Nonparametric Sparse Representation

TL;DR

This paper introduces a robust nonparametric method for sparse signal recovery in underdetermined systems with unknown non-Gaussian noise, outperforming existing techniques under various noise conditions.

Contribution

It proposes a novel nonparametric approach based on rank pseudo norm minimization and l_1-norm, with an iterative steepest descent algorithm for improved robustness.

Findings

Outperforms OMP, BP, Lasso, BCS in non-Gaussian noise environments.

Effective in low SNR conditions with Gaussian noise.

Robust against unknown noise model variations.

Abstract

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.