Fractional generalized splines and signal processing
Signal Processing - Signal processing in UWB communications
Efficient preconditioning for image reconstruction with radial basis functions
Advances in Engineering Software
Computers & Mathematics with Applications
Bidimensional empirical mode decomposition modified for texture analysis
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Analytical footprints: compact representation of elementary singularities in wavelet bases
IEEE Transactions on Signal Processing
A novel method for solving the shape from shading (SFS) problem
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
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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