数值计算与计算机应用 2009, 30(1) 70-80 DOI:     ISSN: 1000-3266 CN: 11-2124/TP

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图像恢复; 正则化; 重开始共轭梯度法; 投影
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PubMed

模糊图像恢复的投影重开始共轭梯度法

曹静杰1, 修乃华2

  1. 中国科学院地质与地球物理研究所, 油气综合地球物理重点实验室, 北京 100029
  2. 北京交通大学理学院, 北京 100044

摘要

针对点扩散函数为线性位移不变的图像恢复问题提出了一种重开始的投影共轭梯度法. 该方法结合正则化技术,分两层迭代,采用阻尼Morozov偏
差原则作为停机准则,在运算中利用快速傅立叶变换减少计算复杂度. 并对二维遥感灰度图像和彩色图像分别进行数值实验, 验证了该方法可以有效的再现原始图像,证明了算法的有效性.

关键词 图像恢复; 正则化; 重开始共轭梯度法; 投影  

A RESTARTED PROJECTED CONJUGATE GRADIENT METHOD FOR IMAGE RESTORATION

Cao Jingjie1, Xiu Naihua2

  1. Key Laboratory of Integrative Researches on Geophysics for Petroleam, Institute of Geology and Geophysics, Chinese Academy of Science, Beijing 100029, China
  2. Department of Mathematics, Beijing Jiaotong University,  Beijing 100044, China

Abstract:

In this paper, we propose a regularized restarted conjugate gradient method with projection technique for image restoration problem. We assume that the point spread kernel function is linear and spatially invariant. The iteration scheme consists of two cycles: the inner iteration (conjugate gradient method) and the outer iteration (restarted conjugate gradient method). The damped Morozov's discrepancy principle is adopted as the stopping rule. For large scale matrix-vector multiplication, the fast Fourier transform is used to reduce the computational complexity. Numerical tests on atmospheric blurred image restoration problems are performed to show that the method can properly retrieve the information of the original image, hence this is a promising method for image restoration problems.

Keywords: image restoration; regularization; restarted conjugate gradient method; projection  
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