A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates

详细

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