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