2D Kernel-Based Empirical Wavelet Transform

Charles-Gérard Lucas (INRIA Grenoble)
November 07, 2025 — 11:00 — Online

Abstract

The empirical wavelet transform (EWT) is a data-driven time-scale representation based on adaptive filters. Its robustness and flexibility have led to significant developments and a growing number of applications over the past decade. However, most studies have focused on theoretical aspects for one-dimensional signals, and extensions to images have been limited to a specific generating function. This presentation introduces a general framework for the multidimensional empirical wavelet transform that can be derived from any generating function. In addition, a numerical implementation is presented and illustrated with examples.

References

[1] Gilles, J. (2013). Empirical wavelet transform. IEEE transactions on signal processing, 61(16), 3999-4010.

[2] Lucas, C. G., & Gilles, J. (2024). Demon Registration for 2D Empirical Wavelet Transforms. Foundations, 4(4), 690-703.

[3] Lucas, C. G., & Gilles, J. (2025). Multidimensional empirical wavelet transform. SIAM Journal on Imaging Sciences, 18(2), 906-935

Bio

My research lies in the field of signal and image processing, with a particular focus on the development of wavelet theory and variational methods. I obtained my Ph.D. from the École Normale Supérieure de Lyon in 2023, after which I held a postdoctoral position at San Diego State University (California). I am currently a postdoctoral researcher at INRIA Grenoble, where my work focuses on the reconstruction of circumstellar disks through the integration of variational approaches and neural network techniques.