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On the Construction of Multiresolution Analysis Compatible with General Subdivisions

Abstract : Subdivision schemes are widely used for rapid curve or surface generation. Recent developments have produced various schemes, in particular non-linear, non-interpolatory or non-uniform.To be used in compression, analysis or control of data, subdivision schemes should be incorporated in a multiresolution analysis that, mimicking wavelet analyses, provides a multi-scale decomposition of a signal, a curve, or a surface. The ingredients needed to define a multiresolution analysis associated with a subdivision scheme are decimation scheme and detail operators. Their construction is straightforward when the multiresolution scheme is interpolatory.This thesis is devoted to the construction of decimation schemes and detail operators compatible with general subdivision schemes. We start with a generic construction in the uniform (but not interpolatory) case and then generalize to non-uniform and non-linear situations. Applying these results, we build multiresolution analyses that are compatible with many recently developed schemes. Analysis of the performances of the constructed analyses is carried out. We present numerical applications in image compression.
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Zhiqing Kui. On the Construction of Multiresolution Analysis Compatible with General Subdivisions. General Mathematics [math.GM]. Ecole Centrale Marseille, 2018. English. ⟨NNT : 2018ECDM0002⟩. ⟨tel-01841362⟩

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