Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization

Handle URI:
http://hdl.handle.net/10754/598555
Title:
Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization
Authors:
Reyes, Juan Carlos De los; Schönlieb, Carola-Bibiane
Abstract:
We propose a nonsmooth PDE-constrained optimization approach for the determination of the correct noise model in total variation (TV) image denoising. An optimization problem for the determination of the weights corresponding to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. © 2013 American Institute of Mathematical Sciences.
Citation:
Reyes JCD los, Schönlieb C-B (2013) Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization. IPI 7: 1183–1214. Available: http://dx.doi.org/10.3934/ipi.2013.7.1183.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Inverse Problems and Imaging
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Nov-2013
DOI:
10.3934/ipi.2013.7.1183
Type:
Article
ISSN:
1930-8337
Sponsors:
Research partially supported by the Alexander von Humboldt Foundation. CBS acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the Royal Society International Exchanges Award IE110314 for the project High-order Compressed Sensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse & Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust Small Grant on Non-smooth geometric reconstruction for highresolution MRI imaging of fluid transport in bed reactors. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorReyes, Juan Carlos De losen
dc.contributor.authorSchönlieb, Carola-Bibianeen
dc.date.accessioned2016-02-25T13:32:05Zen
dc.date.available2016-02-25T13:32:05Zen
dc.date.issued2013-11en
dc.identifier.citationReyes JCD los, Schönlieb C-B (2013) Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization. IPI 7: 1183–1214. Available: http://dx.doi.org/10.3934/ipi.2013.7.1183.en
dc.identifier.issn1930-8337en
dc.identifier.doi10.3934/ipi.2013.7.1183en
dc.identifier.urihttp://hdl.handle.net/10754/598555en
dc.description.abstractWe propose a nonsmooth PDE-constrained optimization approach for the determination of the correct noise model in total variation (TV) image denoising. An optimization problem for the determination of the weights corresponding to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. © 2013 American Institute of Mathematical Sciences.en
dc.description.sponsorshipResearch partially supported by the Alexander von Humboldt Foundation. CBS acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the Royal Society International Exchanges Award IE110314 for the project High-order Compressed Sensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse & Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust Small Grant on Non-smooth geometric reconstruction for highresolution MRI imaging of fluid transport in bed reactors. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectHuber regularizationen
dc.subjectImage denoisingen
dc.subjectNoise distributionen
dc.subjectPDE-constrained optimizationen
dc.titleImage denoising: Learning the noise model via nonsmooth PDE-constrained optimizationen
dc.typeArticleen
dc.identifier.journalInverse Problems and Imagingen
dc.contributor.institutionEscuela Politecnica Nacional Ecuador, Quito, Ecuadoren
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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