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Article Dans Une Revue Mathematics of Computation Année : 2021

On the construction of multiresolution analyses Associated to general subdivision schemes

Résumé

Subdivision schemes are widely used in numerical mathematics such as signal/image approximation, analysis and control of data or numerical analysis. However, to develop their full power, subdivision schemes should be incorporated into a multiresolution analysis that, mimicking wavelet analyses, provides a multi-scale decomposition of a function, a curve, or a surface. The ingredients needed to define a multiresolution analysis associated to a subdivision scheme are a decimation scheme and detail operators. Their construction is not straightforward as soon as the subdivision scheme is non-interpolatory. This paper is devoted to the construction of decimation schemes and detail operators compatible with general subdivision schemes, including non-linear ones. Analysis of the performances of the constructed analyses is carried out. Some numerical applications are presented in the framework of image approximation.
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Dates et versions

hal-03377373 , version 1 (14-10-2021)

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Zhiqing Kui, Jean Baccou, Jacques Liandrat. On the construction of multiresolution analyses Associated to general subdivision schemes. Mathematics of Computation, 2021, 90, pp.2185-2208. ⟨10.1090/mcom/3646⟩. ⟨hal-03377373⟩
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