Three-scale wavelet transforms
Raghuveer Rao, J. Scott Bundonis, Harold H Szu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
Two different problems are investigated. The first is the construction of orthogonal, bandlimited, triadic decompositions. It is shown that the solution involves a scaling function that is a generalization of the Meyer scaling function to the triadic case. The squared sum of the Fourier transform magnitudes of the corresponding wavelet pair displays properties that are a generalization of properties of the Fourier transform of the Meyer wavelet. The paper formulates equations for splitting the sum into two orthogonal wavelets. The second problem is the formulation of a simple, iterative, pseudo-inverse algorithm to provide solution to a triadic extension of the Cohen- Daubechies-Feasuveau method of designing regular, compact biorthogonal wavelets and filter banks.