Aubert, Gilles; Aujol, Jean-François A variational approach to removing multiplicative noise. (English) Zbl 1151.68713 SIAM J. Appl. Math. 68, No. 4, 925-946 (2008). Summary: This paper focuses on the problem of multiplicative noise removal. We draw our inspiration from the modeling of speckle noise. By using a MAP estimator, we can derive a functional whose minimizer corresponds to the denoised image we want to recover. Although the functional is not convex, we prove the existence of a minimizer and we show the capability of our model on some numerical examples. We study the associated evolution problem, for which we derive existence and uniqueness results for the solution. We prove the convergence of an implicit scheme to compute the solution. Cited in 2 ReviewsCited in 126 Documents MSC: 68U10 Computing methodologies for image processing 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory 49J40 Variational inequalities 35A15 Variational methods applied to PDEs 35B45 A priori estimates in context of PDEs 35B50 Maximum principles in context of PDEs Keywords:calculus of variation; functional analysis; \(BV\); variational approach; multiplicative noise; speckle noise; image restoration PDFBibTeX XMLCite \textit{G. Aubert} and \textit{J.-F. Aujol}, SIAM J. Appl. Math. 68, No. 4, 925--946 (2008; Zbl 1151.68713) Full Text: DOI