Domain decompsition for Total Variation Minimization

  • Speaker(s)Professor Xue-Cheng Tai (Department of Mathematics, University of Bergen)
  • DateFrom 2014-07-18 To 2014-07-18
  • VenueRoom 29 at Quan Zhai, BICMR

Speaker: Professor Xue-Cheng Tai (Department of Mathematics, University of Bergen)

Time: Fri, 07/18/2014 - 16:00

Place: Room 29 at Quan Zhai, BICMR

Abstract: This talk is concerned with overlapping domain decomposition methods (DDMs), based on successive subspace correction (SSC) and parallel subspace correc- tion (PSC), for the Rudin, Osher and Fatemi (ROF) model in image restoration. In contrast to recent attempts, we work with a dual formulation of the ROF model, where one significant difficulty lies in the decomposition of the global constraint of the dual problem. We propose a stable ”Unit Decomposition” and this leads us to come natural overlapping domain decomposition schemes for the dual problem. We further analyze the convergence of the proposed algorithms, and obtain the rate O(n−1/2) where n is the number of iterations. Move, the dependence of the convergence rate on the overlapping size, regularization parameter and relaxation parameter is clearly given. To the best of our knowledge, such a convergence has not been claimed so far for domain decomposition related algorithms the ROF model.

This talk is based on joint work with: Huibin Chang, Lilian Wang and Danping Yang.