an:05853155
Zbl 1209.94004
Chambolle, Antonin; Caselles, Vicent; Cremers, Daniel; Novaga, Matteo; Pock, Thomas
An introduction to total variation for image analysis
EN
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).
2010
a
94A08 26B30 26B15 49-01 49M25 49M29 65-01 65K15
total variation; variational image reconstruction; functions with bounded variation; level sets; convex optimization; splitting algorithms; denoising; deconvolution; stereo
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].