IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip1s0960077923008263.html
   My bibliography  Save this article

Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising

Author

Listed:
  • Ben-Loghfyry, Anouar
  • Charkaoui, Abderrahim

Abstract

This work tackles a novel partial differential equation based on a time-fractional order derivative for image denoising and restoration. We ameliorate the classical Perona–Malik model by considering Caputo time-fractional order derivative with a regularized diffusion. We start by investigating the existence of the solution to the proposed model. As a first result, we use the Faedo–Galerkin approach to prove the existence and uniqueness of a weak solution to an auxiliary fractional problem. Secondly, we establish the existence and uniqueness of a weak solution to our model via Schauder fixed point method. To validate the efficiency of our model, we present some numerical experiments on images with different features and various noise levels. We begin by introducing an adaptive discrete scheme to the proposed model. We illustrate the sensitivity of the time-fractional order derivative with respect to some well-known criteria. Finally, the obtained numerical results show a great efficiency and robustness against noise compared to the competitive models.

Suggested Citation

  • Ben-Loghfyry, Anouar & Charkaoui, Abderrahim, 2023. "Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008263
    DOI: 10.1016/j.chaos.2023.113925
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008263
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113925?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. Wang, Xin-Wei & Chen, Zhen & Han, Chao, 2016. "Scheduling for single agile satellite, redundant targets problem using complex networks theory," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 125-132.
    2. Raj, Vimal & Renjini, A. & Swapna, M.S. & Sreejyothi, S. & Sankararaman, S., 2020. "Nonlinear time series and principal component analyses: Potential diagnostic tools for COVID-19 auscultation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Panwar, Harsh & Gupta, P.K. & Siddiqui, Mohammad Khubeb & Morales-Menendez, Ruben & Singh, Vaishnavi, 2020. "Application of deep learning for fast detection of COVID-19 in X-Rays using nCOVnet," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Pitsik, Elena N. & Maximenko, Vladimir A. & Kurkin, Semen A. & Sergeev, Alexander P. & Stoyanov, Drozdstoy & Paunova, Rositsa & Kandilarova, Sevdalina & Simeonova, Denitsa & Hramov, Alexander E., 2023. "The topology of fMRI-based networks defines the performance of a graph neural network for the classification of patients with major depressive disorder," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. Ouchicha, Chaimae & Ammor, Ouafae & Meknassi, Mohammed, 2020. "CVDNet: A novel deep learning architecture for detection of coronavirus (Covid-19) from chest x-ray images," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Altan, Aytaç & Karasu, Seçkin, 2020. "Recognition of COVID-19 disease from X-ray images by hybrid model consisting of 2D curvelet transform, chaotic salp swarm algorithm and deep learning technique," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Jiang, Congshi & Chen, Quan, 2020. "Construction of blind restoration model for super-resolution image based on chaotic neural network," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    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. Zeng, Yue & Zhang, Yao-jia & Huang, Nan-jing, 2024. "A stochastic fractional differential variational inequality with Lévy jump and its application," Chaos, Solitons & Fractals, Elsevier, vol. 178(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. Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Alotaibi, Naif D., 2021. "A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Tayarani N., Mohammad-H., 2021. "Applications of artificial intelligence in battling against covid-19: A literature review," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Renjini, Ammini & Swapna, Mohanachandran Nair Sindhu & Satheesh Kumar, Krishnan Nair & Sankararaman, Sankaranarayana Iyer, 2023. "Time series and mel frequency analyses of wet and dry cough signals: A neural net classification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    4. Srinka Basu & Sugata Sen, 2023. "COVID 19 Pandemic, Socio-Economic Behaviour and Infection Characteristics: An Inter-Country Predictive Study Using Deep Learning," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 645-676, February.
    5. Oleg E. Karpov & Elena N. Pitsik & Semen A. Kurkin & Vladimir A. Maksimenko & Alexander V. Gusev & Natali N. Shusharina & Alexander E. Hramov, 2023. "Analysis of Publication Activity and Research Trends in the Field of AI Medical Applications: Network Approach," IJERPH, MDPI, vol. 20(7), pages 1-17, March.
    6. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Ban, Jung-Chao & Chang, Chih-Hung & Hong, Jyy-I & Wu, Yu-Liang, 2021. "Mathematical Analysis of Spread Models: From the viewpoints of Deterministic and random cases," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Alharbi, Njud S. & Bekiros, Stelios & Jahanshahi, Hadi & Mou, Jun & Yao, Qijia, 2024. "Spatiotemporal wavelet-domain neuroimaging of chaotic EEG seizure signals in epilepsy diagnosis and prognosis with the use of graph convolutional LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    9. Zhang, Boyi & Shang, Pengjian & Zhou, Qin, 2021. "The identification of fractional order systems by multiscale multivariate analysis," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    10. Chen, Xi & Yu, Ruyi & Ullah, Sajid & Wu, Dianming & Li, Zhiqiang & Li, Qingli & Qi, Honggang & Liu, Jihui & Liu, Min & Zhang, Yundong, 2022. "A novel loss function of deep learning in wind speed forecasting," Energy, Elsevier, vol. 238(PB).
    11. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    12. Dingding Wang & Jiaqing Mo & Gang Zhou & Liang Xu & Yajun Liu, 2020. "An efficient mixture of deep and machine learning models for COVID-19 diagnosis in chest X-ray images," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-15, November.
    13. Prabhjot Kaur & Shilpi Harnal & Rajeev Tiwari & Fahd S. Alharithi & Ahmed H. Almulihi & Irene Delgado Noya & Nitin Goyal, 2021. "A Hybrid Convolutional Neural Network Model for Diagnosis of COVID-19 Using Chest X-ray Images," IJERPH, MDPI, vol. 18(22), pages 1-17, November.
    14. Guo, Lei & Liu, Chengjun & Wu, Youxi & Xu, Guizhi, 2023. "fMRI-based spiking neural network verified by anti-damage capabilities under random attacks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    15. Singh, Harendra & Baleanu, Dumitru & Singh, Jagdev & Dutta, Hemen, 2021. "Computational study of fractional order smoking model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    16. Chen, Xiaolu & Weng, Tongfeng & Yang, Huijie, 2023. "Synchronization of spatiotemporal chaos and reservoir computing via scalar signals," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    17. Cui, Li & Luo, Wenhui & Ou, Qingli, 2021. "Analysis of basins of attraction of new coupled hidden attractor system," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    18. Mohammad Khishe & Fabio Caraffini & Stefan Kuhn, 2021. "Evolving Deep Learning Convolutional Neural Networks for Early COVID-19 Detection in Chest X-ray Images," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    19. Yao, Qijia, 2021. "Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    20. Zhu, Cheng-Cheng & Zhu, Jiang, 2021. "Dynamic analysis of a delayed COVID-19 epidemic with home quarantine in temporal-spatial heterogeneous via global exponential attractor method," Chaos, Solitons & Fractals, Elsevier, vol. 143(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:chsofr:v:175:y:2023:i:p1:s0960077923008263. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.