Scientific Computation and Applied & Industrial Mathematics Seminar: Maryam Fazel
- Date: 03/26/2013
- Time: 12:30
University of British Columbia
Recovery and Denoising for Simultaneously Structured Models
We consider models or signals with simultaneous structure, for example a matrix that is simultaneously sparse and low-rank. Our goal is to find suitable convex penalties that allow us to reconstruct such signals given random measurements and noisy observations.
Often penalties that promote each individual structure are known and yield an order-wise optimal number of measurements (e.g., \ell 1 norm for sparsity, nuclear norm for matrix rank), so it is reasonable to minimize a combination of such norms. We show that, surprisingly, if we use multi-objective optimization with the individual norms, then we can do no better (order-wise) in terms of required measurements than an algorithm that exploits only one of the structures. This result suggests that to fully exploit the multiple structures, we need an entirely new convex relaxation, not one that is a function of convex relaxations used for each structures.
Bio: Maryam Fazel is an assistant professor in Electrical Engineering at the University of Washington since 2008. She received her MS and PhD in EE from Stanford University and her BS in EE from Sharif University in Iran, and was a Postdoctoral Scholar at Caltech prior to joining UW. Maryam is a recipient of the NSF Career Award (2009), and the UW EE Outstanding Teaching Award (2009).