"An optimization approach to multidimensional wavelets"
Hogan, JeffIngrid Daubechies' construction of compactly supported smooth orthogonal MRA wavelets on the line relied heavily on techniques of complex analysis (such as spectral factorization), many of which are unavailable in the higher-dimensional setting. Constructions of compactly supported, smooth orthogonal MRA wavelets in higher dimensions (with isotropic dilations), on the other hand have proven to be elusive. I will report on unfinished joint work with David Franklin (Newcastle) and Matthew Tam (Goettingen) in which we search for (non-separable) multidimensional wavelets with the help of techniques from optimisation. Potential extension of these constructions to the Clifford-valued case leaves open the possibility of fast algorithms for the processing of multi-variable, multi-channel signals such colour images.