Stable Interpolatory Multiresolution in 3D

Multiresolution transforms are powerful tools in video processing applications because of its flexibility in representing nonstationary signals. For a proper adaptation to the singularities, it is crucial to develop nonlinear schemes. In these applications where some coefficients are modified or discarded we need to have some stability properties. In this paper, three-dimensional multiresolution processing algorithms that ensure this stability are introduced. A prescribed accuracy in various norms is ensured by these strategies. Explicit error bounds are presented. Finally, a numerical experiment using linear and non-linear schemes is performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)