On the construction of multiresolution analyses associated to general subdivision schemes

Kui, Zhiqing; Baccou, Jean; Liandrat, Jacques

doi:10.1090/mcom/3646

On the construction of multiresolution analyses associated to general subdivision schemes
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Math. Comp. 90 (2021), 2185-2208 Request permission

Abstract:

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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