CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI.
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| Title: | CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI. |
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| Authors: | Simeoni, Matthieu1 (AUTHOR) matthieu.simeoni@epfl.ch, Besson, Adrien2 (AUTHOR) adribesson@gmail.com, Hurley, Paul3 (AUTHOR) Paul.Hurley@westernsydney.edu.au, Vetterli, Martin4 (AUTHOR) martin.vetterli@epfl.ch |
| Source: | IEEE Transactions on Signal Processing. 2021, Vol. 69, p42-57. 16p. |
| Subjects: | Signal reconstruction, Genealogy, Length measurement, Constrained optimization, Computer simulation, Fourier series |
| Abstract: | Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for handling cases with arbitrary linear measurement models. In this context, signal reconstruction amounts to solving a joint constrained optimisation problem, yielding estimates of both the Fourier series coefficients of the Dirac stream and its so-called annihilating filter, involved in the regularisation term. This optimisation problem is however highly non convex and non linear in the data. Moreover, the proposed numerical solver is computationally intensive and without convergence guarantee. In this work, we propose an implicit formulation of the genFRI problem. To this end, we leverage a novel regularisation term which does not depend explicitly on the unknown annihilating filter yet enforces sufficient structure in the solution for stable recovery. The resulting optimisation problem is still non convex, but simpler since linear in the data and with less unknowns. We solve it by means of a provably convergent proximal gradient descent (PGD) method. Since the proximal step does not admit a simple closed-form expression, we propose an inexact PGD method, coined Cadzow plug-and-play gradient descent (CPGD). The latter approximates the proximal steps by means of Cadzow denoising, a well-known denoising algorithm in FRI. We provide local fixed-point convergence guarantees for CPGD. Through extensive numerical simulations, we demonstrate the superiority of CPGD against the state-of-the-art in the case of non uniform time samples. [ABSTRACT FROM AUTHOR] |
| Copyright of IEEE Transactions on Signal Processing is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 148948579 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Simeoni%2C+Matthieu%22">Simeoni, Matthieu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> matthieu.simeoni@epfl.ch</i><br /><searchLink fieldCode="AR" term="%22Besson%2C+Adrien%22">Besson, Adrien</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> adribesson@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Hurley%2C+Paul%22">Hurley, Paul</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> Paul.Hurley@westernsydney.edu.au</i><br /><searchLink fieldCode="AR" term="%22Vetterli%2C+Martin%22">Vetterli, Martin</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> martin.vetterli@epfl.ch</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Signal+Processing%22">IEEE Transactions on Signal Processing</searchLink>. 2021, Vol. 69, p42-57. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Signal+reconstruction%22">Signal reconstruction</searchLink><br /><searchLink fieldCode="DE" term="%22Genealogy%22">Genealogy</searchLink><br /><searchLink fieldCode="DE" term="%22Length+measurement%22">Length measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Constrained+optimization%22">Constrained optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+series%22">Fourier series</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for handling cases with arbitrary linear measurement models. In this context, signal reconstruction amounts to solving a joint constrained optimisation problem, yielding estimates of both the Fourier series coefficients of the Dirac stream and its so-called annihilating filter, involved in the regularisation term. This optimisation problem is however highly non convex and non linear in the data. Moreover, the proposed numerical solver is computationally intensive and without convergence guarantee. In this work, we propose an implicit formulation of the genFRI problem. To this end, we leverage a novel regularisation term which does not depend explicitly on the unknown annihilating filter yet enforces sufficient structure in the solution for stable recovery. The resulting optimisation problem is still non convex, but simpler since linear in the data and with less unknowns. We solve it by means of a provably convergent proximal gradient descent (PGD) method. Since the proximal step does not admit a simple closed-form expression, we propose an inexact PGD method, coined Cadzow plug-and-play gradient descent (CPGD). The latter approximates the proximal steps by means of Cadzow denoising, a well-known denoising algorithm in FRI. We provide local fixed-point convergence guarantees for CPGD. Through extensive numerical simulations, we demonstrate the superiority of CPGD against the state-of-the-art in the case of non uniform time samples. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IEEE Transactions on Signal Processing is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1109/TSP.2020.3041089 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 42 Subjects: – SubjectFull: Signal reconstruction Type: general – SubjectFull: Genealogy Type: general – SubjectFull: Length measurement Type: general – SubjectFull: Constrained optimization Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Fourier series Type: general Titles: – TitleFull: CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Simeoni, Matthieu – PersonEntity: Name: NameFull: Besson, Adrien – PersonEntity: Name: NameFull: Hurley, Paul – PersonEntity: Name: NameFull: Vetterli, Martin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 1053587X Numbering: – Type: volume Value: 69 Titles: – TitleFull: IEEE Transactions on Signal Processing Type: main |
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