A General Framework for a Class of First Order Primal Dual Algorithms for Convex Optimization in Imaging Science

Series: 
Applied and Computational Mathematics Seminar
Monday, November 8, 2010 - 13:00
1 hour (actually 50 minutes)
Location: 
Skiles 002
,  
University of California, Irvine
Organizer: 
In this talk, based on joint work with Xiaoqun Zhang and Tony Chan, we showhow to generalize the primal dual hybrid gradient (PDHG) algorithm proposedby Zhu and Chan to a broader class of convex optimization problems. A mainfocus will also be to survey several closely related methods and explain theconnections to PDHG. We point out convergence results for some modifiedversions of PDHG that have similarly good empirical convergence rates fortotal variation (TV) minimization problems.  We also show how to interpretPDHG applied to TV denoising as a projected averaged gradient method appliedto the dual functional.  We present some numerical comparisons of thesealgorithms applied to TV denoising and discuss some novel applications suchas convexified multiphase segmentation.