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| HAL : hal-00722743, version 3 |
| DOI : 10.1007/s10851-013-0420-0 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Mathematical Imaging and Vision (2013) - |
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| Versions disponibles : | v1 (05-08-2012) | v2 (16-10-2012) | v3 (06-02-2013) |
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| Fully smoothed ℓ1-TV models: Bounds for the minimizers and parameter choice |
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| F. Baus 1Mila Nikolova 2 |
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| (2013) |
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| We consider a class of convex functionals that can be seen as C1 smooth approximations of the ℓ1-TV model. The minimizers of such functionals were shown to exhibit a qualitatively different behavior compared to the nonsmooth ℓ1-TV model [12]. Here we focus on the way the parameters involved in these functionals determine the features of the minimizers u*. We give explicit relationships between the minimizers and these parameters. Given an input digital image f, we prove that the error ∥u*−f∥_infty obeys b−ε ≤ ∥u*−f∥_infty ≤b where b is a constant independent of the input image. Further we can set the parameters so that ε > 0 is arbitrarily close to zero. More precisely, we exhibit explicit formulae relating the model parameters, the input image f and the values b and ε. Conversely, we can fix the parameter values so that the error ∥u*−f∥_infty satisfy some prescribed b, ε. All theoretical results are confirmed using numerical tests on natural digital images of different sizes with disparate content and quality. |
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| 1 : | University of Kaiserslautern |
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University of Kaiserslautern |
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| 2 : | Centre de Mathématiques et de Leurs Applications (CMLA) |
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CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan |
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| Domaine | : | Mathématiques/Analyse numérique |
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| Parameter estimation for smoothed ℓ1−TV model – Histogram specification – Quantisation noise – ℓ∞ error – Convex optimization – image processing |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00722743, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00722743 | |
| oai:hal.archives-ouvertes.fr:hal-00722743 | |
| Contributeur : Mila Nikolova | |
| Soumis le : Lundi 4 Février 2013, 20:03:24 | |
| Dernière modification le : Mercredi 6 Février 2013, 09:29:51 | |
