A primal-dual multiplier method for total variation image restoration

Zhang, Benxin; Zhu, Zhibin; Xu, Chuanpei

doi:10.1016/j.apnum.2019.06.006

Cited by 16 publications

(16 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This function is strongly convex satisfying assumption 1 with σ = (2β) −1 , refer to [10]. During the computation, the minimization problem associated with R in (3.3) is solved by primal dual hybrid gradient method [36] with maximum number of iterations 200. We assume that the exact data u(c † ) of the forward problem (4.1) with c = c † is corrupted by Gaussian noise; thus only noisy data u δ is available.…”

Section: Elliptic Parameter Identificationmentioning

confidence: 99%

Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems

Han

et al. 2023

Inverse Problems

View full text Add to dashboard Cite

Inexact Newton regularization methods are a family of prominent regularization methods for solving nonlinear ill-posed problems, which consist of an outer Newton iteration and an inner scheme providing increments by applying the regularization technique to the local linearized equations. In this paper, we propose a heuristic stopping rule for the inexact Newton regularization method, where the inner scheme is deﬁned by Landweber iteration and the strong convex function is incorporated as the penalty term. In contrast to a prior and a posteriori stopping rules, our heuristic rule is purely data driven and does not require the information on noise level, which renders the method feasible when the noise level is unknown or unreliable. Under certain assumptions on the random noise, we establish a new convergence analysis for the inexact Newton-Landweber method under the heuristic rule. The numerical simulations are provided to demonstrate the performance of our heuristic rule.

show abstract

Section: Elliptic Parameter Identificationmentioning

confidence: 99%

Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems

Han

et al. 2023

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…which is non-smooth and convex. In these simulations, we will use the primal dual hybrid gradient (PDHG) method introduced in [23] to solve (67). We will next report numerical results to indicate the performance of NHP-DBTS method with various choices of the convex function θ and the Banach space Y.…”

Section: Numerical Examplesmentioning

confidence: 99%

An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty

Xia

Han

2021

Inverse Problems

View full text Add to dashboard Cite

We propose and analyze an accelerated homotopy perturbation iteration based on Nesterov strategy for nonlinear inverse problems in Banach spaces. The method allows to use L 1 -like and total variation-like penalty terms. Therefore, it can cope with the situation where the sought solution is sparse and piece-wise constant. Under some standard assumptions, we show the convergence and regularization properties of the method. Numerical experiments are presented to show the effectiveness as well as the acceleration effect of the proposed method.

show abstract

“…). This problem can be solved by many classes of operator splitting algorithms, e.g., Douglas-Rachford splitting (DRS) [31], primal-dual splitting (PDS) [51,11], the alternating direction method of multipliers (ADMM) [22,21], Bregman methods [35,49,23,50], and so on 2 .…”

Section: Introductionmentioning

confidence: 99%

The operator splitting schemes revisited: primal-dual gap and degeneracy reduction by a unified analysis

Xue¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

A primal-dual multiplier method for total variation image restoration

Cited by 16 publications

References 16 publications

Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems

Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems

An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty

The operator splitting schemes revisited: primal-dual gap and degeneracy reduction by a unified analysis

Contact Info

Product

Resources

About