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

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.

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Correspondence to M. Fuchs.

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Translated from Problemy Matematicheskogo Analiza 90, January 2018, pp. 91-105.

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Fuchs, M., Müller, J. A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates. J Math Sci 228, 705–722 (2018). https://doi.org/10.1007/s10958-017-3648-1

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