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Exponential-Spline Wavelet Bases

I. Khalidov, M. Unser

Proceedings of the Thirtieth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'05), Philadelphia PA, USA, March 18-23, 2005, pp. IV-625-IV-628.

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 L2, 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.

AUTHOR="Khalidov, I. and Unser, M.",
TITLE="Exponential-Spline Wavelet Bases",
BOOKTITLE="Proceedings of the {IEEE} Thirtieth International Conference
        on Acoustics, Speech, and Signal Processing ({ICASSP'05})",
address="Philadelphia PA, USA",
month="March 18-23,",

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