The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images

TL;DR

This paper introduces a bidimensional synchrosqueezing transform based on monogenic signals for decomposing and demodulating multicomponent images, extending the 1D approach to 2D image analysis.

Contribution

It develops a novel 2D synchrosqueezing transform using monogenic signals, enabling effective decomposition and processing of multicomponent images.

Findings

Effective decomposition of multicomponent images demonstrated

Numerical tests validate the method's accuracy and robustness

Extension of 1D synchrosqueezing to 2D images achieved

Abstract

The synchrosqueezing method aims at decomposing 1D functions as superpositions of a small number of "Intrinsic Modes", supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time-frequency plane, together with a reconstruction of each mode. In this paper, a bidimensional version of the synchrosqueezing transform is defined, by considering a well-adapted extension of the concept of analytic signal to images: the monogenic signal. The natural bidimensional counterpart of the notion of Intrinsic Mode is then the concept of "Intrinsic Monogenic Mode" that we define. Thereafter, we investigate the properties of its associated Monogenic Wavelet Decomposition. This leads to a natural bivariate extension of the Synchrosqueezed Wavelet Transform, for decomposing and processing multicomponent images. Numerical tests validate the effectiveness of the method for different examples.