On the construction of multiresolution analyses associated to general subdivision schemes

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