Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspaces

We present constructions of biorthogonal wavelets and associated filter banks with optimality using pseudoframes for subspaces (PFFS). PFFS extends the theory of frames in that pseudoframe sequences need not reside within the subspace of interest. In particular, when PFFS is applied to biorthogonal wavelets the underlying flexibility presents opportunities to incorporate optimality, regularity as well as perfect reconstruction into one parametric design approach. This approach reduces certain filter optimization problems to optimization over a free parameter. While past constructions can be reproduced, results with additional optimality are also obtained and presented here with numerical examples. Filter coeffiecients are provided along with graphs are provided and Matlab implementation code is available upon request from the authors.