Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means

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• 作者：Haijuan Hu ; Bing Li ; Quansheng Liu
• 关键词：Gaussian noise ; Impulse noise ; Mixed noise ; Trilateral filter ; Non ; local means filter ; Convergence theorems ; Degree of similarity ; Estimation of PSNR
• 刊名：Journal of Scientific Computing
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：67
• 期：1
• 页码：103-129
• 全文大小：2,276 KB
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• 作者单位：Haijuan Hu (1) (2) (3)
  Bing Li (4)
  Quansheng Liu (3)
  
  1. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China
  2. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China
  3. CNRS UMR 6205, LMBA, Université de Bretagne-Sud, Campus de Tohannic, 56000, Vannes, France
  4. Department of Mathematics, Zhongshan Polytechnic, Zhongshan, 528404, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

We first establish a law of large numbers and a convergence theorem in distribution to show the rate of convergence of the non-local means filter for removing Gaussian noise. Based on the convergence theorems, we propose a patch-based weighted means filter for removing an impulse noise and its mixture with a Gaussian noise by combining the essential idea of the trilateral filter and that of the non-local means filter. Experiments show that our filter is competitive compared to recently proposed methods. We also introduce the notion of degree of similarity to measure the impact of the similarity among patches on the non-local means filter for removing a Gaussian noise, as well as on our new filter for removing an impulse noise or a mixed noise. Using again the convergence theorem in distribution, together with the notion of degree of similarity, we obtain an estimation for the PSNR value of the denoised image by the non-local means filter or by the new proposed filter, which is close to the real PSNR value.