分数傅里叶变换与里兹势和图像处理的结合

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE SIAM Journal on Imaging Sciences Pub Date : 2024-02-27 DOI:10.1137/23m1555442

Zunwei Fu, Yan Lin, Dachun Yang, Shuhui Yang

{"title":"分数傅里叶变换与里兹势和图像处理的结合","authors":"Zunwei Fu, Yan Lin, Dachun Yang, Shuhui Yang","doi":"10.1137/23m1555442","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 476-500, March 2024. <br/>Abstract.Via chirp functions from fractional Fourier transforms, we introduce fractional Riesz potentials related to chirp functions, which are further used to give a new image encryption method with double phase coding. In a comparison with the image encryption method based on fractional Fourier transforms, via a series of image encryption and decryption experiments, we demonstrate that the symbols of fractional Riesz potentials related to chirp functions and the order of fractional Fourier transforms essentially provide greater flexibility and information security. We also establish the relations of fractional Riesz potentials related to chirp functions with fractional Fourier transforms, fractional Laplace operators, and fractional Riesz transforms, and we obtain their boundedness on rotation invariant spaces.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"36 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional Fourier Transforms Meet Riesz Potentials and Image Processing\",\"authors\":\"Zunwei Fu, Yan Lin, Dachun Yang, Shuhui Yang\",\"doi\":\"10.1137/23m1555442\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 476-500, March 2024. <br/>Abstract.Via chirp functions from fractional Fourier transforms, we introduce fractional Riesz potentials related to chirp functions, which are further used to give a new image encryption method with double phase coding. In a comparison with the image encryption method based on fractional Fourier transforms, via a series of image encryption and decryption experiments, we demonstrate that the symbols of fractional Riesz potentials related to chirp functions and the order of fractional Fourier transforms essentially provide greater flexibility and information security. We also establish the relations of fractional Riesz potentials related to chirp functions with fractional Fourier transforms, fractional Laplace operators, and fractional Riesz transforms, and we obtain their boundedness on rotation invariant spaces.\",\"PeriodicalId\":49528,\"journal\":{\"name\":\"SIAM Journal on Imaging Sciences\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Imaging Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1555442\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Imaging Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1555442","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 影像科学期刊》，第 17 卷第 1 期，第 476-500 页，2024 年 3 月。摘要.通过分数傅里叶变换的啁啾函数，我们引入了与啁啾函数相关的分数里兹电势，并进一步利用这些电势给出了一种新的双相位编码图像加密方法。在与基于分数傅里叶变换的图像加密方法的比较中，通过一系列图像加密和解密实验，我们证明了与啁啾函数相关的分数 Riesz 势的符号和分数傅里叶变换的阶数本质上提供了更大的灵活性和信息安全性。我们还建立了与啁啾函数相关的分数里兹势与分数傅里叶变换、分数拉普拉斯算子和分数里兹变换的关系，并得到了它们在旋转不变空间上的有界性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Fractional Fourier Transforms Meet Riesz Potentials and Image Processing

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 476-500, March 2024.
Abstract.Via chirp functions from fractional Fourier transforms, we introduce fractional Riesz potentials related to chirp functions, which are further used to give a new image encryption method with double phase coding. In a comparison with the image encryption method based on fractional Fourier transforms, via a series of image encryption and decryption experiments, we demonstrate that the symbols of fractional Riesz potentials related to chirp functions and the order of fractional Fourier transforms essentially provide greater flexibility and information security. We also establish the relations of fractional Riesz potentials related to chirp functions with fractional Fourier transforms, fractional Laplace operators, and fractional Riesz transforms, and we obtain their boundedness on rotation invariant spaces.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.