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Home | Seminars and Symposia | Past seminars/symposia: Thursday, April 3, 2014

DTC Seminar Series

Universal Signal Estimation

by

Dror Baron
Department of Electrical and Computer Engineering
North Carolina State University

Thursday, April 3, 2014
2:15 p.m. reception
2:45 p.m. seminar

401/402 Walter Library

Dror Baron

Consider the universal setting where an unknown source generates an input signal x, and we have access to noisy measurements y=A(x)+z, where A is a measurement operator and z is additive noise. Our setting is quite general, and supports scalar channels (A is an identity operator), linear systems (matrix A), and even nonlinear operators. The goal is to estimate x given the noisy measurements y, where the measurement operator A and the statistical properties of z are known, but x is generated by an unknown statistical source.

We propose two approaches to this problem. The first approach, which is inspired by Donoho, resembles maximum a posteriori (MAP) estimation, where a universal source code is used instead of the unknown prior for x. The universal MAP estimator achieves twice the Bayesian minimum mean square error (MMSE). In order to approach the MMSE, our second approach resembles conditional expectation, where a universal prior for x allows to denoise a scalar channel problem, y=x+z, despite not knowing the input distribution. Finally, we have applied our universal denoising to linear compressed sensing problems, y=A*x+z, by plugging in our denoiser into an approximate message passing algorithm. Numerical results are favorable; our compressed sensing achieves the MMSE for different settings despite not knowing the input distribution.

 

Dror Baron received the B.Sc. (summa cum laude) and M.Sc. degrees from the Technion — Israel Institute of Technology, Haifa, Israel, in 1997 and 1999, and the Ph.D. degree from the University of Illinois at Urbana-Champaign in 2003, all in electrical engineering.

From 1997 to 1999, he worked at Witcom Ltd. in modem design. From 1999 to 2003, he was a research assistant at the University of Illinois at Urbana-Champaign, where he was also a Visiting Assistant Professor in 2003. From 2003 to 2006, he was a Postdoctoral Research Associate in the Department of Electrical and Computer Engineering at Rice University, Houston, TX. From 2007 to 2008, he was a quantitative financial analyst with Menta Capital, San Francisco, CA. From 2008 to 2010 he was a visiting scientist in the Department of Electrical Engineering at the Technion. Dr. Baron joined the Department of Electrical and Computer Engineering at North Carolina State University in 2010 as an assistant professor. His research interests include information theory and statistical signal processing.