Stable, robust and super fast reconstruction of tensors using multi-way projections
- Autores
- Caiafa, Cesar Federico; Cichocki, Andrzej
- Año de publicación
- 2015
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an Nth-order data tensor X from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order N. In addition, it is proved that, in the matrix case and in a particular case with 3rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction X is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter t = 0 > 0 exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using t = 0, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets.
Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina
Fil: Cichocki, Andrzej. Brain Science Institute. Riken; Japón - Materia
-
Compressed sensing
Kronecker-CS
Low-rank approximations
Multiway analysis - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/5832
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Stable, robust and super fast reconstruction of tensors using multi-way projectionsCaiafa, Cesar FedericoCichocki, AndrzejCompressed sensingKronecker-CSLow-rank approximationsMultiway analysishttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an Nth-order data tensor X from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order N. In addition, it is proved that, in the matrix case and in a particular case with 3rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction X is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter t = 0 > 0 exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using t = 0, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets.Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); ArgentinaFil: Cichocki, Andrzej. Brain Science Institute. Riken; JapónInstitute of Electrical and Electronics Engineers2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/5832Caiafa, Cesar Federico; Cichocki, Andrzej; Stable, robust and super fast reconstruction of tensors using multi-way projections; Institute of Electrical and Electronics Engineers; IEEE Transactions On Signal Processing; 63; 3; 1-2015; 780-7931053-587Xenginfo:eu-repo/semantics/altIdentifier/doi/10.1109/TSP.2014.2385040info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6994852info:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1406.3295v2info:eu-repo/semantics/altIdentifier/arxiv/1406.3295v2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:58:05Zoai:ri.conicet.gov.ar:11336/5832instacron: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 09:58:06.073CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
title |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
spellingShingle |
Stable, robust and super fast reconstruction of tensors using multi-way projections Caiafa, Cesar Federico Compressed sensing Kronecker-CS Low-rank approximations Multiway analysis |
title_short |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
title_full |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
title_fullStr |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
title_full_unstemmed |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
title_sort |
Stable, robust and super fast reconstruction of tensors using multi-way projections |
dc.creator.none.fl_str_mv |
Caiafa, Cesar Federico Cichocki, Andrzej |
author |
Caiafa, Cesar Federico |
author_facet |
Caiafa, Cesar Federico Cichocki, Andrzej |
author_role |
author |
author2 |
Cichocki, Andrzej |
author2_role |
author |
dc.subject.none.fl_str_mv |
Compressed sensing Kronecker-CS Low-rank approximations Multiway analysis |
topic |
Compressed sensing Kronecker-CS Low-rank approximations Multiway analysis |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an Nth-order data tensor X from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order N. In addition, it is proved that, in the matrix case and in a particular case with 3rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction X is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter t = 0 > 0 exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using t = 0, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets. Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina Fil: Cichocki, Andrzej. Brain Science Institute. Riken; Japón |
description |
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an Nth-order data tensor X from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order N. In addition, it is proved that, in the matrix case and in a particular case with 3rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction X is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter t = 0 > 0 exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using t = 0, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-01 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/5832 Caiafa, Cesar Federico; Cichocki, Andrzej; Stable, robust and super fast reconstruction of tensors using multi-way projections; Institute of Electrical and Electronics Engineers; IEEE Transactions On Signal Processing; 63; 3; 1-2015; 780-793 1053-587X |
url |
http://hdl.handle.net/11336/5832 |
identifier_str_mv |
Caiafa, Cesar Federico; Cichocki, Andrzej; Stable, robust and super fast reconstruction of tensors using multi-way projections; Institute of Electrical and Electronics Engineers; IEEE Transactions On Signal Processing; 63; 3; 1-2015; 780-793 1053-587X |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1109/TSP.2014.2385040 info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6994852 info:eu-repo/semantics/altIdentifier/doi/ info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1406.3295v2 info:eu-repo/semantics/altIdentifier/arxiv/1406.3295v2 |
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 application/pdf |
dc.publisher.none.fl_str_mv |
Institute of Electrical and Electronics Engineers |
publisher.none.fl_str_mv |
Institute of Electrical and Electronics Engineers |
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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1842269500708225024 |
score |
13.13397 |