Signal Recovery from Randomized Measurements Using Structured Sparsity Models

March 3, 2011
Time: 11:00am-12:00pm
Speaker: Marco Duarte, Duke University


We are in the midst of a digital revolution spawned by the proliferation of sensing devices with ever increasing fidelity and resolution. The resulting data deluge has motivated compression schemes that rely on transform coding, where a suitable transformation of the data provides a sparse representation that compacts the signal energy into a few transform coefficients. This standard approach, however, still requires signal acquisition at the full Nyquist rate, which cannot be achieved in many emerging applications using current sensing technology. The emerging acquisition paradigm of compressive sensing (CS) leverages signal sparsity for recovery from a small set of randomized measurements. The standard CS theory dictates that robust recovery of a K-sparse, N-length signal is possible from M=O(K log(N/K)) measurements. New sensing devices that implement this measurement process have been developed for applications including imaging, communications, and biosensing.

In this talk, we show that it is possible to substantially decrease the number of measurements M without sacrificing robustness by leveraging more concise signal models that go beyond simple sparsity and compressibility. We present a modified CS theory for structured sparse signals that exploits the dependencies between values and locations of the significant signal coefficients; we provide concrete guidelines on how to create new recovery algorithms for structured sparse signals with provable performance guarantees that require as few as M=O(K) measurements. We also review example applications of structured sparsity for natural images, signal ensembles, and multiuser detection.

Speaker Biography

Marco F. Duarte received the B.Sc. degree in computer engineering (with distinction) and the M.Sc. degree in electrical engineering from the University of Wisconsin-Madison in 2002 and 2004, respectively, and the Ph.D. degree in electrical engineering from Rice University, Houston, TX, in 2009. During 2009-2010, he was a Visiting Postdoctoral Research Fellow in the Program of Applied and Computational Mathematics at Princeton University. He is currently the NSF/IPAM Mathematical Sciences Postdoctoral Research Fellow in the Department of Computer Science at Duke University.

Dr. Duarte received the Rice University Presidential Fellowship and the Texas Instruments Distinguished Fellowship in 2004, and the Hershel M. Rich Invention Award in 2007 for his work on the single pixel camera. He was a coauthor on a paper with Chinmay Hegde and Volkan Cevher that won the Best Student Paper Award at the 2009 International Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS). His research interests include compressive sensing, low-dimensional signal models, dimensionality reduction, and distributed signal processing.

500 W. 120th St., Mudd 1310, New York, NY 10027    212-854-3105               
©2014 Columbia University