A structural characterization of compactly supported OEP-based balanced dual multiframelets

Abstract

Compared to scalar framelets, multiframelets have certain advantages, such as relatively smaller supports on generators, high vanishing moments, etc. The balancing property of multiframelets is very desired, as it reflects how efficient vector-valued data can be processed under the corresponding discrete multiframelet transform. Most of the literature studying balanced multiframelets is from the point of view of the function setting, but very few approaches are from the aspect of multiframelet filter banks. In this paper, we study structural characterizations of balanced dual multiframelets from the point of view of the Oblique Extension Principle (OEP). The OEP naturally connects framelets with filter banks, which makes it a very handy tool for analyzing the properties of framelets. With the OEP, we shall characterize compactly supported balanced dual multiframelets through the concept of balanced moment correction filters, which is the key notion that will be introduced in our investigation. The results of this paper demonstrate what essential structures a balanced dual multiframelet has in the most general setting, and bring us a more complete picture to understand balanced multiframelets and their underlying discrete multiframelet transforms.