Optimization in the construction of nearly cardinal and nearly symmetric wavelets
Neil D. Dizon, Jeffrey A. Hogan, Joseph D. Lakey · 2019
We present two approaches to the construction of scaling functions and wavelets that generate nearly cardinal and nearly symmetric wavelets on the line. The first approach casts wavelet construction as an optimization problem by imposing constraints on the integer samples of the scaling function and its associated wavelet and with an objective function that minimizes deviation from cardinality or symmetry. The second method is an extension of the feasibility approach by Franklin, Hogan, and Tam to allow for symmetry by considering variables generated from uniform samples of the quadrature mirror filter, and is solved via the Douglas-Rachford algorithm.