Abstract: We present a framework for sampling a wide class of wideband analog signals with finite rate of innovation, at rates far below that dictated by the Nyquist rate. We refer to this methodology as Xampling: A combination of compression and sampling, performed simultaneously. Using the Cramer-Rao bound we develop a generic low-rate sampling architecture that is optimal in a mean-squared error sense, and can be applied to a wide variety of wideband inputs. We show that this approach improves upon several alternative sampling mechanisms proposed in the literature. Another advantage of our scheme is that it can be readily implemented in hardware, and is easily modified to incorporate correlations between signals. We consider in detail an application of these ideas to ultrasound imaging and demonstrate recovery of noisy ultrasound images from sub-Nyquist samples while performing beamforming in the compressed domain. Finally, motivated by problems in optics, we extend these principles to nonlinear problems leading to quadratic and more general nonlinear compressed sensing techniques. We demonstrate applications to phase recovery from magnitude measurements and super-resolution imaging.
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 2002. 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 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, in 2010 the Michael Bruno Memorial Award from the Rothschild Foundation, and in 2011 the Weizmann Prize for Exact Sciences.
She is a Signal Processing Society Distinguished Lecturer, a member of the IEEE Bio Imaging Signal Processing technical committee, and an Associate Editor for several IEEE and SIAM journals.
Robert Ghrist University of Pennsylvania Monday 1 PM - 2 PM, August 6
Title:Topological Signal Processing
Abstract: This talk will survey some recent advances in a qualitative approach to signal processing using tools from geometric and algebraic topology. Topology --- the mathematics of qualitative description and local-to-global inference --- is an ideal tool-set for several signal processing applications, especially in settings that are coordinate-free or otherwise minimalist.
Biography: After earning an undergraduate degree in Mechanical Engineering from the University of Toledo, Ghrist went on to earn a Ph.D. in Applied Mathematics from Cornell University, writing a thesis on knotted flowlines in 1995. Ghrist has held positions at the University of Texas, Austin; Georgia Institute of Technology; and the University of Illinois, Urbana-Champaign. He is currently the Andrea Mitchell University Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. Ghrist's work focuses on topological methods in applied mathematics, with applications ranging from fluid dynamics to robotics to sensor networks and more. His work has been honored by Scientific American as a "SciAm50 Top Research Innovation" in 2007. He specialized in transferring technology from pure to applied mathematics.
Robert Nowak University of Wisconsin-Madison Tuesday 8:30 AM - 9:30 AM, August 7
Abstract: Progress in science and engineering relies on building good models. Modern applications often involve huge systems of many variables, and researchers have turned to flexible nonparametric and high-dimensional statistical models to capture the complexity of such problems. Most of the work in this direction has focused on non-adaptive measurements. Alternatively, adaptive measurement procedures can improve the accuracy of statistical inference. These procedures automatically adapt the measurements in order to focus and optimize the gathering of new information. Sequential experimental design and testing are classic examples of adaptive approaches. Adaptive measurement procedures for high-dimensional and nonparametric inference are largely unexplored, but researchers in several communities have begun to develop promising new tools. For example, machine learning researchers have devised “active learning" algorithms that can dramatically reduce the number of labeled training examples needed to design good classifiers. In signal processing, new results show that "adaptive sensing" can significantly improve the recovery of sparse signals in noise. This talk takes a modern look at adaptive measurement, highlighting the potential of adaptivity in challenging statistical inference problems.
Biography: Robert Nowak received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Wisconsin-Madison in 1990, 1992, and 1995, respectively. He was a Postdoctoral Fellow at Rice University in 1995-1996, an Assistant Professor at Michigan State University from 1996-1999, held Assistant and Associate Professor positions at Rice University from 1999-2003, and is now the McFarland-Bascom Professor of Engineering at the University of Wisconsin-Madison. Professor Nowak has held visiting positions at INRIA, Sophia-Antipolis (2001), and Trinity College, Cambridge (2010). He has served as an Associate Editor for the IEEE Transactions on Image Processing and the ACM Transactions on Sensor Networks, and as the Secretary of the SIAM Activity Group on Imaging Science. He was General Chair for the 2007 IEEE Statistical Signal Processing workshop and Technical Program Chair for the 2003 IEEE Statistical Signal Processing Workshop and the 2004 IEEE/ACM International Symposium on Information Processing in Sensor Networks. Professor Nowak received the General Electric Genius of Invention Award (1993), the National Science Foundation CAREER Award (1997), the Army Research Office Young Investigator Program Award (1999), the Office of Naval Research Young Investigator Program Award (2000), the IEEE Signal Processing Society Young Author Best Paper Award (2000), the IEEE Signal Processing Society Best Paper Award (2011), and the ASPRS Talbert Abrams Paper Award (2012). He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE). His research interests include signal processing, machine learning, imaging and network science, and applications in communications, bioimaging, and systems biology. His Google Scholar page contains further information about his research and publications.
Persi Diaconis Stanford University Tuesday 1 PM - 2 PM, August 7 Photo credit: Linda A. Cicero / Stanford University News Service
Abstract: When a column of digits is added in the usual way, "carries" occur. If the digits are random, the carries form a point process with interesting properties. It is stationary, one-dependent, and determinental. This allows standard theory to answer "any reasonable question." A raft of such processes occur in a variety of applications: random matrix theory, combinatorics, zeros of random functions, and software design. The mathematics involves various parts of algebra, in rare conjunction with probability. All of this is joint work with Alexei Borodin.
