A low-rank matrix completion approach to data-driven signal processing

ELEC seminar room

Speaker: Ivan Markovsky

Abstract: In filtering, control, and other mathematical engineering areas it is common to use a model-based approach, which splits the problem into two steps: 1) model identification and 2) model-based design. Despite its success, the model-based approach has the shortcoming that the design objective is not taken into account at the identification step, i.e., the model is not optimized for its intended use. In this talk, I show a data-driven approach, which combines the identification and the model-based design into one joint problem. The signal of interest is modeled as a missing part of a trajectory of the data generating system. Subsequently, the missing data estimation problem is reformulated as a mosaic-Hankel structured matrix low-rank approximation/completion problem. The missing data estimation approach for data-driven signal processing and a local optimization method for its practical implementation are illustrated on examples of control, state estimation, filtering/smoothing, and prediction. Development of fast algorithms with provable properties in the presence of measurement noise and disturbances is a topic of current research.

Blind and off-grid acoustic echoes retrieval using multichannel annihilating filters

ELEC seminar room

Speaker: Antoine Deleforge, Inria Nancy

Abstract: When a sound wave propagates from a point source through a medium and is reflected on surfaces before reaching microphones, the measured signals consist of mixtures of the direct path signal with delayed and attenuated copies of itself. This acoustical phenomenon is referred to as echoes, or reverberation, and is generally considered as a nuisance in audio signal processing. After introducing some basic signal processing and acoustic background, this seminar will present recent works showing how acoustic echoes can be blindly estimated from audio recordings, using a method combining annihilating filter estimation and polynomial rooting. We will then show how the knowledge of such echoes can in fact help some audio signal processing tasks such as beamforming, source separation or sound source localization.


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