A remark on the denoising of greyscale images using energy densities with varying growth rates

Martin Fuchs; Jan Mueller

doi:10.1007/s10958-017-3648-1

paper

A remark on the denoising of greyscale images using energy densities with varying growth rates

arXiv:1803.10534 · doi:10.1007/s10958-017-3648-1

Abstract

We prove the solvability in Sobolev spaces for a class of variational problems related to the TV-model proposed by Rudin, Osher and Fatemi in [1] for the denoising of greyscale images. In contrast to their approach we discuss energy densities with variable growth rates depending on $∣\nabla u ∣$ in a rather general form including functionals of $(1, p)$ -growth.