An Efficient Primal-Dual Hybrid Gradient Algorithm For Total Variation Image Restoration 一种高效的全变差图像恢复的原始-对偶混合梯度算法

课程讲义. 作者: My T. Thai

成像和计算机视觉中的逆问题通常作为数据保真度优化问题来解决，其中包括 H1 或 TV（总变异）等数据正则化器以呈现问题的适定性。 然而，虽然已知 H1 正则化会产生过度平滑的重建，但 TV（或 ROF）模型是保留特征的，但会引入阶梯伪影。 Sochen、Kimmel 和 Malladi (1998) 引入的几何衍生的 Beltrami 框架在特征保留和避免楼梯伪影之间提供了理想的折衷方案。 到目前为止，Beltrami 正则化器的主要限制因素之一是缺乏真正有效的优化方案。 在这里，我们从最有效的 TV 优化方法之一开始，原始对偶投影梯度，并将其应用于 Beltrami 泛函。 这样做，我们在基本灰度去噪问题上获得了比 ROF 去噪更好的性能，然后将该方法扩展到更复杂的问题，如修复、去卷积和颜色情况，所有这些都以一种简单的方式。 与最先进的 TV/ROF 正则化器相比，使用所提出的原始对

Dual and primal-dual methods for solving strictly convex quadratic programs.pdf

In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issue relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrota's predictor-correction algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems. Some background in linear programming and its associated duality theory, linear algebra, and numerical analysis is helpful, although an extensive appendix ensures that the book is largely self-contained. The book is useful for graduate students and researchers in the sciences and engineering who are interested in using large-scale optimization techniques in their research, including those interested in original research in interior-point methods. Engineers may also find applications to problems of process control, predictive control, or design optimization. The book may also be used as a text for a special topics course in optimization or a unit of a general course in optimization or linear programming. Researchers and students in the field of interior-point methods will find the book invaluable as a reference to the key results, the basic analysis in the

凸优化工具

this packet codes are about primal dual algorithms for image processing such as image denoising based on ROF model and TV-L1 and Huber ROF, image restoration like deconvolution, image zooming, image inpainting,optical flow for motion estimation and Mumford-Shah multi-label image segmentation problem. these codes are base on the following paper,"a first-order primal-dual algorithm for convex problems with application to imaging", and are organized corresponding to the structure of this paper, therefore these codes are what so-called sample codes of this paper, so they are really convenient to learn and to use. to use them, what you need to do is just to open a folder, and run the corresponding .m file, then you will collect the processing result. to understand these codes,you are recommended to read the paper first, in this case, you can get a better comprehension about these codes. and before you use them, you are also recommended first to read the instructions included in the zip packet,because in all the codes,the primal variables and dual variables are both vectorized which are different from the general situations. if you have any questions about these codes,don't hesitate to contact me via email: Pock, Thomas:pock@icg.tugraz.at Chen, Yunijn:cheny@icg.tugraz.at enjoy them,and good luck with you.