Hubert Leterme

Postdoctoral researcher

Laboratoire GREYC, Ensicaen

14000 Caen, France

I am a postdoctoral researcher in astrostatistics at Ensicaen (Caen, France) and CEA Paris-Saclay (Paris metropolitan area, France), under the supervision of Jalal Fadili (Ensicaen) and Jean-Luc Starck (CEA). My research is part of the the TOSCA project, focusing on weak lensing statistics for cosmology, which explores the synergies between Euclid and SKAO. My work will contribute to the reconstruction of mass maps from radio shear measurements using deep learning techniques, with a specific emphasis on uncertainty quantification.

I completed my PhD in June 2023 at the University of Grenoble Alpes and Inria (Thoth team), supervised by Valérie Perrier, Karteek Alahari, and Kévin Polisano. My research lied at the intersection between computer vision and image processing, with a focus on convolutional neural networks, wavelets and stochastic signal processing.

Before my PhD, I received an engineering degree (MSc) from CentraleSupelec, University of Paris-Saclay, with a focus on industrial engineering, supply chain management, and operations research. After a few years working in the industry, including a two-year experience in Sweden, I decided to take a 180 degree turn and to embark in the research adventure. This brought me to Grenoble in 2018, where I received a MSc degree in industrial and applied mathematics from the University of Grenoble Alpes and Grenoble INP Institute of Engineering and Management.

News

Sep 20, 2024	I spent the week in Edinburgh attending the UQIPI24 Workshop on Uncertainty Quantification (UQ) for Inverse Problems and Imaging. I had the opportunity to present a poster about distribution-free UQ. I spent a great time there and engaged in constructive discussions with several people, in particular Julian Tachella, Rémi Laumont and Barbara Pascal.
Aug 30, 2024	I attended the EUSICPO 2024 conference in Lyon. It was nice catching up with Kévin Polisano and Valérie Perrier, my former colleagues and advisors from Grenoble! On Wednesday 28th, I presented our accepted paper, “From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets.”
Jun 3, 2024	I am currently spending the week in Heraklion to collaborate with researchers at FORTH, particularly Andreas Tersenov. On Thursday and Friday, I will attend the joint ARGOS-TITAN-TOSCA meeting, where I will be giving a talk about uncertainty quantification for weak lensing mass mapping.
Oct 1, 2023	This is my first day as a postdoctoral researcher in Caen, working with Jalal Fadili and Jean-Luc Starck.
Jun 14, 2023	PhD defense. Title: “A Complex Wavelet Approach for Shift-Invariant Convolutional Neural Networks.”

Selected Publications

Under review

Distribution-Free Uncertainty Quantification for Inverse Problems: Application to Weak Lensing Mass Mapping

Leterme, Hubert, Fadili, Jalal, and Starck, Jean-Luc

2024
Conference paper

From CNNs to Shift-Invariant Twin Models Based on Complex Wavelets

Leterme, Hubert, Polisano, Kévin, Perrier, Valérie, and Alahari, Karteek

In 2024 32nd European Signal Processing Conference (EUSIPCO) 2024

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We propose a novel antialiasing method to increase shift invariance in convolutional neural networks (CNNs). More precisely, we replace the conventional combination "real-valued convolutions + max pooling" ({}mathbb R\Max) by "complex-valued convolutions + modulus" ({}mathbb C\Mod), which produce stable feature representations for band-pass filters with well-defined orientations. In a recent work, we proved that, for such filters, the two operators yield similar outputs. Therefore, {}mathbb C\Mod can be viewed as a stable alternative to {}mathbb R\Max. To separate band-pass filters from other freely-trained kernels, in this paper, we designed a "twin" architecture based on the dual-tree complex wavelet packet transform, which generates similar outputs as standard CNNs with fewer trainable parameters. In addition to improving stability to small shifts, our experiments on AlexNet and ResNet showed increased prediction accuracy on natural image datasets such as ImageNet and CIFAR10. Furthermore, our approach outperformed recent antialiasing methods based on low-pass filtering by preserving high-frequency information, while reducing memory usage.
Preprint

On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks

Leterme, Hubert, Polisano, Kévin, Perrier, Valérie, and Alahari, Karteek

Sep 2022

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In this paper, we aim to improve the mathematical interpretability of convolutional neural networks for image classification. When trained on natural image datasets, such networks tend to learn parameters in the first layer that closely resemble oriented Gabor filters. By leveraging the properties of discrete Gabor-like convolutions, we prove that, under specific conditions, feature maps computed by the subsequent max pooling operator tend to approximate the modulus of complex Gabor-like coefficients, and as such, are stable with respect to certain input shifts. We then compute a probabilistic measure of shift invariance for these layers. More precisely, we show that some filters, depending on their frequency and orientation, are more likely than others to produce stable image representations. We experimentally validate our theory by considering a deterministic feature extractor based on the dual-tree wavelet packet transform, a particular case of discrete Gabor-like decomposition. We demonstrate a strong correlation between shift invariance on the one hand and similarity with complex modulus on the other hand.