The near shift-invariance of the dual-tree complex wavelet transform revisited

TL;DR

This paper provides a quantitative proof demonstrating that the dual-tree complex wavelet transform (DTCWT) offers superior shift-invariance and directional selectivity compared to the traditional discrete wavelet transform (DWT), especially with modulated wavelets.

Contribution

It offers a rigorous quantitative analysis confirming the near shift-invariance property of the DTCWT over the DWT for modulated wavelets.

Findings

DTCWT has higher shift-invariance than DWT.

DTCWT provides better directional selectivity.

Quantitative proof of DTCWT's superiority with modulated wavelets.

Abstract

The dual-tree complex wavelet transform (DTCWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and image processing. This paper presents a quantitative proof of the superiority of the DTCWT over the DWT in case of modulated wavelets.