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Blind deconvolution using bilateral total variation regularization: a theoretical study and application

Abstract : Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong, consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chanâs approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the sharp image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations.
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https://hal-enpc.archives-ouvertes.fr/hal-03177198
Contributeur : Mohammed El Rhabi <>
Soumis le : mardi 23 mars 2021 - 07:22:16
Dernière modification le : mardi 1 juin 2021 - 11:56:16
Archivage à long terme le : : jeudi 24 juin 2021 - 18:08:11

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Idriss El Mourabit, Mohammed El Rhabi, Abdelilah Hakim. Blind deconvolution using bilateral total variation regularization: a theoretical study and application. Applicable Analysis, Taylor & Francis, 2021, pp.1-14. ⟨10.1080/00036811.2021.1903442⟩. ⟨hal-03177198⟩

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