IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v542y2020ics0378437119319612.html
   My bibliography  Save this article

A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing

Author

Listed:
  • Ghanbari, Behzad
  • Atangana, Abdon

Abstract

Based on a new definition for derivative and integral of fractional-order, several fractional masks have been presented for the use of image denoising. In each method, the process involves constructing a square and then applying it to all the corresponding blocks in the noisy image. We have measured the denoising performance of our proposed masks by employing some known indexes. They are the peak signal-to-noise ratio (PSNR), ENTROPY, and SSIM. The obtained experimental results show that our proposed masks are computationally efficient, and their performances are compatible with other standard and fractional smoothing filters.

Suggested Citation

  • Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    • Handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119319612
    DOI: 10.1016/j.physa.2019.123516
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119319612
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123516?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Imran, M.A. & Aleem, Maryam & Riaz, M.B. & Ali, Rizwan & Khan, Ilyas, 2019. "A comprehensive report on convective flow of fractional (ABC) and (CF) MHD viscous fluid subject to generalized boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 274-289.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Ai-Min Yang & Yu-Zhu Zhang & Carlo Cattani & Gong-Nan Xie & Mohammad Mehdi Rashidi & Yi-Jun Zhou & Xiao-Jun Yang, 2014. "Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    4. Akgül, Ali & Modanli, Mahmut, 2019. "Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 10-16.
    5. Gao, Wei & Ghanbari, Behzad & Baskonus, Haci Mehmet, 2019. "New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 34-43.
    6. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    7. Hamid A. Jalab & Rabha W. Ibrahim, 2012. "Denoising Algorithm Based on Generalized Fractional Integral Operator with Two Parameters," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-14, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Shoaib, Muhammad & Abbasi, Aqsa Zafar & Raja, Muhammad Asif Zahoor & Nisar, Kottakkaran Sooppy, 2022. "A design of predictive computational network for the analysis of fractional epidemical predictor-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Mohammad, Mutaz & Trounev, Alexander, 2020. "Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Mohammad, Mutaz & Trounev, Alexander, 2020. "On the dynamical modeling of COVID-19 involving Atangana–Baleanu fractional derivative and based on Daubechies framelet simulations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Xin Liu & Lili Chen & Yanfeng Zhao, 2023. "Existence Theoremsfor Solutions of a Nonlinear Fractional-Order Coupled Delayed System via Fixed Point Theory," Mathematics, MDPI, vol. 11(7), pages 1-15, March.
    8. Khan, Zeshan Aslam & Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor, 2022. "Generalized fractional strategy for recommender systems with chaotic ratings behavior," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    10. Li, Xuhui & Agarwal, Ravi P. & Gómez-Aguilar, J.F. & Badshah, Qaisar & Rahman, Ghaus ur, 2022. "Threshold dynamics: Formulation, stability & sensitivity analysis of co-abuse model of heroin and smoking," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    11. Malik, Muhammad Faizan & Chang, Ching-Lung & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa kausar & Shu, Chi-Min & Raja, Muhammad Asif Zahoor, 2023. "Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    12. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Ghanbari, Behzad & Kumar, Sunil & Kumar, Ranbir, 2020. "A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Zafar, Zain Ul Abadin & Younas, Samina & Hussain, Muhammad Tanveer & Tunç, Cemil, 2021. "Fractional aspects of coupled mass-spring system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Allahviranloo, Tofigh & Ghanbari, Behzad, 2020. "On the fuzzy fractional differential equation with interval Atangana–Baleanu fractional derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 171-179.
    9. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
    10. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Peng, Li & Zhou, Yong & Debbouche, Amar, 2019. "Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 234-241.
    12. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    13. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    14. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    15. Tajani, Asmae & El Alaoui, Fatima-Zahrae & Boutoulout, Ali, 2022. "Regional boundary controllability of semilinear subdiffusion Caputo fractional systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 481-496.
    16. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    17. Doungmo Goufo, Emile F. & Mbehou, Mohamed & Kamga Pene, Morgan M., 2018. "A peculiar application of Atangana–Baleanu fractional derivative in neuroscience: Chaotic burst dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 170-176.
    18. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.
    19. Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    20. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119319612. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.