An improved method for image denoising based on fractional-order integration
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Frontiers of Information Technology & Electronic Engineering www.jzus.zju.edu.cn; engineering.cae.cn; www.springerlink.com ISSN 2095-9184 (print); ISSN 2095-9230 (online) E-mail: [email protected]
An improved method for image denoising based on fractional-order integration* Li XU1,2, Guo HUANG†‡3, Qing-li CHEN3, Hong-yin QIN3, Tao MEN3, Yi-fei PU2 1
College of Electronics and Materials Engineering, Leshan Normal University, Leshan 614000, China 2
College of Computer Science, Sichuan University, Chengdu 610064, China
3
Key Lab of Internet Natural Language Processing of Sichuan Provincial Education Department, Leshan Normal University, Leshan 614000, China †
E-mail: [email protected]
Received Dec. 24, 2019; Revision accepted Mar. 14, 2020; Crosschecked Aug. 28, 2020
Abstract: Given that the existing image denoising methods damage the texture details of an image, a new method based on fractional integration is proposed. First, the fractional-order integral formula is deduced by generalizing the Cauchy integral, and then the approximate value of the fractional-order integral operator is estimated by a numerical method. Finally, a fractional-order integral mask operator of any order is constructed in eight pixel directions of the image. Simulation results show that the proposed image denoising method can protect the edge texture information of the image while removing the noise. Moreover, this method can obtain higher image feature values and better image vision after denoising than the existing denoising methods, because a texture protection mechanism is adopted during the iterative processing. Key words: Fractional-order integral; Cauchy integral; Image denoising; Fractional gradient; Texture protection https://doi.org/10.1631/FITEE.1900727 CLC number: TP391
1 Introduction With the rapid development of computer technology, digital image filtering technology has been widely used. Image denoising is an important part of image filtering. Fractional calculus is an important branch of mathematical analysis (Pu et al., 2014; Shao et al., 2014; Nandal et al., 2018). However, its application in signal analysis and processing, especially ‡
Corresponding author Project supported by the National Natural Science Foundation of China (No. 61201438), the Key Project of Education Department of Sichuan Province, China (No. 18ZA0235), the Research Fund of Key Laboratory of Internet Natural Language Processing of Sichuan Education Department, China (No. INLP201904), and the Research Fund of Leshan Normal University, China (No. LZD003) ORCID: Li XU, https://orcid.org/0000-0002-1376-1779; Guo HUANG, https://orcid.org/0000-0001-8109-7833 © Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 *
in digital image processing, is still a new research direction (Jiang and Wang, 2012; Jalab and Ibrahim, 2015; Yu et al., 2017; Jain et al., 2018). So far, researchers have proposed many conventional methods for image denoising (Chen DL et al., 2013; Zhang GM et al., 2016; Wu GC et al., 2019a). The frac
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