Research Interests for Rayan Saab

My current research focuses on both the mathematical and practical aspects of signal processing, including sparse approximation and compressed sensing. For example, I work on developing and analyzing algorithms for reconstruction from compressed sensing measurements. My current work also includes quantization of redundant representations and quantization of compressed sensing measurements. My research areas generally draw upon tools from information theory, probability theory, geometric functional analysis, and applied harmonic analysis.

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 (Accepted, 2011) [pdf]
2. M. P. Friedlander, H. Mansour, R. Saab, Ö. Yilmaz, Recovering Compressively Sampled Signals Using Partial Support Information, IEEE Transactions on Information Theory (Accepted, 2011) [1010.4612v2]
3. S. Güntürk, M. Lammers, A. Powell, R. Saab, O. Yilmaz., Sobolev duals for random frames and Sigma-Delta quantization of compressed sensing measurements (Submitted, 2010)
4. R. Saab, O. Yilmaz, Sparse recovery by non-convex optimization -- instance optimality, Applied and Computational Harmonic Analysis. (2009) [002]
5. E. van den Berg, M.P. Friedlander, G. Hennenfent, F. J. Herrmann, R. Saab, O. Yilmaz., Sparco: a testing framework for sparse reconstruction, ACM Transactions on Mathematical Software (2009) [pdf]