Section: New Results

Robust non Gaussian models

Robust Locally linear mapping with mixtures of Student distributions

Participants : Florence Forbes, Emeline Perthame, Brice Olivier.

The standard GLLiM model [6] for high dimensional regression assumes Gaussian noise models and is in its unconstrained version equivalent to a joint GMM. The fact that response and independent variables $(X,Y)$ are jointly a mixture of Gaussian distribution is the key for all derivations in the model. In this work, we show that similar developments are possible based on a joint Student Mixture model, joint SMM. It follows a new model referred to as SLLiM for Student Locally linear mapping for which we investigate the robustness to outlying data in a high dimensional regression context [71]. The corresponding code is available on the CRAN in the xLLiM package.

Rectified binaural ratio: A complex T-distributed feature for robust sound localization

Participant : Florence Forbes.

Joint work with: Antoine Deleforge, Inria panama team in Rennes.

Most existing methods in binaural sound source localization rely on some kind of aggregation of phase-and level-difference cues in the time-frequency plane. While different aggregation schemes exist, they are often heuristic and suffer in adverse noise conditions. In this work, we introduce the rectified binaural ratio as a new feature for sound source localization. We show that for Gaussian-process point source signals corrupted by stationary Gaussian noise, this ratio follows a complex t-distribution with explicit parameters. This new formulation provides a principled and statistically sound way to aggregate binaural features in the presence of noise. We subsequently derive two simple and efficient methods for robust relative transfer function and time-delay estimation. Experiments on heavily corrupted simulated and speech signals demonstrate the robustness of the proposed scheme. This work has been presented at the Eusipco conference in 2016 [30].

Statistical reconstruction methods for multi-energy tomography

Participants : Florence Forbes, Pierre-Antoine Rodesch.

Joint work with: Veronique Rebuffel from CEA Grenoble.

In the context of Pierre-Antoine Rodesh's PhD thesis, we investigate new statistical and optimization methods for tomographic reconstruction from non standard detectors providing multiple energy signals.