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

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.