An accelerated primal-dual iterative scheme for the L2-TV regularized model of linear inverse problems. (18th January 2019)

• Record Type: Journal Article
• Authors: Tian, Wenyi; Yuan, Xiaoming
• Is Part Of: Inverse problems. Volume 35:Number 3(2019)
• Publication Date: 2019-01-18
• Subjects: linear inverse problem -- primal-dual method -- saddle-point problem -- finite element method -- convergence rate -- error estimate; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaf70a
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A model with the and total variational (TV) regularization terms for linear inverse problems is considered. The regularized model is reformulated as a saddle-point problem, and the primal and dual variables are discretized in the piecewise affine and piecewise constant finite element spaces, respectively. An accelerated primal-dual iterative scheme with an convergence rate is proposed for the discretized problem, where is the iteration counter. Both the regularization and perturbation errors of the regularized model, and the finite element discretization and iteration errors of the accelerated primal-dual scheme, are estimated. Preliminary numerical results are reported to show the efficiency of the proposed iterative scheme.