CONSTRUCTION OF MULTISCALING FUNCTIONS WITH APPROXIMATION AND SYMMETRY

This paper presents a new and efficient way to create multiscaling fun ctions with given approximation order, regularity, symmetry, and short support. Previous techniques were operating in time domain and requir ed the solution of large systems of nonlinear equations. By switching to the frequency domain and employing the latest results of the multiw avelet theory we are able to elaborate a simple and efficient method o f construction of multiscaling functions. Our algorithm is based on a recently found factorization of the refinement mask through the two-sc ale similarity transform (TST). Theoretical results and new examples a re presented.