Fully symmetric frame scaling functions and derived framelets

Abstract

Due to resilience to background noise, avoidance of linear phase distortion, and stability of redundant representation, various simply symmetric frame scaling functions and derived framelets are becoming widely-used tools in data processing and transmission systems. In this study, we will reveal topological features (range, diameter, origin behavior, etc.) of spectral domain of fully symmetric frame scaling functions in the higher-dimensional space. Moreover, we present sufficient and necessary conditions for fully symmetric frame scaling functions with cube-shaped, sphere-shaped and ellipsoid-shape spectral domains. At the same time, we give the construction of fully symmetric frame scaling function and derived framelets with fully symmetry.