Multiple wavelet analysis of amplitude/frequency modulated images

We consider characterisation and analysis of images with dominant local frequencies: this class contains two-dimensional signals written as sums of amplitude and frequency modulated components. We introduce the usage of the multiple vector-valued continuous Morse wavelets for analysis of such signals. We calculate the continuous wavelet transform and the associated scalogram of an image to extract its local amplitude, frequency and dominant orientation. For images contaminated by additive noise, we estimate the local features of the image using several orthogonal mother wavelet functions with optimal localisation: this allows for the construction of estimators of local image features with reduced variability and bias