Teaching Image Processing with Geometry
Vivek K Goyal and Jelena Kovacevic
Abstract
The theory and practice of image 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 image processing, the purpose of the tutorial is to share the presenters' experience on teaching image 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. Also, many important results are corollaries of the projection theorem. Unifying results geometrically helps students generalize beyond Fourier-domain insights, taking them farther, faster.
Speakers
Vivek K Goyal
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 conference series.
Jelena Kovacevic
Jelena Kovacevic is a Professor of Biomedical Engineering and Electrical and Computer Engineering and the Director of the Center for Bioimage Informatics at Carnegie Mellon University. Her research interests include biomedical signal and image processing as well as multiresolution techniques such as wavelets and frames.
She received the Dipl. Electr. Eng. degree from the EE Department, Univ. of Belgrade, Yugoslavia, in 1986, and the MS and PhD degrees from Columbia University, New York, NY, in 1988 and 1991, respectively. From 1991-2002, she was with Bell Labs, Murray Hill, NJ. She was a co-founder and Technical VP of xWaveforms, based in New York City, NY. She was also an Adjunct Professor at Columbia University. In 2003, she joined Carnegie Mellon University.
She is a Fellow of the IEEE and a coauthor (with Martin Vetterli) of the book Wavelets and Subband Coding (Englewood Cliffs, NJ: Prentice Hall, 1995). She coauthored a top-10 cited paper in the Journ. of Applied and Computational Harmonic Analysis, a top-100 downloaded paper on IEEE Xplore and the paper for which Aleksandra Mojsilovic received the Young Author Best Paper Award. Her paper on multidimensional filter banks and wavelets (with Martin Vetterli) was selected as one of the Fundamental Papers in Wavelet Theory. She received the Belgrade October Prize in 1986 and the E.I. Jury Award at Columbia University in 1991. She was the recipient of the 2010 CIT Philip L. Dowd Fellowship Award from the College of Engineering at Carnegie Mellon University.
She served as the Editor-in-Chief of the IEEE Trans. on Image Processing from 2002-2006 and an Associate Editor of the IEEE Trans. on Signal Processing, as a Guest Co-Editor (with Ingrid Daubechies) of the Special Issue on Wavelets of the Proceedings of the IEEE, Guest Co-Editor (with Martin Vetterli) of the Special Issue on Transform Coding of the IEEE Signal Processing Magazine and Guest Co-Editor (with Robert F. Murphy) of the Special Issue on Molecular and Cellular Bioimaging of the IEEE Signal Processing Magazine. She is/was on the Editorial Boards of the Springer-Birkhauser Applied and Numerical Harmonic Analysis, Foundations and Trends in Signal Processing, SIAM book series on Computational Science and Engineering, Journ. of Applied and Computational Harmonic Analysis, Journ. of Fourier Analysis and Applications and the IEEE Signal Processing Magazine.
She is a regular member of the NIH EBIT Study Section. From 2000-2002, she served as a Member-at-Large of the IEEE Signal Processing Society Board of Governors. She is the past Chair of the Bio Imaging and Signal Processing Technical Committee and on the ISBI Steering Committee. She was the General Chair of ISBI 06, General Co-Chair (with Vivek Goyal) of the DIMACS Workshop on Source Coding and Harmonic Analysis and General Co-Chair (with Jan Allebach) of the Ninth IMDSP Workshop.
She is/was/will be a plenary/keynote speaker at the Mathematics and Image Analysis 2012, IS&T/SPIE Electronic Imaging Symposium 2011, From Banach Spaces to Frame Theory and Applications 2010, 20 Years of Wavelets 2009, European Women in Mathematics 2009, MIAAB Workshop 2007, Statistical Signal Processing Workshop 2007, Wavelet Workshop 2006, NORSIG 2006, ICIAR 2005, Fields Workshop 2005, DCC 1998 as well as SPIE 1998.