Tutorial 14: Teaching Signal Processing with Geometry
Presented by
Vivek K Goyal, Martin Vetterli
Abstract
The theory and practice of signal processing benefit greatly from extending "real world" (Euclidean) geometric insights to abstract signals. However, typical electrical engineering curricula do not promote geometric thinking, especially at the undergraduate level. While the attendees of this tutorial may gain some geometric insights into signal processing, the purpose of the tutorial is to share the presenters' experience on teaching signal processing with an emphasis on Hilbert space geometry. With this approach, results in finite dimensions, discrete time, and continuous time are often unified, thus making it easier to focus on the few essential differences. Unifying results geometrically helps students generalize beyond Fourier-domain insights, taking them farther, faster. For example, many important results are corollaries of the projection theorem or follow from recognizing certain operators as adjoint pairs.
The tutorial is particularly timely as more undergraduate EE curricula get restructured to start with integrative experiences, leaving less time in which to squeeze the conventional foundation courses. It is thus a key time in which to rethink how to teach signal processing to students who may be more mature overall and have less time to reach contemporary topics.
The tutorial is not intended to teach signal processing, but rather to give highlights on how to emphasize geometric concepts in teaching signal processing. The basic sequence of topics will be: extending from the Euclidean world to Hilbert spaces; the projection theorem and its consequences; decompositions; bases; frames; sampling; approximation; time-frequency localization; structured bases. The presenters will alternate in roughly 30 minute blocks.
Along with Jelena Kovacevic, the presenters are coauthors of forthcoming textbooks on signal processing that are distributed online under-open access terms. The first volume will be published before the conference, and excerpts will be provided to participants along with the presentation slides.
Speaker Biography
Martin Vetterli received the Dipl. El.-Ing. degree from ETH Zurich (ETHZ), Switzerland, in 1981, the MS degree from Stanford University in 1982, and the Doctorat és Sciences degree from EPF Lausanne (EPFL), Switzerland, in 1986.
He was a Research Assistant at Stanford and EPFL, and has worked for Siemens and AT&T Bell Laboratories. In 1986 he joined Columbia University in New York, where he was last an Associate Professor of Electrical Engineering and co-director of the Image and Advanced Television Laboratory. In 1993 he joined the University of California at Berkeley, where he was a Professor in the Department of Electrical Engineering and Computer Sciences until 1997, and now holds an Adjunct Professor position.
Since 1995 he is a Professor of Communication Systems at EPF Lausanne, Switzerland, where he chaired the Communications Systems Division (1996/97), and heads the Audiovisual Communications Laboratory. From 2001 to 2004 he directed the National Competence Center in Research on mobile information and communication systems. He is also a Vice-President for Institutional Affairs at EPFL since October 2004. He has held visiting positions at ETHZ (1990) and Stanford (1998).
He is a fellow of the IEEE, a fellow of ACM, a member of SIAM. He is on the editorial boards of Applied and Computational Harmonic Analysis, The Journal of Fourier Analysis and Application and IEEE Journal on Selected Topics in Signal Processing.
He received the Best Paper Award of EURASIP in 1984 for his paper on multidimensional subband coding, the Research Prize of the Brown Bovery Corporation (Switzerland) in 1986 for his doctoral thesis, the IEEE Signal Processing Society's Senior Awards in 1991, in 1996 and in 2007 (for papers with D. LeGall, K. Ramchandran, and Marziliano and Blu, respectively). He won the Swiss National Latsis Prize in 1996, the SPIE Presidential award in 1999, and the IEEE Signal Processing Technical Achievement Award in 2001. He was a member of the Swiss Council on Science and Technology until Dec. 2003.
He was a plenary speaker at various conferences (e.g. IEEE ICIP, ICASSP, ISIT) and is the co-author of books with J. Kovacevic, Wavelets and Subband Coding , with P. Prandoni, Signal Processing for Communications, and with J. Kovacevic and V. K. Goyal, Fourier and Wavelet Signal Processing.
He has published about 150 journal papers on a variety of topics in signal/image processing and communications, holds a dozen patents and is an ISI highly cited researcher in engineering.
His research interests include sampling, wavelets, multirate signal processing, computational complexity, signal processing for communications, digital image/video processing, joint source/channel coding and signal processing for sensor networks.
Vivek K Goyal received the B.S. degree in mathematics and the B.S.E. degree in electrical engineering from the University of Iowa, where he received the John Briggs Memorial Award for the top undergraduate across all colleges. He received the M.S. and Ph.D. degrees in electrical engineering from the University of California, Berkeley, where he received the Eliahu Jury Award for outstanding achievement in systems, communications, control, or signal processing.
He was a Member of Technical Staff in the Mathematics of Communications Research Department of Bell Laboratories, Lucent Technologies, 1998-2001; and a Senior Research Engineer for Digital Fountain, Inc., 2001-2003. He joined the Massachusetts Institute of Technology in 2004, where he is currently Associate Professor of Electrical Engineering and a member of the Research Laboratory of Electronics. His research interests include source coding theory, sampling, quantization, magnetic resonance imaging, and optical imaging.
Dr. Goyal is a member of Phi Beta Kappa, Tau Beta Pi, Sigma Xi, Eta Kappa Nu, and SIAM. He is a Senior Member of the IEEE. He was awarded the 2002 IEEE Signal Processing Society Magazine Award and an NSF CAREER Award, and his students have been awarded several thesis and conference best paper awards. He served a six-year term on the IEEE Signal Processing Society's Image and Multiple Dimensional Signal Processing Technical Committee and was a plenary speaker at IEEE Data Compression Conference and IEEE Multimedia Signal Processing Workshop. He is a Technical Program Committee Co-chair of IEEE ICIP 2016 and a permanent Conference Co-chair of the SPIE Wavelets and Sparsity conference series.