UCL Discovery

Abstract

We propose a method for analysis of localised relationships between multiple two-dimensional signals, or images, that naturally treats the local phase structure and local orientation of any variation in the observed images. The method is based on using several non-separable wavelet decompositions of the images. The set of mother wavelets used are optimally concentrated isotropic orthogonal wavelet functions extended to a triplet of functions using the Riesz transform, so that directional structure can be detected. The full set of triplet wavelet transform coefficients of two images can be used to extract local oscillatory components of the images present at a given spatial and scale point, and subsequently used to determine the local coherence and phase shift between the two images. The determination of the local phase and orientation involves calculating the continuous wavelet transform (CWT) of the images, then forming the scalogram matrix from these CWTs, and calculating the wavelet coherence. Robust estimates can be constructed by averaging over wavelet coefficients. extending Thomson's method to isotropically localised two-dimensional decompositions.