Construction of Orthonormal Quasi-Shearlets based on quincunx dilation subsampling

TL;DR

This paper develops a new family of orthonormal quasi-shearlet bases using quincunx dilation, ensuring efficient directional analysis with minimal redundancy within the MRA framework.

Contribution

It introduces a novel construction method for orthonormal quasi-shearlet bases based on shift cancellation and identity summation conditions, matching shearlet frequency support.

Findings

Established conditions for orthonormality in quincunx-based wavelets

Constructed a family of quasi-shearlet orthonormal bases

Analyzed limitations imposed by shift cancellation conditions

Abstract

We consider the construction of orthonormal directional wavelet bases in the multi-resolution analysis (MRA) framework with quincunx dilation downsampling. We show that the Parseval frame property in MRA is equivalent to the identity summation and shift cancellation conditions on M functions, which essentially characterize the scaling (father) function and all directional (mother) wavelets. Based on these two conditions, we further derive sufficient conditions for orthonormal bases and build a family of quasishearlet orthonormal bases, that has the same frequency support as that of the least redundant shearlet system. In addition, we study the limitation of our proposed bases design due to the shift cancellation conditions.