Gulliver: A laboratory crosses borders

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Florent Krzakala Crédits ESPCI ParisTech

What do their projects involve? Florent Krzakala and compressed sensing

MP3, JPEG… The whole world knows about data compression: a signal is acquired then compressed. An algorithm thus makes it possible to compress a high-definition photographs into a file whose size is no more than a few hundred kilobytes (kB). During the 2000s a new concept appeared: compressed sensing. Three people opened up this still virgin field: Terry Tao, David Donoho and Emanuel Kandes. They attempted to capture the 100 kB of data essential to the information rather than acquiring the entire signal. Their aim: measuring the useful part before reconstructing it. They found a way of to more precise, faster (less data to acquire) and take up less memory in a machine.
“Their idea - and their discovery - was remarkable,” explains Florent Krzakala. They very quickly found a working application: nuclear magnetic resonance (NMR), the time taken for which is an important limiting factor. Their results made it possible to halve the acquisition time using this method, doubling the availability of scanners for patients, or halving the waiting time for a sometimes vital diagnosis. This is a great achievement.” Yet even though the methods used do extract a relevant part of the signal, they have remained limited. Problem: a threshold effect below which it is not possible to go.

Florent Krzakala and his colleagues enter the stage

The team in full : Statistical Physics Approach to Reconstruction in Compressed Sensing

Florent Krzakala (ESPCI ParisTech)

Lenka Zdeborova (Saclay – CEA)

Marc Mezard (ENS)

Sun Yifan (Beihang University)

François Sausset (Université Paris Sud)

“With other physicist colleagues, we realise that the problem confronting these specialists in compressed sensing was very similar to the problems of glass transition, which we have studied in physics for years.
Water, for example, crystallises at low temperature but sometimes becomes a supercooled liquid: it remains in the liquid phase even though its temperature is below its solidification point. The situation is the same for compressed data. They remain confined at their minimum values which were not the ones sought. »

5 degrees of Florent Krzakala
- 1999-2002 : Awarded his thesis at Orsay (LPTMS) under the supervision of Prof. Olivier Martin,
- 2002-2004 : Postdoc at the Sapienza University of Rome, in the group led by Pr. Giorgio Parisi,
- 2004 : Maître de conférences at ESPCI ParisTech, in the PCT theoretical physical chemistry group (UMR Gulliver)
- 2008-2010 : Visiting researcher at the Los Alamos National Laboratories (USA),
- 2012 : Receives an ERC grant.

“Using our physicist methods as inspiration, we developed a technique which makes it possible to cross this threshold. That was an enormous surprise in the compressed sensing community: we achieved much better compression levels!”

“At present, one fundamental problem has been resolved. What was not possible before our work now is, and what we have proposed has a strong impact on information theory. Our next objective is implementation in the fields of application and industry, which will be the subject of the work financed by this European grant.”

Next page: How Pierre Sens works with biologists to understand the mobility of cancer cells.

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