Construction of Multiscaling Functions with Approximation and Symmetry
Gerlind Plonka, Vasily Strela · SIAM Journal on Mathematical Analysis · 1998
This paper presents a new and efficient way to create multiscaling functions with given approximation order, regularity, symmetry, and short support. Previous techniques were operating in time domain and required the solution of large systems of nonlinear equations. By switching to the frequency domain and employing the latest results of the multiwavelet theory we are able to elaborate asimple and efficient method of construction of multiscaling functions. Our algorithm is based on a recently found factorization of the refinement mask through the two-scale similarity transform (TST). Theoretical results and new examples are presented.