Biography: Persi Diaconis is professor of mathematics and statistics at Stanford University. He works in various parts of statistics (graphics, Bayesian statistics, data analysis for large networks), probability (random matrix theory, Markov chain theory), and combinatorics (symmetric functions, combinatorial group theory).An early Macarthur winner and a member of the national academy, he is also well-known for 10 years spent as a professional magician.
Yoram Bresler University of Illinois, Urbana-Champaign Wednesday 8:30 - 9:30 AM, August 8
Abstract: Compressive sensing (CS), also known as compressive sampling, has become widely popular in recent years. In the first part of the talk, we review the little known fact, that the invention of CS preceded the papers that popularized it by almost a decade. Spectrum-blind sampling (SBS), proposed by Bresler and Feng in the mid-90’s, and further developed into “image compression on the fly,” with Venkataramani, and Gastpar, is the first known compressed sensing technique. This work from the 1990's already included the conceptual breakthrough of sampling at the sparsity level, theoretical guarantees and computationally efficient algorithms, treatment of both finite-length vectors and analog sampling, of the single-vector case and of jointly-sparse recovery (the so-called multiple measurement vector problem), and applications to imaging.
In the second part of the talk, guided by the applications that originally spurred the invention of CS in the 1990's, and which have continued to motivate much of the work on CS to date, we examine the current status of CS theory and algorithms. We find that in spite of deep and seminal contributions in this area, the available results have some limitations. The most powerful performance guarantees for polynomial-time algorithms have been obtained for unstructured random Gaussian or sub-Gaussian sensing matrices. However, in most practical applications, such sensing matrices are infeasible, owing to either the physics of the acquisition system, or computational cost. On the other hand, the performance guarantees for structured sensing matrices that arise in practice are too conservative, or inapplicable. Another weakness of current CS has been the extension to jointly-sparse recovery: algorithms that perform well in practice are computationally expensive, and those that are fast, have inferior performance. We describe new results that address both of these limitations of current theory and algorithms. Expanding on the ideas first proposed for SBS and image compression on the fly, we describe new guaranteed algorithms for jointly-sparse recovery, which provide the best of both worlds: they are fast, and perform at least as well as the best known (but expensive) algorithms. Addressing the broader problem of sensing with structured matrices, we develop new tools for performance guarantees, and new efficient algorithms to which these guarantees are applicable. The new algorithm are not only guaranteed under more lenient conditions that are satisfied in practical compressive sensing systems, but, in numerical experiments, they also perform better than existing algorithms.
Biography: Yoram Bresler (F'99) received the B.Sc. (cum laude) and M.Sc. degrees from the Technion, Israel Institute of Technology, in 1974 and 1981 respectively, and the Ph.D degree from Stanford University, in 1986, all in Electrical Engineering. In 1987 he joined the University of Illinois at Urbana-Champaign, where he is currently a Professor at the Departments of Electrical and Computer Engineering and Bioengineering, and at the Coordinated Science Laboratory. Yoram Bresler is also President and Chief Technology Officer at InstaRecon, Inc., a startup he co-founded to commercialize breakthrough technology for tomographic reconstruction developed in his academic research. His current research interests include multi-dimensional and statistical signal processing and their applications to inverse problems in imaging, and in particular computed tomography, magnetic resonance imaging, and compressed sensing.
Dr. Bresler has served on the editorial board of a number of journals, and on various committees of the IEEE. Currently he serves on th editorial board for the SIAM Journal on Imaging Science. Dr. Bresler is a fellow of the IEEE and of the AIMBE. He received two Senior Paper Awards from the IEEE Signal Processing society, and a paper he coauthored with one of his students received the Young Author Award from the same society in 2002. He is the recipient of a 1991 NSF Presidential Young Investigator Award, the Technion (Israel Inst. of Technology) Fellowship in 1995, and the Xerox Senior Award for Faculty Research in 1998. He was named a University of Illinois Scholar in 1999, appointed as an Associate at the Center for Advanced Study of the University in 2001-2, and Faculty Fellow at NCSA in 2006.
Randy Moses Ohio State University Wednesday 9:45 AM - 10:45 AM, August 8
The steady advance in digital processing hardware and sampling systems are enabling significant new opportunities in radar signal processing. In the same way that increasing processor speed realized a revolution first in digital audio, then in digital video, digital radar is rapidly growing. Digital radar systems are enabling new architectures and new capabilities; examples include 3D imaging, multifunctional systems, and waveform adaptation. This talk will describe some recent advances and highlight emerging opportunities for next-generation digital radar systems.
Biography: Randolph L. Moses received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from Virginia Tech 1979, 1980, and 1984, respectively. Since 1985 he has been on the faculty at The Ohio State University, and holds appointments as Associate Dean for Research in the College of Engineering and Professor in Electrical and Computer Engineering. Professor Moses has also been a visiting researcher with the Air Force Research Laboratory (1983; 2002-03), Eindhoven University of Technology in The Netherlands (1984), Uppsala University in Sweden (1994-95), and Massachusetts Institute of Technology (2003). Professor Moses serves on the ASEE Engineering Research Council, and on the IEEE Sensors Council, and the IEEE Signal Processing Society Sensor Array and Multichannel Technical Committee. He serves on the Board of Directors for the Edison Materials Technology Center (EMTEC) and the Dayton Area Graduate Studies Institute (DAGSI). He is a past associated editor of IEEE Transactions on Image Processing (2008-09) and of IEEE Transactions on Signal Processing (2000-04). He was the founding chairman of the Columbus Ohio Section of the IEEE Signal Processing Society.
Professor Moses' research interests are in statistical signal processing, and include parametric time series analysis, radar signal processing, sensor array processing, and sensor networks. He has published more than 150 technical papers and co-authored two textbooks. He is a Fellow of the IEEE.