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Research Interests for Rayan Saab

Research Interests:

My research draws upon and develops tools in information theory, random matrix theory, frame theory, and geometric functional analysis to solve problems motivated by the acquisition, digitization and processing of signals. My research interests include sparse and low-dimensional representations of high dimensional data, as well as compressed sensing. I am also interested in the digitization of data and in developing and analyzing quantization approaches for both oversampled and compressively sampled signals. In general, I take an active interest in all areas of signal processing and analysis. For example, I am interested in the source separation problem and have worked on the theory of blind source separation and its application to the cocktail party problem and to seismic signal decomposition, as well as on image processing applications.

Current projects:
Quantization of frame expansions
Quantization of compressed sensing measurements
Generalizations of the empirical mode decomposition
Areas of Interest:

Compressed Sensing/Sparse Approximation
Quantization
Geometric Functional Analysis
Frame Theory

Recent Publications
  1. F. Krahmer, R. Saab, R. Ward, Root-exponential accuracy for coarse quantization of finite frame expansions, IEEE Transactions on Information Theory (February, 2012) [pdf]
  2. M. P. Friedlander, H. Mansour, R. Saab, Ö. Yilmaz, Recovering Compressively Sampled Signals Using Partial Support Information, IEEE Transactions on Information Theory (February, 2012) [1010.4612v2]
  3. A. Powell, R. Saab, O. Yilmaz, Quantization and finite frames, in Finite frames, edited by P. Casazza, G. Kutyniok (2012), ISBN 978-0-8176-8373-3
  4. N. Strawn, A. Armagan, R.Saab, L. Carin, D. Dunson, Finite sample posterior concentration in high-dimensional regression (Submitted, 2012)
  5. S. Güntürk, M. Lammers, A. Powell, R. Saab, O. Yilmaz., Sobolev duals for random frames and Sigma-Delta quantization of compressed sensing measurements, Foundations of Computational Mathematics (Accepted, 2012)

 

dept@math.duke.edu
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320