Construction of Pseudo-Spline Tight Wavelet Frames Via Multiresulution Analysis

Abstract

The constructions of pseudo-spline tight frames were first introduced for the first time by I. Daubechies et al to construct tight framelets with desired approximation orders via the unitary extension principle (UEP). Pseudo-splines provide a rich family of refinable functions and the tight frame system derived from them normally gives better approximation order and other good properties than that derived from B-splines which are one of the special classes of pseudo-splines. This paper discusses the construction of tight wavelet frame with some essential properties, such as regularity and high approximation, and presents the construction of tight wavelet frames derived from the pseudo-splines via UEP and OEP (Oblique Extension Principle).