An Upwind Finite-Difference Method for Total Variation-Based Image Smoothing

作者：Chambolle Antonin^*; Levine Stacey E; Lucier Bradley J

来源：SIAM Journal on Imaging Sciences, 2011, 4(1): 277-299.

DOI：10.1137/090752754

• total variation
• image denoising
• finite-difference schemes
• multiscale methods
• upwind schemes

In this paper we study finite-difference approximations to the variational problem using the bounded variation (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 the first author for a simpler, less isotropic, finite-difference approximation to the (isotropic) BV seminorm. We introduce a multiscale method for speeding up the approximation of both Chambolle's 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.

• 出版日期2011