Graduate Exam Abstract

Ramin Zahedi

Ph.D. Preliminary
April 29, 2013, 1:00 p.m. to 3:00 p.m.
Natural Resources 115
Measurement Design Methods for Detecting and Estimating Sparse Signals

Abstract: We study the problem of designing compressive measurement matrices for two sets of problems. In the first set, we consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, our goal is to design compressive measurements to maximize the measurement signal-to-noise ratio (SNR), i.e., optimize the performance of the detector. In the second set, we present an adaptive approach to measurement selection in compressive sensing for estimating sparse signals. We consider the sequential selection of the rows of a compressive measurement matrix to maximize the mutual information between the measurements and the support of the sparse signal. For this, we formulate our problem as a partially observable Markov decision process and apply an approximation method known as rollout to find a solution.

Adviser: Edwin K. P. Chong
Co-Adviser: Ali Pezeshki
Non-ECE Member: Donald Estep, MATH
Member 3: Peter Young, ECE
Addional Members: N/A

R. Zahedi, L. W. Krakow, E. K. P. Chong, and A. Pezeshki, "Adaptive compressive measurement design using approximate dynamic programming", Accepted in the 2013 American Control Conference (ACC 2013).

R. Zahedi, L. W. Krakow, E. K. P. Chong, and A. Pezeshki, "Adaptive compressive sampling using partially observable Markov decision processes," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012), Kyoto, Japan, March 25--30, 2012, pp. 5265--5272 (Invited Paper).

R. Zahedi, A. Pezeshki, and E. K. P. Chong, "Measurement design for detecting sparse signals," Physical Communication, vol. 5, no. 2, pp. 64--75, June 2012.

R. Zahedi, A. Pezeshki, and E. K. P. Chong, "Robust measurement design for detecting sparse signals: Equiangular uniform tight frames and Grassmannian packings," in Proceedings of the 2010 American Control Conference (ACC 2010), Baltimore, Maryland, June 30--July 2, 2010, Paper ThC05.1, pp. 4070--4075.

Program of Study:
ECE 516
MATH 517
MATH 560
ECE 752
STAT 720