A new well-posed nonlinear nonlocal diffusion
نویسندگان
چکیده
منابع مشابه
A new well-posed nonlinear nonlocal diffusion
Nonlinear diffusions have successfully been employed to perform a variety of tasks in image processing. In the context of denoising, the Perona-Malik equation is a particularly successful example. In spite of its cherished qualities, it is mathematically ill-posed and has some practical short-comings. In this short paper a new nonlocal nonlinear diffusion is reported upon, which is locally well...
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A modification of the Perona-Malik equation is proposed for which the local nonlinear diffusion term is replaced by a nonlocal term of slightly reduced “strength”. The new equation is globally well-posed (in spaces of classical regularity) and possesses desirable properties from the perspective of image processing. It admits characteristic functions as (formally linearly “stable”) stationary so...
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A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona-Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2010
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.02.040