Name
Abstract | ||
|---|---|---|
Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together ...through fractals. First, we identify and characterize the whole class of self-similar radial basis functions that can be localized to yield conventional multiresolution wavelet bases. Conversely, we prove that for any compactly supported scaling function φ(x), there exists a one-sided central basis function ρ+ (x) that spans the same multiresolution subspaces. The central property is that the multiresolution bases are generated by simple translation of ρ+ without any dilation. We also present an explicit time-domain representation of a scaling function as a sum of harmonic splines. The leading term in the decomposition corresponds to the fractional splines: a recent, continuous-order generalization of the polynomial splines |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1109/78.984733 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
fractals,polynomial approximation,radial basis function networks,signal representation,signal resolution,splines (mathematics),time-domain analysis,wavelet transforms,RBF,compactly supported scaling function,continuous-order generalization,fractals,fractional splines,harmonic splines,linear splines,multiresolution subspaces,multiresolution wavelet bases,nonuniform grids,one-sided central basis function,polynomial splines,self-similar radial basis functions,shifted basis functions,signals representation,time-domain representation | Spline (mathematics),Mathematical optimization,Radial basis function,Mathematical analysis,Fractional wavelet transform,Multiresolution analysis,Linear subspace,Basis function,Mathematics,Wavelet transform,Wavelet | Journal |
Volume | Issue | ISSN |
50 | 3 | 1053-587X |
Citations | PageRank | References |
28 | 1.79 | 17 |
Authors | ||
2 | ||