Processus gaussiens pour la séparation de sources et le codage informé

La séparation de sources est la tâche qui consiste à récupérer plusieurs signaux dont on observe un ou plusieurs mélanges. Ce problème est particulièrement difficile et de manière à rendre la séparation possible, toute information supplémentaire connue sur les sources ou le mélange doit pouvoir être prise en compte. Dans cette thèse, je propose un formalisme général permettant d inclure de telles connaissances dans les problèmes de séparation, où une source est modélisée comme la réalisation d un processus gaussien. L approche a de nombreux intérêts : elle généralise une grande partie des méthodes actuelles, elle permet la prise en compte de nombreux a priori et les paramètres du modèle peuvent être estimés efficacement. Ce cadre théorique est appliqué à la séparation informée de sources audio, où la séparation est assistée d'une information annexe calculée en amont de la séparation, lors d une phase préliminaire où à la fois le mélange et les sources sont disponibles. Pour peu que cette information puisse se coder efficacement, cela rend possible des applications comme le karaoké ou la manipulation des différents instruments au sein d'un mix à un coût en débit bien plus faible que celui requis par la transmission séparée des sources. Ce problème de la séparation informée s apparente fortement à un problème de codage multicanal. Cette analogie permet de placer la séparation informée dans un cadre théorique plus global où elle devient un problème de codage particulier et bénéficie à ce titre des résultats classiques de la théorie du codage, qui permettent d optimiser efficacement les performances.Source separation consists in recovering different signals that are only observed through their mixtures. To solve this difficult problem, any available prior information about the sources must be used so as to better identify them among all possible solutions. In this thesis, I propose a general framework, which permits to include a large diversity of prior information into source separation. In this framework, the sources signals are modeled as the outcomes of independent Gaussian processes, which are powerful and general nonparametric Bayesian models. This approach has many advantages: it permits the separation of sources defined on arbitrary input spaces, it permits to take many kinds of prior knowledge into account and also leads to automatic parameters estimation. This theoretical framework is applied to the informed source separation of audio sources. In this setup, a side-information is computed beforehand on the sources themselves during a so-called encoding stage where both sources and mixtures are available. In a subsequent decoding stage, the sources are recovered using this information and the mixtures only. Provided this information can be encoded efficiently, it permits popular applications such as karaoke or active listening using a very small bitrate compared to separate transmission of the sources. It became clear that informed source separation is very akin to a multichannel coding problem. With this in mind, it was straightforwardly cast into information theory as a particular source-coding problem, which permits to derive its optimal performance as rate-distortion functions as well as practical coding algorithms achieving these bounds.PARIS-Télécom ParisTech (751132302) / SudocSudocFranceF

Asymptotically optimal model estimation for quantization

International audienceUsing high-rate theory approximations we introduce flexible practical quantizers based on possibly non-Gaussian models in both the constrained resolution (CR) and the constrained entropy cases. We derive model estimation criteria optimizing asymptotic (with increasing rate) quantizer performance. We show that in the CR case the optimal criterion is different from the maximum likelihood criterion commonly used for that purpose and introduce a new criterion that we call constrained resolution minimum description length (CR-MDL). We apply these principles to the generalized Gaussian scaled mixture model, which is accurate for many real-world signals. We provide an explanation of the reason why the CR-MDL improves quantization performance in the CR case and show that CR-MDL can compensate for a possible mismatch between model and data distribution. Thus, this criterion is of a great interest for practical applications. Our experiments apply the new quantization method to controllable artificial data and to the commonly used modulated lapped transform representation of audio signals. We show that both the CR-MDL criterion and a non-Gaussian modeling have significant advantages