In  this  talk,  we  introduced  an  efficient  prime-dual  hybrid  gradient  algorithm  for  total  variation minimization problems. This descent-type algorithm alternates between primal and dual variables and  could  be  connected  to  several  popular  existing  methods  such  as  CGM  and  Chambolle’s algorithms. As a numerical experiment, we also present a comparison of the performance of these algorithms  applied  to  a  benchmark  denoising  problem  in  the  image  processing  realm. 

 

Reference: 

Esser,  Ernie,  Xiaoqun  Zhang,  and  Tony  F.  Chan.  "A  general  framework  for  a  class  of  first  order primal-dual  algorithms  for  convex  optimization  in  imaging  science."  SIAM  Journal  on  Imaging Sciences 3.4 (2010): 1015-1046.