Applications of singular entropy to signals and singular smoothness to images

[EN] This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into orthogonal subspaces. While SVD is a well-established tool...

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Autores: Romero Martínez, José Oscar|||0000-0003-4081-9005, Thome, Néstor|||0000-0001-5328-6637
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:dnet:riunet______::af7f8dff5fbeb91e894ebceff36433d5
Acceso en línea:https://riunet.upv.es/handle/10251/233832
Access Level:acceso abierto
Palabra clave:Singular Value Decomposition (SVD)
Energy Gap Variation (EGV)
Numerical experiments
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spelling Applications of singular entropy to signals and singular smoothness to imagesRomero Martínez, José Oscar|||0000-0003-4081-9005Thome, Néstor|||0000-0001-5328-6637Singular Value Decomposition (SVD)Energy Gap Variation (EGV)Numerical experiments[EN] This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into orthogonal subspaces. While SVD is a well-established tool in ECG analysis, particularly for source separation, this work proposes a refined method for selecting a threshold to distinguish between maternal and fetal components more effectively. In the first part of the paper, the focus is on medical signal analysis, where the concepts of Energy Gap Variation (EGV) and Singular Energy are introduced to isolate fetal and maternal ECG signals, improving the known ones. Furthermore, the approach is significantly enhanced by the application of GSVD, which provides additional discriminative power for more accurate signal separation. The second part introduces a novel technique called Singular Smoothness, developed for image analysis. This method incorporates Singular Entropy and the Frobenius norm to evaluate information density, and is applied to the detection of natural anomalies such as mountain fractures and burned forest regions. Numerical experiments are presented to demonstrate the effectiveness of the proposed approaches.Research supported by Universidad Nacional de La Pampa (Grant Resol. 172/2024); by Grant PGI 24/ZL22, Departamento de Matematica, Universidad Nacional del Sur (UNS), Argentina; and by Ministerio de Ciencia, Innovacion y Universidades of Spain ¿ (Grant Redes de Investigacion, MICINN-RED2022-134176-T).National Library of SerbiaEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaDepartamento de ComunicacionesInstituto Universitario de Matemática MultidisciplinarInstituto de Investigación para la Gestión Integrada de Zonas CosterasMinisterio de Ciencia e InnovaciónUniversidad Nacional del Sur, ArgentinaUniversidad Nacional de La Pampa, ArgentinaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/233832reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengUniversidad Nacional de La Pampa, Argentina Universidad Nacional de La Pampa, Argentina 172%2F2024 Análisis Matricial de Inversas Generalizadas con aplicacionesUniversidad Nacional del Sur, Argentina Universidad Nacional del Sur, Argentina 24%2FZL22 Estudio de estructuras ordenadas definidas sobre el anillo de matrices complejasMinisterio de Ciencia e Innovación Ministerio de Ciencia e Innovación RED2022-134176-T RED TEMÁTICA DE ÁLGEBRA LINEAL, ANÁLISIS MATRICIAL Y APLICACIONES.open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:dnet:riunet______::af7f8dff5fbeb91e894ebceff36433d52026-06-13T07:49:27Z
dc.title.none.fl_str_mv Applications of singular entropy to signals and singular smoothness to images
title Applications of singular entropy to signals and singular smoothness to images
spellingShingle Applications of singular entropy to signals and singular smoothness to images
Romero Martínez, José Oscar|||0000-0003-4081-9005
Singular Value Decomposition (SVD)
Energy Gap Variation (EGV)
Numerical experiments
title_short Applications of singular entropy to signals and singular smoothness to images
title_full Applications of singular entropy to signals and singular smoothness to images
title_fullStr Applications of singular entropy to signals and singular smoothness to images
title_full_unstemmed Applications of singular entropy to signals and singular smoothness to images
title_sort Applications of singular entropy to signals and singular smoothness to images
dc.creator.none.fl_str_mv Romero Martínez, José Oscar|||0000-0003-4081-9005
Thome, Néstor|||0000-0001-5328-6637
author Romero Martínez, José Oscar|||0000-0003-4081-9005
author_facet Romero Martínez, José Oscar|||0000-0003-4081-9005
Thome, Néstor|||0000-0001-5328-6637
author_role author
author2 Thome, Néstor|||0000-0001-5328-6637
author2_role author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Departamento de Comunicaciones
Instituto Universitario de Matemática Multidisciplinar
Instituto de Investigación para la Gestión Integrada de Zonas Costeras
Ministerio de Ciencia e Innovación
Universidad Nacional del Sur, Argentina
Universidad Nacional de La Pampa, Argentina
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Singular Value Decomposition (SVD)
Energy Gap Variation (EGV)
Numerical experiments
topic Singular Value Decomposition (SVD)
Energy Gap Variation (EGV)
Numerical experiments
description [EN] This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into orthogonal subspaces. While SVD is a well-established tool in ECG analysis, particularly for source separation, this work proposes a refined method for selecting a threshold to distinguish between maternal and fetal components more effectively. In the first part of the paper, the focus is on medical signal analysis, where the concepts of Energy Gap Variation (EGV) and Singular Energy are introduced to isolate fetal and maternal ECG signals, improving the known ones. Furthermore, the approach is significantly enhanced by the application of GSVD, which provides additional discriminative power for more accurate signal separation. The second part introduces a novel technique called Singular Smoothness, developed for image analysis. This method incorporates Singular Entropy and the Frobenius norm to evaluate information density, and is applied to the detection of natural anomalies such as mountain fractures and burned forest regions. Numerical experiments are presented to demonstrate the effectiveness of the proposed approaches.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/233832
url https://riunet.upv.es/handle/10251/233832
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Universidad Nacional de La Pampa, Argentina Universidad Nacional de La Pampa, Argentina 172%2F2024 Análisis Matricial de Inversas Generalizadas con aplicaciones
Universidad Nacional del Sur, Argentina Universidad Nacional del Sur, Argentina 24%2FZL22 Estudio de estructuras ordenadas definidas sobre el anillo de matrices complejas
Ministerio de Ciencia e Innovación Ministerio de Ciencia e Innovación RED2022-134176-T RED TEMÁTICA DE ÁLGEBRA LINEAL, ANÁLISIS MATRICIAL Y APLICACIONES.
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv National Library of Serbia
publisher.none.fl_str_mv National Library of Serbia
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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