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Applied Mathematics Colloquium

Monday, February 6, 2012
4:15pm to 5:15pm
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Annenberg 105
Compressive Sensing: Dynamics, Multichannel Sampling, and Parametric Estimation
Justin Romberg, Associate Professor , Electrical and Computer Engineering, Georgia Tech,
We will discuss three related research projects in the area of compressive sensing that have a nice mix of theoretical, algorithmic, and practical results.

* Dynamical compressive sensing. We will discuss efficient techniques for updating the solutions of non-smooth optimization program (e.g. the LASSO or L1-regularized least-squares) from streaming measurements. We will show how the solution update essentially breaks down into a series of low-rank updates, giving us an algorithmic framework reminiscent of the Kalman filter for jointly tracking and reconstructing a signal.

* Multichannel sampling. We will discuss architectures for efficient sampling of signals which have latent correlation structure. We will show that even if this structure is unknown, the signals can be dramatically undersampled if they "pre-coded'' using simple analog computations.

* Compressed parametric estimation. It is often the case that we are only interested in some key parameters of a signal (the time-of-arrival of a pulse, for example, or the slope of a linear chirp). We will discuss some quantitative bounds on our ability to estimate such parameters, and demonstrate the methods numerically with an acoustic source localization problem.
For more information, please contact Sydney Garstang by phone at x4555 or by email at [email protected] or visit http://www.acm.caltech.edu.