Date & Time:
Friday, June 3, 2011; 11:00 AM
In this talk, I will discuss our recent work on Recursive Sparse Recovery (RecSparsRec) and show how it provides novel solutions to two very different problems in dynamic imaging. RecSparsRec refers to recursive approaches to causally recover a time sequence of signals/images from a greatly reduced number of measurements (compared to existing approaches), by utilizing their sparsity.
The motivating application for RecSparsRec is fast recursive dynamic magnetic resonance imaging (MRI) for real-time applications like MRI-guided surgery. MRI is a technique for cross-sectional imaging that acquires Fourier projections of the cross-section to be reconstructed, one-at-a-time. Thus, the ability to accurately reconstruct using fewer measurements directly translates into reduced scan times. This, along with online (causal) and fast (recursive) reconstruction algorithms, can enable real-time imaging of fast changing physiological phenomena, and thus make real-time MRI feasible. Cross-sectional images of the brain, heart, or other organs are known to be wavelet sparse. Our recent work was the first to observe that, in a time sequence, their sparsity pattern changes quite slowly. Using this fact, we were able to reformulate the RecSparsRec problem as one of sparse reconstruction with partially known support. We introduced a simple, but very powerful, approach called!
Modified-CS that achieves provably exact reconstruction (in the noise-free case) and whose error is provably stable over time (in the noisy case), with using much fewer measurements than existing work. Our preliminary experiments indicate that Modified-CS needs roughly 5-times fewer measurements than existing MR scanner technology and 1.5-times fewer than existing research literature.
I will briefly also discuss our ongoing work on the difficult video analysis problem of separating foreground moving objects from a background scene that is itself is changing and dong this in real-time. This can be posed as a recursive robust principal components analysis (PCA) problem in the presence of correlated sparse outliers or equivalently, as a problem of recursive sparse recovery in the presence of very large, but ``low rank" noise (noise with a low rank covariance matrix).
Prof. Namrata Vaswani
Iowa State University
Namrata Vaswani received a B.Tech. from the Indian Institute of Technology (IIT), Delhi, in August 1999 and a Ph.D. from the University of Maryland, College Park, in August 2004, both in Electrical Engineering. During 2004-05, she was a research scientist at Georgia Tech. Since Fall 2005, she has been an Assistant Professor in the Electrical and Computer Engineering department at Iowa State University. She held the Harpole-Pentair assisant professorship during 2008-09. Since 2009, she is serving as an Associate Editor for the IEEE Transactions on Signal Processing. Her research interests are in statistical signal processing, medical imaging and computer vision. Her current work focuses on recursive sparse recovery (compressive sensing), recursive robust PCA, dynamic MRI and vision-based tracking.