A Dual Formulation of the TV-Stokes Algorithm for Image Denoising

Authors:
Christoffer A. Elo;Alexander Malyshev;Talal Rahman
Affiliations:
Department of Mathematics, University of Bergen, Bergen, Norway 5007;Department of Mathematics, University of Bergen, Bergen, Norway 5007;Faculty of Engineering, Bergen University College, Bergen, 5020
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

We propose a fast algorithm for image denoising, which is based on a dual formulation of a recent denoising model involving the total variation minimization of the tangential vector field under the incompressibility condition stating that the tangential vector field should be divergence free. The model turns noisy images into smooth and visually pleasant ones and preserves the edges quite well. While the original TV-Stokes algorithm, based on the primal formulation, is extremely slow, our new dual algorithm drastically improves the computational speed and possesses the same quality of denoising. Numerical experiments are provided to demonstrate practical efficiency of our algorithm.