TY - JOUR
T1 - Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization
AU - Li , Xue
AU - Zhang , Zhenwei
AU - Chang , Huibin
AU - Duan , Yuping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1017
EP - 1041
PY - 2021
DA - 2021/09
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0146 
UR - https://global-sci.org/intro/article_detail/nmtma/19528.html
KW - Non-overlapping domain decomposition method, primal-dual algorithm, total variation, Rudin-Osher-Fatemi model, Chan-Vese model.
AB - <p style="text-align: justify;">We concern with fast domain decomposition methods for solving the total
variation minimization problems in image processing. By decomposing the image
domain into non-overlapping subdomains and interfaces, we consider the primal-dual problem on the interfaces such that the subdomain problems become independent problems and can be solved in parallel. Suppose both the interfaces and
subdomain problems are uniformly convex, we can apply the acceleration method
to achieve an $\mathcal{O}(1 / n^2)$ convergent domain decomposition algorithm. The convergence analysis is provided as well. Numerical results on image denoising, inpainting, deblurring, and segmentation are provided and comparison results with existing
methods are discussed, which not only demonstrate the advantages of our method
but also support the theoretical convergence rate.</p>