https://hal-enpc.archives-ouvertes.fr/hal-03177198El Mourabit, IdrissIdrissEl MourabitEcole Supérieure de Technologie d'Essaouira - UCA - Université Cadi Ayyad [Marrakech]El Rhabi, MohammedMohammedEl RhabiINTERACT - Innovation, Territoire, Agriculture et Agro-industrie, Connaissance et Technologie - UniLaSalleHakim, AbdelilahAbdelilahHakimUCA - Université Cadi Ayyad [Marrakech]Blind deconvolution using bilateral total variation regularization: a theoretical study and applicationHAL CCSD2021Blind deconvolutionDeblurringTotal VariationBilateral Total VariationRegularizationRelaxationAlternating Minimization[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA][MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA][MATH] Mathematics [math][INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA][SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processingEl Rhabi, Mohammed2021-03-23 07:22:162022-11-14 12:32:272021-03-24 09:46:53enJournal articleshttps://hal-enpc.archives-ouvertes.fr/hal-03177198/document10.1080/00036811.2021.1903442application/pdf1Blind 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.