Sparse Overcomplete Representations of Audio:
A Way to Combine Signal Models with
Waveform Analysis / Synthesis.

Professor Laurent Daudet

Laboratoire d'Acoustique Musicale

Université Pierre et Marie Curie (Paris 6)

Date: Friday, January 12, 2007
Place: Buchanan 1930
Time: 2:00 pm — 3:00 pm


Abstract:

This talk will be focused on signal modeling using sparse decompositions on overcomplete dictionaries, with a strong focus on audio signals. In such models, a signal is approximated by a small number of elementary waveforms ("atoms") taken from a large collection ("dictionary"). Sparse decompositions offer a greater flexibility over fixed orthogonal bases: for instance one is not limited by the use of a single window size, which avoids--apparently at least--uncertainty constraints. The price paid is the non-uniqueness of the decomposition. Finding the best decomposition for a given signal is in general not possible in finite time. However, greedy suboptimal techniques have been developed that provide near-optimal decompositions at a reasonable computational cost. These methods are thus applicable to multimedia data. In the work presented here, we detail techniques for including signal models (for instance structure constraints between coefficients) directly at the decomposition stage, by grouping together semantically relevant atoms into clusters ("molecules"). We will discuss possible applications for scalable coding and audio classification.

LAURENT DAUDET studied at the Ecole Normale Supérieure, Paris, France, from 1993 to 1997, where he received a degree in statistical and nonlinear physics. In 2000, he received a Ph.D. degree in mathematical modeling from the Université de Provence, Marseille, France, on audio coding and physical modeling of piano strings. In 2001 and 2002, he was a EU Marie Curie post-doctoral fellow at the Department of Electronic Engineering, Queen Mary, University of London, U.K. Since 2002, he has been a Lecturer at the Université Pierre et Marie Curie (Paris 6), Paris, France's leading science university, where he now heads a small audio signal processing team at the Laboratory for Musical Acoustics (LAM). His research interests include audio coding and indexing, time-frequency and time-scale transforms, analysis of transient signals, and sparse representations for audio.

Host: Professor Curtis Roads, Media Arts and Technology