed technique with respect to a wide collection of well known algorithms for sparse representation.