Multidimensional empirical wavelet transform

TL;DR

This paper introduces a comprehensive framework for multidimensional empirical wavelet transforms that are adaptable to any wavelet kernel, enhancing their applicability to signals and images with proven theoretical conditions and numerical demonstrations.

Contribution

It extends the empirical wavelet transform to multiple dimensions using any wavelet kernel and establishes conditions for wavelet frame construction in both continuous and discrete cases.

Findings

Framework applicable to signals and images

Conditions for wavelet frame construction provided

Numerical simulations demonstrate transform effectiveness

Abstract

The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last decade. However, it has been mostly studied theoretically for signals and its extension to images is limited to a particular generating function. This work presents a general framework for multidimensional empirical wavelet transform based on any wavelet kernel. It also provides conditions to build wavelet frames for both continuous and discrete transforms. Moreover, numerical simulations of transforms are given.