TY - EJOUR
DO - 10.1109/ICASSP.2005.1416086
AB - 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.
T1 - Exponential-Spline Wavelet Bases
IS - Philadelphia PA, USA
DA - 2005
AU - Khalidov, I.
AU - Unser, M.
JF - Proceedings of the IEEE Thirtieth International Conference on Acoustics, Speech, and Signal Processing (ICASSP'05)
SP - 625–628
EP - 625–628
PB - IEEE
ID - 211355
UR - http://bigwww.epfl.ch/publications/khalidov0501.html
UR - http://bigwww.epfl.ch/publications/khalidov0501.pdf
UR - http://bigwww.epfl.ch/publications/khalidov0501.ps
ER -