This paper first presents a condensed state of art on multiresolution analysis using polyharmonic splines: definition and main properties of polyharmonic splines, construction of B-splines and wavelets, decomposition and reconstruction filters; properties of the so-obtained operators, convergence result and applications are given. Second this paper presents some new results on this topic: scattered data wavelet, new polyharmonic scaling functions and associated filters. Fourier transform is of extensive use to derive the tools of the various multiresolution analysis. © 2008 Springer Science+Business Media, LLC.
Rabut, C., & Rossini, M. (2008). Polyharmonic multiresolution analysis: an overview and some new results. NUMERICAL ALGORITHMS, 48(1-3), 135-160 [10.1007/s11075-008-9173-z].
Polyharmonic multiresolution analysis: An overview and some new results
ROSSINI, MILVIA FRANCESCA
2008
Abstract
This paper first presents a condensed state of art on multiresolution analysis using polyharmonic splines: definition and main properties of polyharmonic splines, construction of B-splines and wavelets, decomposition and reconstruction filters; properties of the so-obtained operators, convergence result and applications are given. Second this paper presents some new results on this topic: scattered data wavelet, new polyharmonic scaling functions and associated filters. Fourier transform is of extensive use to derive the tools of the various multiresolution analysis. © 2008 Springer Science+Business Media, LLC.
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