Nonparametric Sparse Representation

This paper suggests a nonparametric scheme to find the sparse solution of the underdetermined system of linear equations in the presence of unknown impulsive or nonGaussian noise. This approach is robust against any variations of the noise model and its parameters. It is based on minimization of rank pseudo norm of the residual signal and of the signal of interest, simultaneously. We use the steepest descent method to find the sparse solution via an iterative algorithm. Simulation results show that our proposed method outperforms the existence methods like OMP, BP, Lasso, and BCS whenever the observation vector is contaminated with measurement or environmental nonGaussian noise with unknown parameters. Furthermore, for low SNR condition, the proposed method has better performance in the presence of Gaussian noise.