2D Hilbert-Huang Transform

This paper presents a 2D transposition of the Hilbert-Huang Transform (HHT), an empirical data analysis method designed for studying instantaneous amplitudes and phases of non-stationary data. The principle is to adaptively decompose an image into oscillating parts called Intrinsic Mode Functions (IMFs) using an Empirical Mode Decomposition method (EMD), and then to perform Hilbert spectral analysis on the IMFs in order to recover local amplitudes and phases. For the decomposition step, we propose a new 2D mode decomposition method based on non-smooth convex optimization, while for the instantaneous spectral analysis, we use a 2D transposition of Hilbert spectral analysis called monogenic analysis, based on Riesz transform and allowing to extract instantaneous amplitudes, phases, and orientations. The resulting 2D-HHT is validated on simulated data.