Nonparametric Sparse Representation
This addresses robust sparse representation for signal processing applications, offering incremental improvements over existing methods in handling unknown noise.
The paper tackles the problem of finding sparse solutions in underdetermined linear systems with unknown non-Gaussian or impulsive noise, proposing a nonparametric method that minimizes rank pseudo norm and l_1-norm simultaneously, resulting in outperforming existing methods like OMP, BP, Lasso, and BCS in noisy conditions, including better performance at low SNR with Gaussian noise.
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.