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Title: A Remark on 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 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.

Authors:
;  [1]
  1. Universität des Saarlandes, Fachbereich 6.1 Mathematik (Germany)
Publication Date:
OSTI Identifier:
22771587
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 228; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ENERGY DENSITY; FUNCTIONALS; IMAGES; MATHEMATICAL SPACE; VARIATIONAL METHODS

Citation Formats

Fuchs, M., E-mail: fuchs@math.uni-sb.de, and Müller, J., E-mail: jmueller@math.uni-sb.de. A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates. United States: N. p., 2018. Web. doi:10.1007/S10958-017-3648-1.
Fuchs, M., E-mail: fuchs@math.uni-sb.de, & Müller, J., E-mail: jmueller@math.uni-sb.de. A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates. United States. doi:10.1007/S10958-017-3648-1.
Fuchs, M., E-mail: fuchs@math.uni-sb.de, and Müller, J., E-mail: jmueller@math.uni-sb.de. Thu . "A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates". United States. doi:10.1007/S10958-017-3648-1.
@article{osti_22771587,
title = {A Remark on Denoising of Greyscale Images Using Energy Densities with Varying Growth Rates},
author = {Fuchs, M., E-mail: fuchs@math.uni-sb.de and Müller, J., E-mail: jmueller@math.uni-sb.de},
abstractNote = {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.},
doi = {10.1007/S10958-017-3648-1},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 6,
volume = 228,
place = {United States},
year = {2018},
month = {2}
}