The Dual-Tree Complex Wavelet Transform: A New Technique For Shift Invariance And Directional Filters

Abstract

A new implementation of the Discrete Wavelet Transform is presented, suitable for a range of signal and image processing applications. It employs a dual tree of wavelet filters to obtain the real and imaginary parts of complex wavelet coefficients. This introduces limited redundancy (4:1 for 2-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency. An application to texture synthesis is presented. 1. INTRODUCTION Although the Discrete Wavelet Transform (DWT) in its maximally decimated form (Mallat's dyadic filter tree [1]) has established an impressive reputation as a tool for image compression, its use for other signal analysis and reconstruction tasks has been hampered by two main disadvantages: ffl Lack of shift invariance, which means that small shifts in the input...