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A variational approach to removing multiplicative noise. (English) Zbl 1151.68713
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.

MSC:
 68U10 Image processing (computing aspects) 94A08 Image processing (compression, reconstruction, etc.) 49J40 Variational methods including variational inequalities 35A15 Variational methods (PDE) 35B45 A priori estimates for solutions of PDE 35B50 Maximum principles (PDE)