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Seminar: Quantized compressed sensing and quasi-isometric embeddings

The seminar will be given by Prof. Laurent Jacques, Université Catholique de Louvain, Belgium.

May 18, 2015 from 03:00 PM to 04:00 PM

Where Aula Magna, School of Engineering and Architecture, viale Risorgimento 2, Bologna

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Abstract

The advent of Compressed Sensing (CS) ten years ago has precipitated a radical re-thinking of signal acquisition, sensing, processing and transmission system design. A significant aspect of such systems is quantization (or digitization) of the acquired data before further processing or for the purpose of transmission and compression. Recent literature has tackled various aspects of quantization for CS systems and a large body of work has produced results that are often counter to the intuition stemming from classical sensing system design. This presentation will focus on several scalar quantization procedures of compressive signal measurements, starting from high-resolution scalar quantization till the extreme 1-bit quantization retaining only the sign of compressive measurements.

We will stress the impact of the non-linear transformation induced by quantization on the signal reconstruction guarantees. Conversely to former attempts considering quantization distortion as an additive Gaussian measurement noise, a "signal consistency quest" will be pursued here: we will study geometrically the theoretical upper and lower bounds that any reconstruction methods must respect when their sparse solutions are consistent with the quantized observations. This will lead us to analyze new embedding relations between the sparse signals set and its quantized random projections. Interestingly, these embeddings differ from the common restricted isometry property (RIP) in that they contain an additive distortion term, that is, they display a quasi-isometric nature directly connected to the information loss induced by quantization.

About the speaker

Laurent Jacques received the B.Sc. in Physics, the M.Sc. in Mathematical Physics and the PhD in Mathematical Physics from the Université catholique de Louvain (UCL), Belgium. He was a Postdoctoral Researcher with the Communications and Remote Sensing Laboratory of UCL in 2005–2006. He obtained in Oct. 2006 a four-year (3+1) Postdoctoral funding from the Belgian FRS-FNRS in the same lab. He was a visiting Postdoctoral Researcher, in spring 2007, at Rice University (DSP/ECE, Houston, TX, USA), and from Sep. 2007 to Jul. 2009, at the Swiss Federal Institute of Technology (LTS2/EPFL, Switzerland). Formerly funded by Belgian Science Policy (Return Grant, BELSPO, 2010-2011), and as a F.R.S.-FNRS Scientific Research Worker (2011-2012) in the ICTEAM institute of UCL, he is a FNRS Research Associate since Oct. 2012. His research focuses on Sparse Representations of signals (1-D, 2-D, sphere), Compressed Sensing theory (reconstruction, quantization) and applications, Inverse Problems in general, and Computer Vision.