Non-Redundant, Linear-Phase, Semi-Orthogonal, Directional Complex Wavelets

Abstract

The directionality and phase information provided by non-redundant complex wavelet transforms (NCWTs) provide significant potential benefits for image/video processing and compression applications. However, because existing NCWTs are created by downsampling filtered wavelet coefficients, the finest scale of these transforms has resolution 4x lower than the real input signal. In this paper, we propose a linear-phase, semi-orthogonal, directional NCWT design using a novel <i>triband</i> filter bank. At the finest scale, the resulting transform has resolution 3x lower than the real input signal. We provide a design example to demonstrate three important properties for image/video processing applications: directionality, magnitude coherency, and phase coherency.