The problem of sparse signal recovery has recently received much attention with the development of compressed sensing and results providing insights into the robustness of l1 based recovery methods. The problem of computing sparse solutions to an underdetermined linear system of equations has a much longer history. Prof. Rao and his group have been involved in this area since 1992. His first work was in the context of biomagnetic imaging.

I.F. Gorodnitsky, B. D. Rao and J. George, “Source Localization in Magnetoencephalagraphy using an Iterative Weighted Minimum Norm Algorithm, IEEE Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, Pages: 167-171, Oct. 1992

Recognizing the importance of sparsity and its role in signal processing, Prof. Bresler and Prof. Rao organized a special session on sparsity at ICASSP 1998 titled “SPEC-DSP: SIGNAL PROCESSING WITH SPARSENESS CONSTRAINT.” This is one of the earliest full session, if not the first session, to be dedicated to the issue of sparsity. In this session, Prof. Rao’s paper discusses the importance of sparsity in signal processing in his article titled.

B. D. Rao, “Signal Processing with the Sparseness Constraint,” IEEE Acoustics, Speech and Signal Processing, Seattle, Washington, Vol.1, Pages: 369 - 372, May. 1998

Additional overview and tutorial presentations

Plenary at SPAWC 2009, June 21-24, Perugia, Italy: Sparse Signal Recovery: Theory, Applications and Algorithms

Tutorial at ICASSP 2010, March 14-19, Dallas, Texas: Sparse Signal Recovery: Theory, Applications and Algorithms

His group has been active in this area and a selected list of publications is provided below. Complete publications list can be found here.

Selected Publications:

1)D.P. Wipf, B.D. Rao, and S. Nagarajan, “Latent Variable Bayesian Models for Promoting Sparsity,” Submitted, IEEE Trans. On Information Theory, 2009.

2)Y. Jin, Y-H. Kim and B. D. Rao, ““Support Recovery of Sparse Signals,” Submitted to IEEE Trans. On Information Theory, March 2009.

3)Y. Jin and B. D. Rao, “Performance Limits of Matching Pursuit Algorithms,” IEEE  International Symposium on Information Theory, Toronto, Canada, Jul. 2008

4)D. P. Wipf and B. D. Rao, “An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem," IEEE Transactions on Signal Processing, Vol. 55, Issue 7, pages: 3704-3716, Part 2, Jul. 2007

5)D. P. Wipf, R. R. Ramírez, J.A. Palmer, S. Makeig, and B. D. Rao, ``Analysis of Empirical Bayesian Methods for Neuroelectromagnetic Source Localization,"  B. Schölkopf, J. Platt, and T. Hoffman, editors, Advances in Neural Information Processing Systems 19, MIT Press, 2007

6)J.A. Palmer, D.P. Wipf, K. Kreutz-Delgado, and B.D. Rao, “Variational EM Algorithms for Non-Gaussian Latent Variable Models,” Y. Weiss, B. Schölkopf, and J. Platt, editors, Advances in Neural Information Processing Systems 18, MIT Press, 2006.

7)S. F. Cotter, B. D. Rao, K. Engan, and K. K-Delgado, “Sparse Solutions to Linear Inverse Problems with Multiple Measurement Vectors,” IEEE Transactions on Signal Processing, Vol. 53, Issue. 7, Pages: 2477 - 2488, July 2005

8)D. P. Wipf and B. D. Rao, “Sparse Bayesian Learning for Basis Selection,” IEEE Transactions on Signal Processing, Special Issue on Machine Learning Methods in Signal Processing, Vol. 52, Pages: 2153 - 2164, Aug. 2004

9)D. P. Wipf, J.A. Palmer, and B. D. Rao,  “Perspectives on Sparse Bayesian Learning,” Neural Information Processing Systems, Vol. 16,  Dec. 2004

10) B. D Rao, K. Engan, S.F. Cotter, J. Palmer, and K. K-Delgado, “Subset Selection in Noise Based on Diversity Measure Minimization,” IEEE Transactions on Signal Processing, Vol. 51, Issue: 3, Pages: 760-770, Mar. 2003

11) K. K-Delgado, J. F. Murray, B. D. Rao, K. Engan, T. W. Lee, and T. J. Sejnowski, Dictionary Learning Algorithms for Sparse Representation,” Neural Computation, Vol. 15, Pages: 349-396, Feb. 2003

12) S. F. Cotter and B. D. Rao, “Sparse Channel Estimation Via Matching Pursuit with Application to Equalization'' IEEE Transactions on Communications, Vol. 50, Issue 3, Pages: 374 - 377, Mar. 2002

13) S. F. Cotter, J. Adler, B. D. Rao, K. K-Delgado, “Forward Sequential Algorithms for Best Basis Selection,” Proceedings Vision, Image, and Signal Processing, Pages: 235-244, Oct. 1999

14) B. D. Rao and K. K-Delgado, “An Affine Scaling Methodology for Best Basis Selection,” IEEE Transactions On Signal Processing, Vol. 47, Pages: 187-200, Jan. 1999

15) I. F. Gorodnitsky and B. D. Rao, “Sparse Signal Reconstruction from Limited Data Using FOCUSS: A Re-Weighted Norm Minimization Algorithm,” IEEE Transactions on Signal Processing, Vol. 45, Issue.3, Pages: 600 - 616, Mar. 1997 

16) I. F. Gorodnitsky, J. George and B. D. Rao, “Neuromagnetic Source Imaging with FOCUSS: A Recursive Weighted Minimum Norm Algorithm,” Electrocephalography and Clinical Neurophysiology 95, Pages: 231-251, 1995

The complete list