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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 paper proposes a new class of algorithms to compute the projection onto the set of images with a total variation bounded by a constant. The projection is computed on a dual formulation of the problem that is minimized using either a one-step gradient descent method or a multi-step Nesterov scheme. This yields iterative algorithms that compute soft thresholding of the dual vector fields. We show the convergence of the method with a convergence rate of O(1/k) for the one step method and O(1/k^2) for the multi-step one, where k is the iteration number. The projection algorithm can be used as a building block in several applications, and we illusrtate it by solving linear inverse problems under total variation constraint. Numerical results show that our algorithm competes favorably with state-of-the-art TV projection methods to solve denoising, inpainting and deblurring problems.
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Submitted on : Thursday, July 2, 2009 - 5:03:08 PM
Last modification on : Thursday, November 5, 2020 - 12:58:05 PM
Long-term archiving on: : Monday, October 15, 2012 - 3:01:39 PM

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  • HAL Id : hal-00401251, version 1

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Jalal M. Fadili, Gabriel Peyré. Total Variation Projection with First Order Schemes. ICIP'09, Nov 2009, Cairo, Egypt. pp.1325-1328. ⟨hal-00401251⟩

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