In 1992 Rudin, Osher, and Fatemi (ROF) introduced variational smoothing using the bounded-variation semi-norm as a measure of image smoothness. We investigate the convergence of a new method for numerically approximating the solution of the original variational problem. We also introduce a variational problem that uses a Besov space that is slightly larger than BV to measure smoothness. Here the numerical method is slightly more complicated and the solutions have some different qualitative properties than the original ROF method.
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