Greedy pursuits based gradual weighting strategy for weighted ℓ1-minimization

• Main Authors: Narayanan, Sathiya, Sahoo, Sujit Kumar, Makur, Anamitra
• Other Authors: School of Electrical and Electronic Engineering
• Format: Conference or Workshop Item
• Language: English
• Published: 2019
• Subjects: Weighted ℓ1-minimization; Greedy Pursuits Assisted Basis Pursuit; Engineering::Electrical and electronic engineering
• Online Access: https://hdl.handle.net/10356/81440; http://hdl.handle.net/10220/50384
• Institution: Nanyang Technological University

In Compressive Sensing (CS) of sparse signals, standard ℓ 1 -minimization can be effectively replaced with Weighted ℓ 1 -minimization (Wℓ 1 ) if some information about the signal or its sparsity pattern is available. If no such information is available, Re-Weighted ℓ 1 -minimization (ReWℓ 1 ) can be deployed. ReW ℓ 1 solves a series of Wℓ 1 problems, and therefore, its computational complexity is high. An alternative to ReWℓ 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 Wℓ 1 . Although GPABP is an effective fusion technique, it adapts a binary weighting strategy for running Wℓ 1 , which is very restrictive. In this article, we propose a gradual weighting strategy for Wℓ 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 ℓ 1 -minimization (GP-Wℓ 1 ). For GP-Wℓ 1 , we derive the theoretical upper bound on its reconstruction error. Through simulation results, we show that the proposed GP-Wℓ 1 outperforms ReWℓ 1 and the state-of-the-art GPABP.