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An introduction to total variation for image analysis. (English) Zbl 1209.94004
Fornasier, Massimo (ed.), Theoretical foundations and numerical methods for sparse recovery. Papers based on the presentations of the summer school “Theoretical foundations and numerical methods for sparse recovery”, Vienna, Austria, August 31 – September 4, 2009. Berlin: Walter de Gruyter (ISBN 978-3-11-022614-0/hbk; 978-3-11-022615-7/ebook). Radon Series on Computational and Applied Mathematics 9, 263-340 (2010).
Summary: These notes address various theoretical and practical topics related to total variation based image reconstruction. They focus first on some theoretical results on functions which minimize the total variation, and in a second part, describe a few standard and less standard algorithms to minimize the total variation in a finite-differences setting, with a series of applications from simple denoising to stereo, or deconvolution issues, and even more exotic uses like the minimization of minimal partition problems.
For the entire collection see [Zbl 1195.94005].

MSC:
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
26B30 Absolutely continuous real functions of several variables, functions of bounded variation
26B15 Integration of real functions of several variables: length, area, volume
49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49M25 Discrete approximations in optimal control
49M29 Numerical methods involving duality
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65K15 Numerical methods for variational inequalities and related problems
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