On the Design of Multi-Dimensional Compactly Supported Parseval Framelets with Directional Characteristics

TL;DR

This paper introduces a novel method for designing multi-dimensional, compactly supported, directional framelets with specific vanishing moments and symmetries, useful for signal processing applications.

Contribution

It presents a new construction approach for multi-dimensional framelets with directional features, small support, and customizable filters derived from refinable functions.

Findings

Constructed framelets exhibit directional characteristics and compact support.

Filters have few non-zero coefficients and can serve as finite-difference operators.

The method allows for customizable orientations and symmetries.

Abstract

In this paper, we propose a new method for the construction of multi-dimensional, wavelet-like families of affine frames, commonly referred to as framelets, with specific directional characteristics, small and compact support in space, directional vanishing moments (DVM), and axial symmetries or anti-symmetries. The framelets we construct arise from readily available refinable functions. The filters defining these framelets have few non-zero coefficients, custom-selected orientations and can act as finite-difference operators.