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Multiresolution Framework on the Interval based on Fibonacci Tiling, B–splines and Lifting Scheme

Abstract : In this paper, we introduce a multiresolution analysis on the interval based on non–uniform B– splines defined on the Fibonacci tiling. The construction of the multiscale structure based on the substitution rules of an L–system allows the derivation of a known framework from the regular dyadic setting to a non–uniform setting while limiting the number of different filters to a few and keeping a similar stability. After having explained how our approach fits into a biorthogonal framework, we detail how to build analysis wavelet functions in the B–spline setting. Then the emphasis is put on the definition of boundary scaling and wavelet functions by means of scaling equations. Our implementation of the multiresolution structure is done in such a way that the computation is carried out in place. Finally, a numerical analysis of the stability of the proposed scheme shows its similar behavior to the same multiresolution analysis that would be derived on a dyadic sampling.
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https://hal.archives-ouvertes.fr/hal-01256233
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Last modification on : Wednesday, May 13, 2020 - 4:30:03 PM
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  • HAL Id : hal-01256233, version 1

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Cédric Gérot, Sylvain Meignen. Multiresolution Framework on the Interval based on Fibonacci Tiling, B–splines and Lifting Scheme. [Research Report] GIPSA-lab. 2015. ⟨hal-01256233⟩

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