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 lowdimensional 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
 F. Krahmer, R. Saab, R. Ward, Rootexponential accuracy for coarse quantization of finite frame expansions,
IEEE Transactions on Information Theory
(February, 2012) [pdf]
 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]
 A. Powell, R. Saab, O. Yilmaz, Quantization and finite frames,
in Finite frames, edited by P. Casazza, G. Kutyniok
(2012), ISBN 9780817683733
 N. Strawn, A. Armagan, R.Saab, L. Carin, D. Dunson, Finite sample posterior concentration in highdimensional regression
(Submitted, 2012)
 S. Güntürk, M. Lammers, A. Powell, R. Saab, O. Yilmaz., Sobolev duals for random frames and SigmaDelta quantization of compressed sensing measurements,
Foundations of Computational Mathematics
(Accepted, 2012)
