Error Bounds for Finite-Difference Methods for Rudin-Osher-Fatemi Image Smoothing

Authors:
Jingyue Wang;Bradley J. Lucier
Affiliations:
jwang@math.uga.edu;lucier@math.purdue.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

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Abstract

We bound the difference between the solution to the continuous Rudin-Osher-Fatemi (ROF) image smoothing model and the solutions to various finite-difference approximations to this model. These bounds apply to “typical” images, i.e., images with edges or with fractal structure. These are the first bounds on the error in numerical methods for ROF smoothing.