Walter Scott, Jr. College of Engineering

Graduate Exam Abstract

Ramin Zahedi
Ph.D. Final
Sep 27, 2013, 12:30 - 2:30 p.m.
ECE Conference Room
Compressive Measurement Design for Detection and Estimation of Sparse Signals
Abstract: We consider the problem of designing and selecting
compressive measurement matrices for two problems:
In one problem, our goal is to adaptively estimate
the support of a time-varying sparse signal in the
presence of white noise and erasure given the
measurements collected at different time steps. We
consider two variations of this problem; in one
variation, our goal is to sequentially select the
compressive measurement matrix at each time step
from a prespecified library of measurement
matrices. In another variation, we adaptively
select the number of compressive measurements at
each time step and then, choose the matrix entries
according to a prespecified adaptive scheme. The
performance measure for both variations is the
conditional mutual information between the sparse
signal support and the compressive measurements.
We formulate this problem as a partially
observable Markov decision process (POMDP) and
apply a multi-step lookahead solution method known
as rollout. To reduce the computation involved in
updating the POMDP belief state, we apply two
well-known techniques, MHT and JPDA, in the multi-
target tracking literature.

In the second problem, we concentrate on designing
the compressive measurement matrix for detecting a
sparse signal in the presence of white noise. For
a fixed number of measurements, our goal is to
design the measurement matrix so that the
measurement signal-to-noise ratio (SNR) is
maximized. We consider two different SNR criteria,
namely a worst-case SNR measure, over all possible
realizations of a k-sparse signal, and an average
SNR measure with respect to a uniform distribution
on the locations of up to k nonzero entries in the
signal. We establish a connection between the two
criteria and certain classes of tight frames and
we show that depending on the sparsity level of
the signal, the optimal compressive measurement
matrix belongs to one of these classes.
Adviser: Edwin K. P. Chong
Co-Adviser: Ali Pezeshki
Non-ECE Member: Donald Estep, MATH
Member 3: Peter Young, ECE
Addional Members: N/A
L. W. Krakow, R. Zahedi, E. K. P. Chong, and A. Pezeshki, "Adaptive Compressive Sensing in the presence of noise and erasure," in Proceedings of the 1st IEEE Global Conference on Signal and Information Processing (GlobalSIP), Austin, TX, December 3--5, 2013.

R. Zahedi, L. W. Krakow, E. K. P. Chong, and A. Pezeshki, "Adaptive Estimation of Time-Varying Sparse Signals," IEEE Access, vol. 1, pp. 449--464, July 2013.

R. Zahedi, L. W. Krakow, E. K. P. Chong, and A. Pezeshki, "Adaptive compressive measurement design using approximate dynamic programming," in Proceedings of the 2013 American Control Conference (ACC 2013), Washington, DC, June 17--19, 2013, pp. 2442--2447.

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, MD, June 30--July 2, 2010, Paper ThC05.1, pp. 4070--4075.
Program of Study:
ECE 516
MATH 517
MATH 560
ECE 752
STAT 720