Comparative Analysis of the Prox Penalty and Bregman Algorithms for Image Denoising

IF 1.2 Q2 MATHEMATICS, APPLIED
Soulef Bougueroua, Nourreddine Daili
{"title":"Comparative Analysis of the Prox Penalty and Bregman Algorithms for Image Denoising","authors":"Soulef Bougueroua, Nourreddine Daili","doi":"10.1155/2023/6689311","DOIUrl":null,"url":null,"abstract":"Image restoration is an interesting ill-posed problem. It plays a critical role in the concept of image processing. We are looking for an image that is as near to the original as possible among images that have been skewed by Gaussian and additive noise. Image deconstruction is a technique for restoring a noisy image after it has been captured. The numerical results achieved by the prox-penalty method and the split Bregman algorithm for anisotropic and isotropic TV denoising problems in terms of image quality, convergence, and signal noise rate (SNR) are compared in this paper. It should be mentioned that isotropic TV denoising is faster than anisotropic. Experimental results indicate that the prox algorithm produces the best high-quality output (clean, not smooth, and textures are preserved). In particular, we obtained (21.4, 21) the SNR of the denoising image by the prox for sigma 0.08 and 0.501, such as we obtained (10.0884, 10.1155) the SNR of the denoising image by the anisotropic TV and the isotropic TV for sigma 0.08 and (-1.4635, -1.4733) for sigma 0.501.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/6689311","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

Image restoration is an interesting ill-posed problem. It plays a critical role in the concept of image processing. We are looking for an image that is as near to the original as possible among images that have been skewed by Gaussian and additive noise. Image deconstruction is a technique for restoring a noisy image after it has been captured. The numerical results achieved by the prox-penalty method and the split Bregman algorithm for anisotropic and isotropic TV denoising problems in terms of image quality, convergence, and signal noise rate (SNR) are compared in this paper. It should be mentioned that isotropic TV denoising is faster than anisotropic. Experimental results indicate that the prox algorithm produces the best high-quality output (clean, not smooth, and textures are preserved). In particular, we obtained (21.4, 21) the SNR of the denoising image by the prox for sigma 0.08 and 0.501, such as we obtained (10.0884, 10.1155) the SNR of the denoising image by the anisotropic TV and the isotropic TV for sigma 0.08 and (-1.4635, -1.4733) for sigma 0.501.
Prox罚算法与Bregman算法在图像去噪中的比较分析
图像恢复是一个有趣的不适定问题。它在图像处理概念中起着至关重要的作用。我们要在被高斯和加性噪声扭曲的图像中寻找尽可能接近原始图像的图像。图像解构是一种在捕获有噪声的图像后对其进行恢复的技术。本文比较了prox-penalty算法和split Bregman算法在各向异性和各向同性电视去噪问题上的图像质量、收敛性和信噪比等方面的数值结果。需要指出的是,各向同性电视去噪比各向异性快。实验结果表明,prox算法产生了最好的高质量输出(干净,不光滑,纹理被保留)。特别是,我们通过sigma 0.08和0.501的prox得到去噪图像的信噪比(21.4,21),例如我们通过各向异性电视和各向同性电视得到去噪图像的信噪比(10.0884,10.1155)sigma 0.08和sigma 0.501的信噪比(-1.4635,-1.4733)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信