  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 non-Gaussian 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 l_1-norm 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 non-Gaussian noise with
unknown parameters. Furthermore, for low SNR condition, the proposed method has
better performance in the presence of Gaussian noise.
