Total Variation Projection with First Order Schemes

Jalal M. Fadili 1 Gabriel Peyré 2
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : This article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant. The projection is computed through a dual formulation that is solved by first order non-smooth optimization methods. This yields an iterative algorithm that computes iterative soft thresholding of the dual vector fields. This projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint, or for texture synthesis. Numerical results show that our algorithm competes favorably with state-of-the-art TV projection methods to solve denoising, texture synthesis, inpainting and deconvolution problems.
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Jalal M. Fadili, Gabriel Peyré. Total Variation Projection with First Order Schemes. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2011, 20 (3), pp.657-669. ⟨10.1109/TIP.2010.2072512⟩. ⟨hal-00380491v3⟩

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