In the past couple of decades, non-smooth convex optimization has emerged as a powerful tool for the recovery of structured signals (sparse, low rank, finite constellation, etc.) from (possibly) noisy measurements in a variety of applications in statistics, signal processing, machine learning, and communications, etc. I will describe a fairly general theory for how to determine the performance (minimum number of measurements, mean-square-error, probability-of-error, etc.) of such methods for certain measurement ensembles (Gaussian, Haar, quantized Gaussian, etc.). Among other results, I will show that the expression for the mean-square error of the LASSO algorithm is identical to that of classical least squares, provided the ambient dimension of the unknown signal is replaced by its “statistical dimension” and that the performance of the box relaxation for recovering BPSK signals in communications comes within 3 db of the celebrated “matched filter bound.” The genesis of the theory can be traced back to an inconspicuous 1962 lemma of Slepian (on comparing Gaussian processes).
Babak Hassibi is the Gordon M. Binder/Amgen Professor of Electrical Engineering at the California Institute of Technology, where he has been since 2001, and where he was Executive Officer for Electrical Engineering from 2008 to 2015. From 1998 to 2001, he was a Member of the Technical Staff at the Mathematical Sciences Research Center at Bell Laboratories, Murray Hill, NJ, and prior to that, he obtained his PhD in electrical engineering from Stanford University. His research interests span different aspects of communications, signal processing and control. Among other awards, he is a recipient of the David and Lucille Packard Foundation Fellowship, and the Presidential Early Career Award for Scientists and Engineers (PECASE). He is a Thomson-Reuters highly cited author in computer science and his Erdos number is 2.
For more information contact Professor Suhas Diggavi (firstname.lastname@example.org)
Date(s) - Oct 05, 2015
1:00 pm - 2:00 pm
EE-IV Shannon Room #54-134
420 Westwood Plaza - 5th Flr., Los Angeles CA 90095