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Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization
In signal processing theory, [Formula: see text] -minimization is an important mathematical model. Unfortunately, [Formula: see text] -minimization is actually NP-hard. The most widely studied approach to this NP-hard problem is based on solving [Formula: see text] -minimization ([Formula: see text]...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5740216/ https://www.ncbi.nlm.nih.gov/pubmed/29299017 http://dx.doi.org/10.1186/s13660-017-1590-x |
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author | Wang, Changlong Peng, Jigen |
author_facet | Wang, Changlong Peng, Jigen |
author_sort | Wang, Changlong |
collection | PubMed |
description | In signal processing theory, [Formula: see text] -minimization is an important mathematical model. Unfortunately, [Formula: see text] -minimization is actually NP-hard. The most widely studied approach to this NP-hard problem is based on solving [Formula: see text] -minimization ([Formula: see text] ). In this paper, we present an analytic expression of [Formula: see text] , which is formulated by the dimension of the matrix [Formula: see text] , the eigenvalue of the matrix [Formula: see text] , and the vector [Formula: see text] , such that every k-sparse vector [Formula: see text] can be exactly recovered via [Formula: see text] -minimization whenever [Formula: see text] , that is, [Formula: see text] -minimization is equivalent to [Formula: see text] -minimization whenever [Formula: see text] . The superiority of our results is that the analytic expression and each its part can be easily calculated. Finally, we give two examples to confirm the validity of our conclusions. |
format | Online Article Text |
id | pubmed-5740216 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-57402162018-01-01 Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization Wang, Changlong Peng, Jigen J Inequal Appl Research In signal processing theory, [Formula: see text] -minimization is an important mathematical model. Unfortunately, [Formula: see text] -minimization is actually NP-hard. The most widely studied approach to this NP-hard problem is based on solving [Formula: see text] -minimization ([Formula: see text] ). In this paper, we present an analytic expression of [Formula: see text] , which is formulated by the dimension of the matrix [Formula: see text] , the eigenvalue of the matrix [Formula: see text] , and the vector [Formula: see text] , such that every k-sparse vector [Formula: see text] can be exactly recovered via [Formula: see text] -minimization whenever [Formula: see text] , that is, [Formula: see text] -minimization is equivalent to [Formula: see text] -minimization whenever [Formula: see text] . The superiority of our results is that the analytic expression and each its part can be easily calculated. Finally, we give two examples to confirm the validity of our conclusions. Springer International Publishing 2017-12-21 2017 /pmc/articles/PMC5740216/ /pubmed/29299017 http://dx.doi.org/10.1186/s13660-017-1590-x Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Wang, Changlong Peng, Jigen Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization |
title | Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization |
title_full | Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization |
title_fullStr | Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization |
title_full_unstemmed | Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization |
title_short | Analysis of the equivalence relationship between [Formula: see text] -minimization and [Formula: see text] -minimization |
title_sort | analysis of the equivalence relationship between [formula: see text] -minimization and [formula: see text] -minimization |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5740216/ https://www.ncbi.nlm.nih.gov/pubmed/29299017 http://dx.doi.org/10.1186/s13660-017-1590-x |
work_keys_str_mv | AT wangchanglong analysisoftheequivalencerelationshipbetweenformulaseetextminimizationandformulaseetextminimization AT pengjigen analysisoftheequivalencerelationshipbetweenformulaseetextminimizationandformulaseetextminimization |