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On the role of the BV image model in image restoration. (English) Zbl 1035.94501

Cheng, S. Y. (ed.) et al., Recent advances in scientific computing and partial differential equations. International conference on the occasion of Stanley Osher’s 60th birthday, December 12–15, 2002, Hong Kong, China. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3155-0/pbk). Contemp. Math. 330, 25-41 (2003).
Summary: What we believe images are determines how we take actions in image and lower-level vision analysis. In the Bayesian framework, it is manifest in the importance of a good image prior model. This paper intends to give a concise overview on the foundations of vision, its mathematical theory, its computational algorithms, and various classical as well as unexpected new applications of the bounded variation image model, first introduced into image processing by L. Rudin, S. Osher, and E. Fatemi [Physica D 60, 259–268 (1992; Zbl 0780.49028)].
For the entire collection see [Zbl 1024.00038].

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
68U10 Computing methodologies for image processing
62C10 Bayesian problems; characterization of Bayes procedures
65K10 Numerical optimization and variational techniques

Citations:

Zbl 0780.49028
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