Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

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Austrian Academy of Sciences Press
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ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
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doi:10.1553/etna_vol59s202



doi:10.1553/etna_vol59s202



Thema: natural
Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Alessandro Lanza, Monica Pragliola, Fiorella Sgallari
PDF Icon  Parameter-free restoration of piecewise smooth images ()
S.  202 - 229
doi:10.1553/etna_vol59s202

Open access

Verlag der Österreichischen Akademie der Wissenschaften


doi:10.1553/etna_vol59s202
Abstract:
We propose a novel strategy for the automatic estimation of the two regularization parameters arising in the image decomposition variational model employed for the restoration task when the underlying corrupting noise is known to be additive white Gaussian. In the model of interest, the target image is decomposed in its piecewise constant and smooth components, with a total variation term penalizing the former and a Tikhonov term acting on the latter. The proposed criterion, which relies on the whiteness property of the noise, extends the residual whiteness principle, originally introduced in the case of a single regularization parameter. The structure of the considered decomposition model allows for an efficient estimation of the pair of unknown parameters, that can be automatically adjusted along the iterations with the alternating direction method of multipliers employed for the numerical solution. The proposed multi-parameter residual whiteness principle is tested on different images with different levels of corruption. The performed tests highlight that the whiteness criterion is particularly effective and robust when moving from a single-parameter to a multi-parameter scenario.

Keywords:  image restoration, image decomposition, whiteness principle, ADMM
  2023/10/30 13:49:31
Object Identifier:  0xc1aa5576 0x003e9035
.

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.



Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at