Image decompositions using bounded variation and generalized homogeneous Besov spaces
نویسندگان
چکیده
منابع مشابه
Image Decompositions Using Bounded Variation and Generalized Homogeneous Besov Spaces
This paper is devoted to the decomposition of an image f into u+ v, with u a piecewise-smooth or “cartoon” component, and v an oscillatory component (texture or noise), in a variational approach. Y. Meyer [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series, vol. 22, Amer. Math. Soc., Providence, RI, 2001] proposed refinements of the t...
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We give a corrected proof of Lemma 3.1 in [1]. While the statement of [1, Lemma 3.1] is true, its proof is incorrect. The argument contains a serious defect which can not be easily corrected. The inequality that appears in [1] before (3.5) is not true. If this inequality was true, then we could conclude that, even for a non doubling measure μ, (3.5) was also true. But there exist some non doubl...
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Abstract This paper considers the radial variation function F (r, t) of an analytic function f(z) on the disc D. We examine F (r, t) when f belongs to a Besov space Apq and look for ways in which F imitates the behaviour of f . Regarded as a function of position (r, t) in D, we show that F obeys a certain integral growth condition which is the real variable analogue of that satisfied by f . We ...
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The theory of wavelets and multiresolution analysis is usually developed on R. However, applications of wavelets to image processing and numerical methods for partial differential equations require multiresolution analysis on domains or manifolds in R. The study of multiresolution in these settings is just beginning. Building on the construction of multiresolution on intervals (and cubes in R )...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2007
ISSN: 1063-5203
DOI: 10.1016/j.acha.2007.01.005