09:30 Accueil (Café)
10:15 Irène Waldspurger : Reconstruction de phase pour la transformée en ondelettes
11:15 Emmanuel Amiot : Transformée de Fourier de structures musicales discrètes
14:00 Bruno Torrésani : Analyse spectrale de signaux non stationnaires, avec application à l'analyse et à la synthèse sonore
15:00 Roland Badeau : Un cadre mathématique commun pour la modélisation stochastique de la réverbération
16:00 Présentation des doctorants en salle
16:30 Posters des doctorants (Café)
Irène Waldspurger: Phase retrieval for the wavelet transform
The spectrogram and its cousin, the scalogram, are at the basis of most audio processing algorithms: this signal representation seems to both preserve all the "perceptual" information contained in the signals, which is necessary to analyse them, and discard some "unnecessary" information, which could only confuse the algorithms. To give a theoretical content to this assertion, we will consider the problem of recovering a signal from its scalogram. We will explain that, at least for a specific choice of wavelets, all signals are (almost) uniquely determined by their scalogram, and that the reconstruction satisfies a form of local stability property. And since, for some applications, it would be desirable to have an implementable and efficient reconstruction algorithm, we will devote the last part of the talk to a discussion on possible algorithmic approaches.
Bio: I have defended a Phd in 2015, on phase retrieval for the scalogram and its applications to the scattering transform. After a one-year post-doctoral fellowship at MIT, I was recruited by CNRS. I am now a CNRS researcher at Université Paris Dauphine, and member of the Inria project-team Mokaplan, working on inverse problems and non-convex optimization.
Emmanuel Amiot : Transformée de Fourier de structures musicales discrètes
It is a fairly recent idea to apply DFT to musical structures (scales, rhythms). Not only does the DFT simplify all the operations related to convolution (interval vectors, tilings, etc.) but the two geometric dimensions of its coefficients (modulus and argument) have direct musical meanings.
Bio: Emmanuel Amiot has been working on musical structures, especially discrete ones, from an algebraic point of view since the 1980s. He has notably contributed to the development of the theory of rhythmic canons and the DFT of musical structures. Mathematician, pianist, composer, he has occasionally collaborated with Ircam and left some modules in Open Music. He is the author of the book Music through Fourier Space, published by Springer in 2016.
Bruno Torrésani: Spectral analysis for non-stationary signals, with applications to sound analysis and synthesis
In the statistical signal processing or time series analysis literature, spectral analysis generally corresponds to the problem of estimating the power spectrum of a stationary signal from discrete, finite length realization. However, most real world signals ar not stationary so that such tools do not apply any more. This talk will address the non-stationary spectral analysis problem, with a focus on classes of signals generated by deformation of stationary signals. Besides spectral analysis, synthesis of non-stationary signals will also be addressed.
Bio: B Torrésani is a professor at the Institut de Mathématiques de Marseille, Aix Marseille University, in the Signal-Image team. His domain of interest concerns several domains of mathematical signal processing, including time-frequency and time-scale analysis, statistical modeling and inverse problems and blind source separation, with applications in audio signal processing, analytical chemistry and neuroimaging.
Roland Badeau : Common mathematical framework for stochastic reverberation modeling
In various applications of audio signal processing, including source separation and localization, it is necessary to use signal models that are both realistic and tractable. In recent years, much effort has been devoted to the modeling of source signals, but most often, the acoustic properties of reverberation are ignored. Yet, in the field of room acoustics, various formulas have been established since the 1950s, in order to characterize the statistical properties of reverberation: exponential decay over time, correlations between frequencies and between sensors, time-frequency distribution. In this talk, I will introduce a mathematical framework that unifies all these well-known results. The purpose of this work is to introduce a sound propagation model that is both accurate, and simple enough to be used in audio signal processing applications.
Bio: Roland Badeau is currently a Professor at the Image, Data, Signal (IDS) Department of Télécom Paris, with the Signal, Statistics and Machine Learning (S2A) Group, and the Audio Data Analysis and Signal Processing (ADASP) team. His research focuses on the statistical modeling of nonstationary signals, with applications to audio and music signal processing, including source separation, denoising, dereverberation, multipitch estimation, automatic music transcription, audio coding, and audio inpainting.