Sparse signal reconstruction based on multiparameter approximation function with smoothed \(\ell_0\) norm
type: Item
instance of: scholarly article
title: Sparse signal reconstruction based on multiparameter approximation function with smoothed \(\ell_0\) norm
zbMATH Open document ID: 1407.94036
DOI: 10.1155/2014/416542
author: Xiao-Feng Fang
author: Jiang-She Zhang
author: Yingqi Li
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The smoothed \(\ell_0\) norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothed \(\ell_0\) norm. It introduces a sequence of smoothed functions to approximate the \(\ell_0\) norm and approaches the solution using the specific iteration process with the steepest method. In order to choose an appropriate sequence of smoothed function and solve the optimization problem effectively, we employ approximate hyperbolic tangent multiparameter function as the approximation to the big ``steep nature'' in \(\ell_0\) norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximate \(\ell_0\) norm in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a modified quasi-Newton algorithm. The numerical simulation results show that the proposed algorithms yield improved signal reconstruction quality and performance.
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 7016388
Wikidata QID: Q59066934
describes a project that uses: AIR tools
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/416542
OpenAlex ID: W1979246694
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description: scientific article; zbMATH DE number 7016388