{"title":"Low-cost denoising and deblurring using a novel nonlinear diffusion technique","authors":"Lorella Fatone , Daniele Funaro","doi":"10.1016/j.cam.2024.116423","DOIUrl":null,"url":null,"abstract":"<div><div>An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses an ad-hoc discretization scheme for the Laplace operator, multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is in general needed, leading to significant time savings. The procedure is successfully tested on some standard black&white images.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116423"},"PeriodicalIF":2.6000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037704272400671X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/7 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses an ad-hoc discretization scheme for the Laplace operator, multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is in general needed, leading to significant time savings. The procedure is successfully tested on some standard black&white images.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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