September 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

Publications:

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

N/A

N/A

N/A