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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. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear multiresolution scheme within Harten’s framework [A. Harten, Discrete multiresolution analysis and generalized wavelets, J. Appl. Numer. Math. 12 (1993) 153–192; A. Harten, Multiresolution representation of data II, SIAM J. Numer. Anal. 33 (3) (1996) 1205–1256] is presented. It is based on a centered piecewise polynomial interpolation fully adapted to discontinuities. Compression properties of the multiresolution scheme are studied on various numerical experiments on images. [Copyright &y& Elsevier]