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Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration

The effectiveness of variational methods for restoring images corrupted by Poisson noise strongly depends on the suitable selection of the regularization parameter balancing the effect of the regulation term(s) and the generalized Kullback–Liebler divergence data term. One of the approaches still co...

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Autores principales: Bevilacqua, Francesca, Lanza, Alessandro, Pragliola, Monica, Sgallari, Fiorella
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8777801/
https://www.ncbi.nlm.nih.gov/pubmed/35049842
http://dx.doi.org/10.3390/jimaging8010001
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author Bevilacqua, Francesca
Lanza, Alessandro
Pragliola, Monica
Sgallari, Fiorella
author_facet Bevilacqua, Francesca
Lanza, Alessandro
Pragliola, Monica
Sgallari, Fiorella
author_sort Bevilacqua, Francesca
collection PubMed
description The effectiveness of variational methods for restoring images corrupted by Poisson noise strongly depends on the suitable selection of the regularization parameter balancing the effect of the regulation term(s) and the generalized Kullback–Liebler divergence data term. One of the approaches still commonly used today for choosing the parameter is the discrepancy principle proposed by Zanella et al. in a seminal work. It relies on imposing a value of the data term approximately equal to its expected value and works well for mid- and high-count Poisson noise corruptions. However, the series truncation approximation used in the theoretical derivation of the expected value leads to poor performance for low-count Poisson noise. In this paper, we highlight the theoretical limits of the approach and then propose a nearly exact version of it based on Monte Carlo simulation and weighted least-square fitting. Several numerical experiments are presented, proving beyond doubt that in the low-count Poisson regime, the proposed modified, nearly exact discrepancy principle performs far better than the original, approximated one by Zanella et al., whereas it works similarly or slightly better in the mid- and high-count regimes.
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spelling pubmed-87778012022-01-22 Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration Bevilacqua, Francesca Lanza, Alessandro Pragliola, Monica Sgallari, Fiorella J Imaging Article The effectiveness of variational methods for restoring images corrupted by Poisson noise strongly depends on the suitable selection of the regularization parameter balancing the effect of the regulation term(s) and the generalized Kullback–Liebler divergence data term. One of the approaches still commonly used today for choosing the parameter is the discrepancy principle proposed by Zanella et al. in a seminal work. It relies on imposing a value of the data term approximately equal to its expected value and works well for mid- and high-count Poisson noise corruptions. However, the series truncation approximation used in the theoretical derivation of the expected value leads to poor performance for low-count Poisson noise. In this paper, we highlight the theoretical limits of the approach and then propose a nearly exact version of it based on Monte Carlo simulation and weighted least-square fitting. Several numerical experiments are presented, proving beyond doubt that in the low-count Poisson regime, the proposed modified, nearly exact discrepancy principle performs far better than the original, approximated one by Zanella et al., whereas it works similarly or slightly better in the mid- and high-count regimes. MDPI 2021-12-23 /pmc/articles/PMC8777801/ /pubmed/35049842 http://dx.doi.org/10.3390/jimaging8010001 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Bevilacqua, Francesca
Lanza, Alessandro
Pragliola, Monica
Sgallari, Fiorella
Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration
title Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration
title_full Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration
title_fullStr Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration
title_full_unstemmed Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration
title_short Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration
title_sort nearly exact discrepancy principle for low-count poisson image restoration
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8777801/
https://www.ncbi.nlm.nih.gov/pubmed/35049842
http://dx.doi.org/10.3390/jimaging8010001
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