Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition

Autores
Caiafa, César Federico
Año de publicación
2013
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Tensor decomposition models for multidimensional datasets (multiway arrays) have a long history in Mathematics and applied sciences. While these models have recently been applied to multidimensional signal processing, they were developed independently of the theory of sparse representations and Compressed Sensing (CS). We discuss and illustrate recent results revealing connections among tensor decompositions models, recovery of low-rank multidimensional signals and CS theory. It is shown that, if a multidimensional signal has a good low rank or sparse multilinear representation, in the sense of the Tucker decomposition model, then it can be reconstructed from incomplete measurements. We discuss reconstructions methods for the cases where only a subset of fibers (mode-n vectors) in each dimension of the signal are available (Fiber Sampling Tensor Decomposition - FSTD), or when only the values of a limited set of entries are known (Tensor completion or multidimensional inpainting problem) or when measurements are given in a compressed multilinear format (Kronecker CS). We illustrate these methods by computer simulations taken on real world multidimensional signals including Magnetic Resonance Imaging (MRI) datasets and Hyperspectral images of natural scenes.
Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina
New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013)
Mar del Plata
Argentina
Universidad de Buneos Aires
Materia
Tensors
Compressed Sensing
Multidimensional Signals
Tucker decomposition
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/153408
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor DecompositionCaiafa, César FedericoTensorsCompressed SensingMultidimensional SignalsTucker decompositionhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2Tensor decomposition models for multidimensional datasets (multiway arrays) have a long history in Mathematics and applied sciences. While these models have recently been applied to multidimensional signal processing, they were developed independently of the theory of sparse representations and Compressed Sensing (CS). We discuss and illustrate recent results revealing connections among tensor decompositions models, recovery of low-rank multidimensional signals and CS theory. It is shown that, if a multidimensional signal has a good low rank or sparse multilinear representation, in the sense of the Tucker decomposition model, then it can be reconstructed from incomplete measurements. We discuss reconstructions methods for the cases where only a subset of fibers (mode-n vectors) in each dimension of the signal are available (Fiber Sampling Tensor Decomposition - FSTD), or when only the values of a limited set of entries are known (Tensor completion or multidimensional inpainting problem) or when measurements are given in a compressed multilinear format (Kronecker CS). We illustrate these methods by computer simulations taken on real world multidimensional signals including Magnetic Resonance Imaging (MRI) datasets and Hyperspectral images of natural scenes.Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaNew Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013)Mar del PlataArgentinaUniversidad de Buneos AiresUniversidad de Buenos AiresAldroubi, AkramCabrelli, Carlos2013info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectWorkshopBookhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/153408Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition; New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013); Mar del Plata; Argentina; 2013; 1-1CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.univie.ac.at/nuhag-php/dateien/talks/Caiafa_2013-04_Abstract.pdfinfo:eu-repo/semantics/altIdentifier/url/https://www.univie.ac.at/nuhag-php/event_NEW/make.php?event=cimpa13Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:01:30Zoai:ri.conicet.gov.ar:11336/153408instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:01:30.819CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
title Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
spellingShingle Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
Caiafa, César Federico
Tensors
Compressed Sensing
Multidimensional Signals
Tucker decomposition
title_short Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
title_full Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
title_fullStr Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
title_full_unstemmed Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
title_sort Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition
dc.creator.none.fl_str_mv Caiafa, César Federico
author Caiafa, César Federico
author_facet Caiafa, César Federico
author_role author
dc.contributor.none.fl_str_mv Aldroubi, Akram
Cabrelli, Carlos
dc.subject.none.fl_str_mv Tensors
Compressed Sensing
Multidimensional Signals
Tucker decomposition
topic Tensors
Compressed Sensing
Multidimensional Signals
Tucker decomposition
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Tensor decomposition models for multidimensional datasets (multiway arrays) have a long history in Mathematics and applied sciences. While these models have recently been applied to multidimensional signal processing, they were developed independently of the theory of sparse representations and Compressed Sensing (CS). We discuss and illustrate recent results revealing connections among tensor decompositions models, recovery of low-rank multidimensional signals and CS theory. It is shown that, if a multidimensional signal has a good low rank or sparse multilinear representation, in the sense of the Tucker decomposition model, then it can be reconstructed from incomplete measurements. We discuss reconstructions methods for the cases where only a subset of fibers (mode-n vectors) in each dimension of the signal are available (Fiber Sampling Tensor Decomposition - FSTD), or when only the values of a limited set of entries are known (Tensor completion or multidimensional inpainting problem) or when measurements are given in a compressed multilinear format (Kronecker CS). We illustrate these methods by computer simulations taken on real world multidimensional signals including Magnetic Resonance Imaging (MRI) datasets and Hyperspectral images of natural scenes.
Fil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina
New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013)
Mar del Plata
Argentina
Universidad de Buneos Aires
description Tensor decomposition models for multidimensional datasets (multiway arrays) have a long history in Mathematics and applied sciences. While these models have recently been applied to multidimensional signal processing, they were developed independently of the theory of sparse representations and Compressed Sensing (CS). We discuss and illustrate recent results revealing connections among tensor decompositions models, recovery of low-rank multidimensional signals and CS theory. It is shown that, if a multidimensional signal has a good low rank or sparse multilinear representation, in the sense of the Tucker decomposition model, then it can be reconstructed from incomplete measurements. We discuss reconstructions methods for the cases where only a subset of fibers (mode-n vectors) in each dimension of the signal are available (Fiber Sampling Tensor Decomposition - FSTD), or when only the values of a limited set of entries are known (Tensor completion or multidimensional inpainting problem) or when measurements are given in a compressed multilinear format (Kronecker CS). We illustrate these methods by computer simulations taken on real world multidimensional signals including Magnetic Resonance Imaging (MRI) datasets and Hyperspectral images of natural scenes.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Workshop
Book
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/153408
Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition; New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013); Mar del Plata; Argentina; 2013; 1-1
CONICET Digital
CONICET
url http://hdl.handle.net/11336/153408
identifier_str_mv Reconstruction of Multiway Arrays from Incomplete Information Using the Tucker Tensor Decomposition; New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing and Multifractal Analysis (CIMPA 2013); Mar del Plata; Argentina; 2013; 1-1
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.univie.ac.at/nuhag-php/dateien/talks/Caiafa_2013-04_Abstract.pdf
info:eu-repo/semantics/altIdentifier/url/https://www.univie.ac.at/nuhag-php/event_NEW/make.php?event=cimpa13
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Universidad de Buenos Aires
publisher.none.fl_str_mv Universidad de Buenos Aires
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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