Algorithms to design adaptive biorthogonal MRA generating wavelets
Raghuveer Rao, Joseph O. Chapa · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
The problem of designing a mother wavelet such that this wavelet is as close as possible to a desired signal while it generates, along with a dual, a biorthogonal wavelet decomposition is addressed. It is shown that when the problem is addressed in the frequency domain with bandlimited scaling functions and wavelets, a simple formulation is possible. Further, a closed form sub-optimal solution is possible when the problem is broken down into a series of optimization problems. In the process of the problem formulation, a generalization of the Meyer class of wavelets to the biorthogonal case is obtained.