Greedy Pursuits Based Gradual Weighting Strategy for Weighted <tex>$\ell_{1}$</tex>-Minimization

Abstract

In Compressive Sensing (CS) of sparse signals, standard 1minimization can be effectively replaced with Weighted 1 -minimization (W 1 ) if some information about the signal or its sparsity pattern is available. If no such information is available, Re-Weighted 1 -minimization (ReW 1 ) can be deployed. ReW 1 solves a series of W 1 problems, and therefore, its computational complexity is high. An alternative to ReW 1 is the Greedy Pursuits Assisted Basis Pursuit (GPABP) which employs multiple Greedy Pursuits (GPs) to obtain signal information which in turn is used to run W 1 . Although GPABP is an effective fusion technique, it adapts a binary weighting strategy for running W 1 , which is very restrictive. In this article, we propose a gradual weighting strategy for W 1 , which handles the signal estimates resulting from multiple GPs more effectively compared to the binary weighting strategy of GPABP. The resulting algorithm is termed as Greedy Pursuits assisted Weighted 1 -minimization (GP-W 1 ). For GP-W 1 , we derive the theoretical upper bound on its reconstruction error. Through simulation results, we show that the proposed GP-W 1 outperforms ReW 1 and the state-of-the-art GPABP.

Electrical Faults Signals Restoring Based on Compressed Sensing Techniques

“…1 norm: Assuming a matrix A which satisfy RIP criterion, highly sparse solutions can be obtained by convex optimization. In such a way, the algorithm is commonly know as Basis Pursuit (BP): [22,23].…”