The Signal Processing and Classification team is in the Department d'Informatique of Ecole Normale Superieure, and is a joint research team between École Normale Supérieure de Paris and the Centre National de la Recherche Scientifique : CNRS/ENS UMR 8548.

Our research is devoted to generic mathematical and algorithmic approaches to represent high-dimensional signals for classifications. Wide range of applications are studied for speech and music, images and videos, geophysical seismic data, medical signals such as ECG and EEG, new sensor output including electromagnetic field signals. Revealing the information carried by these very different high-dimensional signals relies on similar principles. They all suffer from a curse of dimensionality, which hides complex structures.

Our approaches are ground on mathematics and algorithms emmerging from harmonic analysis and geometry. They involve wavelet transforms, groups and manifolds, invariant and sparse representations, dictionary and kernel learning, deep neural networks and statistical learning. We also maintain close collaborations with neurophysiological modeling teams, facing similar problems to understand cortical processing of auditory and visual perception.

Research Topics:

Invariant Representations with Scattering:

Signal classes suffer from a considerable variability that needs to be reduced without removing discriminative information. We study the construction of stable, informative invariants over groups mainly responsible for the signal variability. This topic relies on scattering transforms which iterate on wavelet transforms along deep neural networks. Applications are developed to speech and music , images and medical signal analysis.

Sparse Dictionary and Unsupervised Group Learning

Learning representations from unlabeled data amounts to learn important structures in an unknown signal world, from examples. Sparsity and dictionary learning are important tool to search for structure that can be modeled as groups or manifolds. Understanding deep neural network structures

Signal Geometry

Geometric signal representation still play a minor role in classification because of instabilities. Simple approaches including edge and boundary detections appear to not so effective in high dimension. Finding informative and stable geometric signal representation is not only important for images or videos but also for audio signals and music, where rhythm and long range structures are particular forms of geometry. Invariants and symmetry groups are important tools to tackle these issues.

Inverse Problems:

Signal classification often requires to reveal or separate hidden information. Separating multiple information sources is necessary to analyze complex audio signals and images. We study other non-linear inverse problems such as phase recovery , which appear in signal processing but also physics problems. Harmonic analysis, sparsity and convex optimization are major pillars to attack these questions.