基于Chambolle-Pock算法的计算机断层扫描图像重建凸优化问题原型设计

Chambolle-Pock's Primal-Dual Method with Mismatched Adjoint

The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point problems. Each update step involves the application of both the forward linear operator and its adjoint. However, in practical applications like computerized tomography, it is often computationally favourable to replace the adjoint operator by a computationally more efficient approximation. This leads to an adjoint mismatch in the algorithm. In this paper, we analyze the convergence of Chambolle-Pock's primal-dual method under the presence of a m…

On the improved conditions for some primal-dual algorithms

The convex minimization of $f(\mathbf{x})+g(\mathbf{x})+h(\mathbf{A}\mathbf{x})$ over $\mathbb{R}^n$ with differentiable $f$ and linear operator $\mathbf{A}: \mathbb{R}^n\rightarrow \mathbb{R}^m$, has been well-studied in the literature. By considering the primal-dual optimality of the problem, many algorithms are proposed from different perspectives such as monotone operator scheme and fixed point theory. In this paper, we start with a base algorithm to reveal the connection between several algorithms such as AFBA, PD3O and Chambolle-Pock. Then, we prove its convergence under a relaxed assump…

关于原始-对偶混合梯度算法的单调包含版本的收敛性的一个注记

A note on the convergence of the monotone inclusion version of the primal-dual hybrid gradient algorithm

该研究将Chambolle和Pock的原始-对偶混合梯度（PDHG）算法收敛性证明直接拓展到单调包含场景，完善了该算法的理论适用范围。

The Primal-Dual Hybrid Gradient Method for Semiconvex Splittings

This paper deals with the analysis of a recent reformulation of the primal-dual hybrid gradient method [Zhu and Chan 2008, Pock, Cremers, Bischof and Chambolle 2009, Esser, Zhang and Chan 2010, Chambolle and Pock 2011], which allows to apply it to nonconvex regularizers as first proposed for truncated quadratic penalization in [Strekalovskiy and Cremers 2014]. Particularly, it investigates variational problems for which the energy to be minimized can be written as $G(u) + F(Ku)$, where $G$ is convex, $F$ semiconvex, and $K$ is a linear operator. We study the method and prove convergence in the…

基于sinogram约束的TV最小化方法用于CT中的金属伪影消除

Sinogram constrained TV-minimization for metal artifact reduction in CT

本文提出了一种基于凸优化问题和总变分正则化的CT金属伪影消除方法，利用Chambolle-Pock算法求解，并通过合成数据验证了该方法的有效性。

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of i…