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

02/24/2020
by   Jongho Park, et al.
0

In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation minimization adopt the Fenchel–Rockafellar duality, whereas the proposed method is based on the primal formulation. Thus, the proposed method can be applied not only to total variation minimization but also to those with complex dual problems such as higher order models. In the proposed method, an equivalent formulation of the model problem with parallel structure is constructed using a custom overlapping domain decomposition scheme with the notion of essential domains. As a solver for the constructed formulation, we propose a decoupled augmented Lagrangian method for untying the coupling of adjacent subdomains. Convergence analysis of the decoupled augmented Lagrangian method is provided. We present implementation details and numerical examples for various model problems including total variation minimizations and higher order models.

READ FULL TEXT

page 11

page 14

page 17

research
11/15/2019

Pseudo-linear Convergence of an Additive Schwarz Method for Dual Total Variation Minimization

In this paper, we propose an overlapping additive Schwarz method for tot...
research
08/28/2020

An Efficient Augmented Lagrangian Method with Semismooth Newton Solver for Total Generalized Variation

Total generalization variation (TGV) is a very powerful and important re...
research
05/05/2015

Adaptive diffusion constrained total variation scheme with application to `cartoon + texture + edge' image decomposition

We consider an image decomposition model involving a variational (minimi...
research
03/16/2023

Learned Discretization Schemes for the Second-Order Total Generalized Variation

The total generalized variation extends the total variation by incorpora...
research
05/07/2019

Parallel Cut Pursuit For Minimization of the Graph Total Variation

We present a parallel version of the cut-pursuit algorithm for minimizin...
research
03/08/2012

An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems

We present an alternating augmented Lagrangian method for convex optimiz...
research
08/07/2020

Total Variation Diminishing (TVD) method for Elastohydrodynamic Lubrication (EHL) problem on Parallel Computers

In this article, we offer a novel numerical approach for the solution of...

Please sign up or login with your details

Forgot password? Click here to reset