## Departmental Colloquium

Ming-Jun Lai

University of Georgia

Some Recent Advances on Compressed Sensing and Matrix Completion

**Abstract:**I will start with a motivation how to recover a low-rank matrix from a small number of its linear measurements, e.g., a subset of its entries. As such problems share many common features with the recent study of recovering sparse vectors in compressed sensing, I shall give a quick review with some most updated research results on sparse vector recovery and matrix completion. Then I will explain an unconstrained $L^q$ minimization approach and an iteratively reweighted algorithm for recovering sparse vectors as well as for recovering low-rank matrices. A convergence analysis of these iterative algorithms will be given. Finally, I shall present some numerical results for recovering images from their random sampling entries without and with noises.

Friday March 15, 2013 at 3:00 PM in SEO 636