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A second-order model for image denoising. (English) Zbl 1203.94006
Summary: We present a variational model for image denoising and/or texture identification. Noise and textures may be modelled as oscillating components of images. The model involves a $L^{2}$-data fitting term and a Tychonov-like regularization term. We choose the $BV^{2}$ norm instead of the classical $BV$ norm. Here $BV^{2}$ is the bounded hessian function space that we define and describe. The main improvement is that we do not observe staircasing effects any longer, during denoising process. Moreover, texture extraction can be performed with the same method. We give existence results and present a discretized problem. An algorithm close to the one set by {\it A. Chambolle} [An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20, 89--97 (2004; \url{doi:10.1023/B:JMIV.0000011320.81911.38})] is used: we prove convergence and present numerical tests.

##### MSC:
 94A08 Image processing (compression, reconstruction, etc.) 65D18 Computer graphics, image analysis, and computational geometry 68U10 Image processing (computing aspects) 65K10 Optimization techniques (numerical methods)
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##### References:
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