Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a continuous-domain regularized inverse problem wi...

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Autores principales:	Thomas Debarre, Shayan Aziznejad, Michael Unser
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Composite signals total variation Tikhonov regularization B-splines Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/1c7cf37aba1449319c293363c48855cc
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spelling	oai:doaj.org-article:1c7cf37aba1449319c293363c48855cc2021-11-18T00:11:40ZContinuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals2644-132210.1109/OJSP.2021.3116482https://doaj.org/article/1c7cf37aba1449319c293363c48855cc2021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9552595/https://doaj.org/toc/2644-1322We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a continuous-domain regularized inverse problem with multiple penalties. We prove that these penalties induce reconstructed signals that indeed take the desired form of the sum of a sparse and a smooth component. We then discretize this problem using Riesz bases, which yields a discrete problem that can be solved by standard algorithms. Our discretization is exact in the sense that we are solving the continuous-domain problem over the search space specified by our bases without any discretization error. We propose a complete algorithmic pipeline and demonstrate its feasibility on simulated data.Thomas DebarreShayan AziznejadMichael UnserIEEEarticleComposite signalstotal variationTikhonov regularizationB-splinesElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Open Journal of Signal Processing, Vol 2, Pp 545-558 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Composite signals total variation Tikhonov regularization B-splines Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Composite signals total variation Tikhonov regularization B-splines Electrical engineering. Electronics. Nuclear engineering TK1-9971 Thomas Debarre Shayan Aziznejad Michael Unser Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
description	We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a continuous-domain regularized inverse problem with multiple penalties. We prove that these penalties induce reconstructed signals that indeed take the desired form of the sum of a sparse and a smooth component. We then discretize this problem using Riesz bases, which yields a discrete problem that can be solved by standard algorithms. Our discretization is exact in the sense that we are solving the continuous-domain problem over the search space specified by our bases without any discretization error. We propose a complete algorithmic pipeline and demonstrate its feasibility on simulated data.
format	article
author	Thomas Debarre Shayan Aziznejad Michael Unser
author_facet	Thomas Debarre Shayan Aziznejad Michael Unser
author_sort	Thomas Debarre
title	Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
title_short	Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
title_full	Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
title_fullStr	Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
title_full_unstemmed	Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals
title_sort	continuous-domain formulation of inverse problems for composite sparse-plus-smooth signals
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/1c7cf37aba1449319c293363c48855cc
work_keys_str_mv	AT thomasdebarre continuousdomainformulationofinverseproblemsforcompositesparseplussmoothsignals AT shayanaziznejad continuousdomainformulationofinverseproblemsforcompositesparseplussmoothsignals AT michaelunser continuousdomainformulationofinverseproblemsforcompositesparseplussmoothsignals
_version_	1718425147849834496

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

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