Khalidov, I.
Unser, M.
Exponential-Spline Wavelet Bases
Proceedings of the IEEE Thirtieth International Conference on Acoustics, Speech, and Signal Processing (ICASSP'05)
10.1109/ICASSP.2005.1416086
Philadelphia PA, USA
625–628
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 $ 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.
IEEE
2005
http://bigwww.epfl.ch/publications/khalidov0501.html;
http://bigwww.epfl.ch/publications/khalidov0501.pdf;
http://bigwww.epfl.ch/publications/khalidov0501.ps;