English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we propose a novel overlapping domain decomposition methodthat can be applied to various problems in variational imaging such as totalvariation minimization. Most of recent domain decomposition methods for totalvariation minimization adopt the Fenchel--Rockafellar duality, whereas theproposed method is based on the primal formulation. Thus, the proposed methodcan be applied not only to total variation minimization but also to those withcomplex dual problems such as higher order models. In the proposed method, anequivalent formulation of the model problem with parallel structure isconstructed using a custom overlapping domain decomposition scheme with thenotion of essential domains. As a solver for the constructed formulation, wepropose a decoupled augmented Lagrangian method for untying the coupling ofadjacent subdomains. Convergence analysis of the decoupled augmented Lagrangianmethod is provided. We present implementation details and numerical examplesfor various model problems including total variation minimizations and higherorder models.

An Overlapping Domain Decomposition Framework without Dual Formulation for Variational Imaging Problems