2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

TL;DR

This paper introduces a novel 2-D spectral analysis method extending the Hilbert Huang transform to images, utilizing adaptive decomposition and Prony-based local spectral analysis for detailed image characterization.

Contribution

It presents a new 2-D mode decomposition technique and a Prony-based spectral analysis, enhancing image analysis capabilities beyond existing methods.

Findings

Effective decomposition of images into intrinsic mode functions.

Accurate local spectral analysis of image components.

Validated on simulated and real image data.

Abstract

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.