The Split Bregman Method for L1 Projection Problems

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The Split Bregman Method for L1 Projection Problems

更新时间：2025-07-08

- The Split Bregman Method for L1 Projection Problems
- Acta Electronica Sinica Vol. 38, Issue 11, Pages: 2471-2475(2010)
- 作者机构：
  
  1. 西安电子科技大学应用数学系,陕西,西安,710071
  2. 宝鸡文理学院计算机科学系,陕西,宝鸡,721013
  3. 西安电子科技大学应用数学系陕西西安,710071
  4. 宝鸡文理学院计算机科学系陕西宝鸡,721013
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN911
- Published：2010
- 稿件说明：
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The Split Bregman Method for L1 Projection Problems[J]. Acta Electronica Sinica, 2010, 38(11): 2471-2475.
DOI：

The Split Bregman Method for L1 Projection Problems[J]. Acta Electronica Sinica, 2010, 38(11): 2471-2475. DOI：

摘要

为了解决一般的

1投影问题

提出交替分裂Bregman

1投影算法

并给出了算法的收敛性分析和证明.该算法适用于宽泛的

1投影的线性逆问题

以全变差投影为例

该算法比目前所提出的对偶投影算法收敛速度更快

图像恢复的质量更高.通过图像去噪、去模糊和修补的实验结果表明

相比于目前的对偶投影算法

不论是信噪比还是视觉效果

该算法的结果更优.

Abstract

In order to solve general

1 projection problems

this paper proposes Alternating Split Bregman

1 projection algorithm.The convergence of the iteration scheme is analyzed and proved.The algorithm can solve a very broad class of

1-projection problems.Total variation projection as an example

using the proposed algorithm

we can get faster convergence rate and better result of image restoration.Numerical results show that our algorithm is better than state of the art TV projection method (Dual projection algorithm) to solve denoising

deconvolution and inpainting problems.

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Related Institution

School of Mathematics and physicsDalian Jiaotong UniversityDalianLiaoning 116028China

Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianLiaoning 116024China

School of Mathematics and physics,Dalian Jiaotong University

Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology

Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of ChinaInstitute of Intelligent Information ProcessingXidian UniversityXi'anShaanxi 710071China

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