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

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