This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.
@article{arxiv.1404.7680,
title = {2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis},
author = {Jérémy Schmitt and Nelly Pustelnik and Pierre Borgnat and Patrick Flandrin and Laurent Condat},
journal= {arXiv preprint arXiv:1404.7680},
year = {2015}
}