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Pyramidal Algorithms For Littlewood-Paley Decompositions

By M.A. Muschietti, B. Torrésani and B. Torr Esani


. It is well known that with any usual multiresolution analysis of L 2 (IR) is associated a pyramidal algorithm for the computation of the corresponding wavelet coefficients. It is shown that an approximate pyramidal algorithm may be associated with more general Littlewood-Paley decompositions. Accuracy estimates are provided for such approximate algorithms. Finally, some explicit examples are studied. 1. Introduction. Wavelet analysis has emerged in the past ten years as a completely generic methodology for solving problems in many different areas such as mathematical analysis and operator theory, numerical analysis, signal and image processing, computer vision, computer musics, turbulence, astrophysics for instance. Among the advantages of wavelet decompositions, their relative simplicity and the existence of associated fast algorithms are ones of the most important [1] [6]. There exist essentially two different approaches to wavelets, namely the discrete and the continuous ones. R..

Year: 1993
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