Tutorial T-3: Structured Compressed Sensing: From Theory to Applications

Wednesday, March 30, 08:30 - 12:15

Presented by

Yonina Eldar, Department of Electrical Engineering, Israel Institute of Technology, Israel

Description

Compressed sensing (CS) is an exciting and emerging field that has attracted considerable research interest over the past few years. Much of the original work in this area was limited to standard discrete-to-discrete measurement architectures using matrices of randomized nature and discrete signal models based on standard sparsity. In recent years, CS has worked its way into several exciting new application areas including various medical imaging platforms. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured measurement systems that can be implemented efficiently in hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode richer data models including continuous-time signals. In this tutorial, we review the basics of CS along with some of these extensions where the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of these structured CS strategies to emerge from the math to the hardware. Our summary will highlight exciting new directions and relations to more traditional CS as well as recent applications including ultrasound imaging, sub-Nyquist hardware, time delay estimation, source separation, radar and more.

Outline

Introduction
- Motivation: the Shannon-Nyquist bottleneck
- Compressed sensing of discrete data
- Moving to richer signal models including analog signals
Compressed Sensing Basics
- Sparsity models
- Measurement systems
- Recovery algorithms
Structure in Discrete Models
- Multiple measurement vectors
- Block sparsity
- Structured sparse supports
- Exploiting statistical dependencies
Analog compressed Sensing: Sub-Nyquist Sampling
- Union of subspace modeling
- Low-rate multiband sampling
- Time delay estimation
- Ultrasonic imaging
- Hardware design and prototypes

About the Speaker

Yonina C. Eldar received the B.Sc. degree in physics and the B.Sc. degree in electrical engineering both from Tel-Aviv University (TAU), Tel-Aviv, Israel, in 1995 and 1996, respectively, and the Ph.D. degree in electrical engineering and computer science from the Massachusetts Institute of Technology (MIT), Cambridge, in 2001. She is currently a Professor in the Department of Electrical Engineering at the Technion—Israel Institute of Technology, Haifa. She is also a Research Affiliate with the Research Laboratory of Electronics at MIT and a Visiting Professor with the Electrical and Statistics departments at Stanford University, Stanford, CA. Dr. Eldar was a Horev Fellow of the Leaders in Science and Technology program at the Technion and an Alon Fellow. In 2004, she was awarded the Wolf Foundation Krill Prize for Excellence in Scientific Research, in 2005 the Andre and Bella Meyer Lectureship, in 2007 the Henry Taub Prize for Excellence in Research, in 2008 the Hershel Rich Innovation Award, the Award for Women with Distinguished Contributions, the Muriel & David Jacknow Award for Excellence in Teaching, and the Technion Outstanding Lecture Award, in 2009 the Technion's Award for Excellence in Teaching, and in 2010 the Michael Bruno Memorial Award from the Rothschild Foundation. She is a member of the IEEE Signal Processing Theory and Methods technical committee and the Bio Imaging Signal Processing technical committee, and an Associate Editor for several IEEE and SIAM journals.