On a gradient-based algorithm for sparse signal reconstruction in the signal/measurements domain
type: Item
instance of: scholarly article
title: On a gradient-based algorithm for sparse signal reconstruction in the signal/measurements domain
zbMATH Open document ID: 1400.94064
DOI: 10.1155/2016/6212674
author: Miloš Daković
author: Ljubiša Stanković
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common compressive sensing methods the signal is recovered in the sparsity domain. A method for the reconstruction of sparse signals which reconstructs the missing/unavailable samples/measurements is recently proposed. This method can be efficiently used in signal processing applications where a complete set of signal samples exists. The missing samples are considered as the minimization variables, while the available samples are fixed. Reconstruction of the unavailable signal samples/measurements is preformed using a gradient-based algorithm in the time domain, with an adaptive step. Performance of this algorithm with respect to the step-size and convergence are analyzed and a criterion for the step-size adaptation is proposed in this paper. The step adaptation is based on the gradient direction angles. Illustrative examples and statistical study are presented. Computational efficiency of this algorithm is compared with other two commonly used gradient algorithms that reconstruct signal in the sparsity domain. Uniqueness of the recovered signal is checked using a recently introduced theorem. The algorithm application to the reconstruction of highly corrupted images is presented as well.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 6953416
Wikidata QID: Q59140853
describes a project that uses: CONV_QP
describes a project that uses: GPDT
describes a project that uses: CoSaMP
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/6212674
OpenAlex ID: W2441544549
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description: scientific article; zbMATH DE number 6953416