Compressive Sensing Signal Reconstruction Using LO-Norm Normalized Least Mean Fourth Algorithms

摘要

Stochastic gradient-based adaptive algorithm has recently attracted considerable attention as one of the best candidates for solving compressive sensing (CS) problems due to its two obvious advantages: low complexity and robust performance. In this paper, in order to further improve the reconstruction accuracy for CS problems under Gaussian background noise, two novel sparse fourth-order error criterion adaptive algorithms, i.e., the -norm normalized least mean fourth (-NLMF) algorithm and the -norm exponentially forgetting window NLMF (-EFWNLMF) algorithm, are proposed. In addition, to extend the obtained results to non-Gaussian noise environment, the variants of the above two algorithms, i.e., the sign -NLMF (-SNLMF) algorithm and the sign -EFWNLMF (-EFWSNLMF) algorithm, are presented which can effectively mitigate certain impulsive noises. Numerical simulations are also given to demonstrate the evident performance improvement and extensive stability of the proposed algorithms.