Greedy pursuits based gradual weighting strategy for weighted ℓ1-minimization

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...

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Bibliographic Details
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
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Online Access:https://hdl.handle.net/10356/81440
http://hdl.handle.net/10220/50384
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Institution: Nanyang Technological University
Language: English
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Summary: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.