On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis

An approach to sparse signals reconstruction considering its missing measurements/samples as variables is recently proposed. Number and positions of missing samples determine the uniqueness of the solution. It has been assumed that analyzed signals are sparse in the discrete Fourier transform (DFT)...

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Main Authors:	Ljubiša Stanković, Miloš Daković
Format:	Article
Language:	English
Published:	Hindawi Limited 2015-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2015/629759

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spelling	doaj-1c98abc5dbb24916b50428d1626a23092020-11-24T23:55:13ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/629759629759On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation AnalysisLjubiša Stanković0Miloš Daković1University of Montenegro, 81000 Podgorica, MontenegroUniversity of Montenegro, 81000 Podgorica, MontenegroAn approach to sparse signals reconstruction considering its missing measurements/samples as variables is recently proposed. Number and positions of missing samples determine the uniqueness of the solution. It has been assumed that analyzed signals are sparse in the discrete Fourier transform (DFT) domain. A theorem for simple uniqueness check is proposed. Two forms of the theorem are presented, for an arbitrary sparse signal and for an already reconstructed signal. The results are demonstrated on illustrative and statistical examples.http://dx.doi.org/10.1155/2015/629759
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ljubiša Stanković Miloš Daković
spellingShingle	Ljubiša Stanković Miloš Daković On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis Mathematical Problems in Engineering
author_facet	Ljubiša Stanković Miloš Daković
author_sort	Ljubiša Stanković
title	On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis
title_short	On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis
title_full	On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis
title_fullStr	On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis
title_full_unstemmed	On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis
title_sort	on the uniqueness of the sparse signals reconstruction based on the missing samples variation analysis
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2015-01-01
description	An approach to sparse signals reconstruction considering its missing measurements/samples as variables is recently proposed. Number and positions of missing samples determine the uniqueness of the solution. It has been assumed that analyzed signals are sparse in the discrete Fourier transform (DFT) domain. A theorem for simple uniqueness check is proposed. Two forms of the theorem are presented, for an arbitrary sparse signal and for an already reconstructed signal. The results are demonstrated on illustrative and statistical examples.
url	http://dx.doi.org/10.1155/2015/629759
work_keys_str_mv	AT ljubisastankovic ontheuniquenessofthesparsesignalsreconstructionbasedonthemissingsamplesvariationanalysis AT milosdakovic ontheuniquenessofthesparsesignalsreconstructionbasedonthemissingsamplesvariationanalysis
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On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis

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