Exponential-Spline Wavelet Bases

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of $ L _{ 2 } $ , with some remarkable properties. The wavelets, which are characterized by a set of poles and zeros, have an explicit analytical form (exponential spline). They are nonstationary is the sense that they are scale-dependent and that they are not necessarily the dilates of one another. They behave like multi-scale versions of some underlying differential operator L; in particular, they are orthogonal to the exponentials that are in the null space of L. The corresponding wavelet transforms are implemented efficiently using an adaptation of Mallat's filterbank algorithm.


Published in:
Proceedings of the IEEE Thirtieth International Conference on Acoustics, Speech, and Signal Processing (ICASSP'05), Philadelphia PA, USA, 625–628
Year:
2005
Publisher:
IEEE
Laboratories:




 Record created 2015-09-18, last modified 2018-11-14

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