Some Variations on Total Variation-Based Image Smoothing
MINNESOTA UNIV MINNEAPOLIS INST FOR MATHEMATICS AND ITS APPLICATIONS
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In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm this formulation is in the same spirit as one popularized by Chambolle for a simpler, more anisotropic, finite-difference approximation to the BV seminorm. We introduce a multiscale method for speeding the approximation of both Chambolles original method and of the new formulation of the upwind scheme. We demonstrate numerically that the multiscale method is effective, and we provide numerical examples that illustrate both the qualitative and quantitative behavior of the solutions of the numerical formulations.
- Numerical Mathematics
- Theoretical Mathematics