Tutorial 9: Modern Quantization Strategies for Compressive Sensing and Acquisition Systems

Monday, May 27, 9 am-12 noon

Presented by

Petros Boufounos, Laurent Jacques

Abstract

The advent of Compressed Sensing (CS) has precipitated a radical re-thinking of signal acquisition, sensing, processing and transmission system design. A significant aspect of such systems is quantization of the acquired signals 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 work has shown that, while careful design of quantization for CS systems is not straightforward, the benefits of a proper design are worth the effort.

Our goal with this tutorial is to expose all this body of work, the available solutions, the theoretical underpinnings and practical considerations, as well as the problems still open in the field. We will provide a wide treatment of the topic, drawn both from our extensive work in the area, as well as other literature available in the field. Our objective is also to provide a well-balanced presentation of both theory and practice, assuming only minimal background on classical quantization and CS.

More precisely, this tutorial aims at discussing modern quantization strategies, as applied to Compressive Sensing (CS), with focus on practical signal acquisition systems. We will cover high-rate and low-rate scalar quantization - including quantizer design and reconstruction algorithms - as well as Sigma-Delta converters. The presentation will focus both on theory and practice, demonstrating fundamental performance upper and lower bounds, as well as experimental results on optimal designs. As part of the tutorial, we will also present quantized embeddings, such as locality sensitive hashing (LSH), binary epsilon-stable embeddings (BeSE) and universal 1-bit embeddings, which enable efficient nearest-neighbor computation without reconstruction. The tutorial will include discussion of the open problems in the area, future trends and promising research directions.

This 3-hours tutorial will be structured over five topics, namely,

  1. Modern Scalar Quantization,
  2. Compressive Sensing Overview,
  3. CS and Quantization,
  4. 1-bit CS,
  5. Locality Sensitive Hashing and Universal quantization.

Sections (A) and (B) aim at providing a review of the fundamental theory necessary in our subsequent development. Sections (C), (D) and (E) develop the main material of this tutorial. Throughout the tutorial, both theory and practical examples will be provided. Open problems and future research directions will be identified throughout the discussion.

Speaker Biography

Petros T. Boufounos

Petros T. Boufounos is a Principal Member of Research Staff at Mitsubishi Electric Research Laboratories in Cambridge, MA and a visiting scholar at the Rice University Electrical and Computer Engineering department in Houston, TX. Dr. Boufounos completed his undergraduate and graduate studies at MIT. He received the S.B. degree in Economics in 2000, the S.B. and M.Eng. degrees in Electrical Engineering and Computer Science (EECS) in 2002, and the Sc.D. degree in EECS in 2006. Between September 2006 and December 2008, he was a postdoctoral associate with the Digital Signal Processing Group at Rice University. Dr. Boufounos joined MERL in January 2009.

Dr. Boufounos immediate research interests include signal acquisition and processing, quantization and data representations, frame theory, and machine learning applied to signal processing. He is also looking into how signal acquisition interacts with other fields that use sensing extensively, such as robotics and mechatronics. Dr. Boufounos is an associate editor at IEEE Signal Processing Letters. He has received the Ernst A. Guillemin Master Thesis Award for his work on DNA sequencing, the Harold E. Hazen Award for Teaching Excellence, both from the MIT EECS department, and has been an MIT Presidential Fellow. He is also a member of the IEEE, Sigma Xi, Eta Kappa Nu, and Phi Beta Kappa.

Laurent Jacques

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 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 Optics), and Computer Vision. Since 1999, Laurent Jacques has co-authored 18 papers in international journals, 31 conference proceedings and presentations in signal and image processing conferences, and three book chapters.