基于伽马范数最小化的图像去噪算法

王洪雁; 王拓; 潘勉; 汪祖民

doi:10.11959/j.issn.1000-436x.2020190

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基于伽马范数最小化的图像去噪算法

学术通信 | 更新时间：2024-06-05

- 基于伽马范数最小化的图像去噪算法
- Gamma norm minimization based image denoising algorithm
- 通信学报 2020年41卷第10期页码：222-234
- 作者机构：
  
  1. 浙江理工大学信息学院，浙江杭州 310018
  2. 大连大学信息工程学院，辽宁大连 116622
  3. 五邑大学智能制造学部，广东江门 529020
  4. 杭州电子科技大学电子信息学院，浙江杭州 310018
- 作者简介：
  
  [ "王洪雁（1979– ），男，河南南阳人，博士，浙江理工大学特聘教授、硕士生导师，主要研究方向为稀疏学习、阵列信号处理、参数估计、机器视觉等" ]
  [ "王拓（1992– ），男，河南南阳人，大连大学硕士生，主要研究方向为数字图像处理、机器视觉等" ]
  [ "潘勉（1985– ），男，浙江丽水人，博士，杭州电子科技大学讲师、硕士生导师，主要研究方向为稀疏学习、图像处理、机器视觉等" ]
  [ "汪祖民（1975– ），男，河南信阳人，博士，大连大学教授、硕士生导师，主要研究方向为信号处理、机器学习等" ]
- 基金信息：
  
  国家自然科学基金资助项目(61301258);国家自然科学基金资助项目(61271379);国家自然科学基金资助项目(61871164);中国博士后科学基金资助项目(2016M590218)
- DOI：10.11959/j.issn.1000-436x.2020190
  中图分类号： TP391.41
- 网络首发：2020-10，
  
  纸质出版：2020-10-25
- 稿件说明：
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王洪雁, 王拓, 潘勉, 等. 基于伽马范数最小化的图像去噪算法[J]. 通信学报, 2020,41(10):222-234.

Hongyan WANG, Tuo WANG, Mian PAN, et al. Gamma norm minimization based image denoising algorithm[J]. Journal on Communications, 2020, 41(10): 222-234.
王洪雁, 王拓, 潘勉, 等. 基于伽马范数最小化的图像去噪算法[J]. 通信学报, 2020,41(10):222-234. DOI： 10.11959/j.issn.1000-436x.2020190.

Hongyan WANG, Tuo WANG, Mian PAN, et al. Gamma norm minimization based image denoising algorithm[J]. Journal on Communications, 2020, 41(10): 222-234. DOI： 10.11959/j.issn.1000-436x.2020190.

摘要

针对核范数有偏近似秩函数导致基于核范数最小化的传统去噪方法去噪性能较差的问题，基于低秩理论，提出一种基于伽马范数最小化的图像去噪算法。首先对噪声图像重叠分块，然后基于结构相似性指数自适应搜索与当前图像块最相似的若干非局部图像块以组成相似图像块矩阵，进而利用非凸伽马范数无偏近似矩阵秩函数构建低秩去噪模型，最后基于奇异值分解对所得低秩去噪优化问题求解，并将去噪图像块重组为去噪图像。仿真结果表明，与现有主流PID、NLM、BM3D、NNM、WNNM、DnCNN和FFDNet算法相比，所提算法可较显著地消除高斯噪声，且可较好地恢复原始图像细节。

Abstract

Focusing on the issue of rather poor denoising performance of the traditional kernel norm minimization based method caused by the biased approximation of kernel norm to rank function

based on the low-rank theory

a gamma norm minimization based image denoising algorithm was developed.The noisy image was firstly divided into some overlapping patches via the proposed algorithm

and then several non-local image patches most similar to the current image patch were sought adaptively based on the structural similarity index to form the similar image patch matrix.Subsequently

the non-convex gamma norm could be exploited to obtain unbiased approximation of the matrix rank function such that the low-rank denoising model could be constructed.Finally

the obtained low-rank denoising optimization issue could be tackled on the basis of singular value decomposition

and therefore the denoised image patches could be re-constructed as a denoised image.Simulation results demonstrate that

compared to the existing state-of-the-art PID

NLM

BM3D

NNM

WNNM

DnCNN and FFDNet algorithms

the developed method can eliminate Gaussian noise more considerably and retrieve the original image details rather precisely.

关键词

Keywords

references

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