A guide to the TV zoo. (English) Zbl 1342.94014
Burger, Martin (ed.) et al., Level set and PDE based reconstruction methods in imaging. Lecture notes given at the CIME summer school, Cetraro, Italy, September 2008. Cham: Springer; Florence: Fondazione CIME (ISBN 978-3-319-01711-2/pbk; 978-3-319-01712-9/ebook). Lecture Notes in Mathematics 2090. CIME Foundation Subseries, 1-70 (2013).
Summary: Total variation methods and similar approaches based on regularizations with \(\ell^{1}\)-type norms (and seminorms) have become a very popular tool in image processing and inverse problems due to peculiar features that cannot be realized with smooth regularizations. In particular total variation techniques had particular success due to their ability to realize cartoon-type reconstructions with sharp edges. Due to an explosion of new developments in this field within the last decade it is a difficult task to keep an overview of the major results in analysis, the computational schemes, and the application fields. With these lectures we attempt to provide such an overview, of course biased by our major lines of research.
We are focusing on the basic analysis of total variation methods and the extension of the original ROF-denoising model due various application fields. Furthermore we provide a brief discussion of state-of-the art computational methods and give an outlook to applications in different disciplines. 205 Refs.
For the entire collection see [Zbl 1277.94002].
We are focusing on the basic analysis of total variation methods and the extension of the original ROF-denoising model due various application fields. Furthermore we provide a brief discussion of state-of-the art computational methods and give an outlook to applications in different disciplines. 205 Refs.
For the entire collection see [Zbl 1277.94002].
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 90C25 | Convex programming |
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