Time-fractional diffusion equation for signal and image smoothing
| dc.citation.epage | 364 | |
| dc.citation.issue | 2 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 351 | |
| dc.contributor.affiliation | Університет Каді Айяд | |
| dc.contributor.affiliation | University of Cadi Ayyad | |
| dc.contributor.author | Бен-Логфірі, А. | |
| dc.contributor.author | Хакім, А. | |
| dc.contributor.author | Ben-Loghfyry, A. | |
| dc.contributor.author | Hakim, A. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T11:14:23Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | У цій статті використовується рівняння дифузії з дробовою часовою похідною для знешумлення зображення та згладжування сигналу. Подано дискретизацію запропонованої моделі. Числові результати показують деякі чудові результати з високою продуктивністю, як візуально, так і кількісно, порівняно з деякими добре відомими конкурентними моделями. | |
| dc.description.abstract | In this paper, we utilize a time-fractional diffusion equation for image denoising and signal smoothing. A discretization of our model is provided. Numerical results show some remarkable results with a great performance, visually and quantitatively, compared to some well known competitive models. | |
| dc.format.extent | 351-364 | |
| dc.format.pages | 14 | |
| dc.identifier.citation | Ben-Loghfyry A. Time-fractional diffusion equation for signal and image smoothing / A. Ben-Loghfyry, A. Hakim // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 351–364. | |
| dc.identifier.citationen | Ben-Loghfyry A. Time-fractional diffusion equation for signal and image smoothing / A. Ben-Loghfyry, A. Hakim // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 351–364. | |
| dc.identifier.doi | doi.org/10.23939/mmc2022.02.351 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63436 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 2 (9), 2022 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 2 (9), 2022 | |
| dc.relation.references | [1] Ben-loghfyry A., Hakim A. Robust time-fractional diffusion filtering for noise removal. Mathematical Methods in the Applied Sciences. 1–17 (2022). | |
| dc.relation.references | [2] El Alaoui El Fels A., Ben-loghfyry A., El Ghorfi M. Performance of denoising algorithms in the improvement of lithological discrimination. Modeling Earth Systems and Environment. 1–8 (2022). | |
| dc.relation.references | [3] Hakim A., Ben-Loghfyry A. A total variable-order variation model for image denoising. AIMS Mathematics. 4 (5), 1320–1335 (2019). | |
| dc.relation.references | [4] Pan H., Wen Y. W., Zhu H. M. A regularization parameter selection model for total variation based image noise removal. Applied Mathematical Modelling. 68, 353–367 (2019). | |
| dc.relation.references | [5] Laghrib A., Ben-Loghfyry A., Hadri A., Hakim A. A nonconvex fractional order variational model for multiframe image super-resolution. Signal Processing: Image Communication. 67, 1–11 (2018). | |
| dc.relation.references | [6] Hakim M., Ghazdali A., Laghrib A. A multi-frame super-resolution based on new variational data fidelity term. Applied Mathematical Modelling. 87, 446–467 (2020). | |
| dc.relation.references | [7] Baloochian H., Ghaffary H. R., Balochian S. Enhancing fingerprint image recognition algorithm using fractional derivative filters. Open Computer Science. 7 (1), 9–16 (2017). | |
| dc.relation.references | [8] Ferrah I., Chaou A. K., Maadjoudj D., Teguar M. Novel colour image encoding system combined with ANN for discharges pattern recognition on polluted insulator model. IET Science, Measurement & Technology. 14, 718–725 (2020). | |
| dc.relation.references | [9] Nasreddine K., Benzinou A., Fablet R. Signal and image registration: Application to decrypt marine biological archives. Traitement du Signal. 26 (4), 255–268 (2009). | |
| dc.relation.references | [10] Frohn-Schauf C., Henn S., Witsch K. Multigrid based total variation image registration. Computing and Visualization in Science. 11 (2), 101–113 (2008). | |
| dc.relation.references | [11] Alaa H., Alaa N. E., Aqel F., Lefraich H. A new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement. Mathematical Modeling and Computing. 9 (2), 187–202 (2022). | |
| dc.relation.references | [12] Alaa K., Atouni M., Zirhem M. Image restoration and contrast enhancement based on a nonlinear reactiondiffusion mathematical model and divide & conquer technique. Mathematical Modeling and Computing. 8 (3), 549–559 (2021). | |
| dc.relation.references | [13] Guichard F., Moisan L., Morel J. M. A review of PDE models in image processing and image analysis. Journal de Physique IV. 12 (1), 137–154 (2002). | |
| dc.relation.references | [14] Chan T. F., Shen J., Vese L. Variational PDE models in image processing. Notices of the American Mathematical Society. 50 (1), 14–26 (2003). | |
| dc.relation.references | [15] Aubert G., Kornprobst P. Mathematical problems in image processing: partial differential equations and the calculus of variations. Vol. 147. Springer Science & Business Media (2006). | |
| dc.relation.references | [16] Perona P., Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on pattern analysis and machine intelligence. 12 (7), 629–639 (1990). | |
| dc.relation.references | [17] Catt´e F., Lions P. L., Morel J. M., Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical analysis. 29 (1), 182–193 (1992). | |
| dc.relation.references | [18] Weickert J. Applications of nonlinear diffusion in image processing and computer vision. Acta Math. Univ. Comenianae. 70 (1), 33–50 (2001). | |
| dc.relation.references | [19] Sabatier J., Agrawal O. P., Machado J. T. Advances in fractional calculus. Vol. 4. Springer (2007). | |
| dc.relation.references | [20] Machado J. T., Kiryakova V. The chronicles of fractional calculus. Fractional Calculus and Applied Analysis. 20 (2), 307–336 (2017). | |
| dc.relation.references | [21] Yang Q., Chen D., Zhao T., Chen Y. Fractional calculus in image processing: a review. Fractional Calculus and Applied Analysis. 19 (5), 1222–1249 (2016). | |
| dc.relation.references | [22] Uchaikin V. V. On time-fractional representation of an open system response. Fractional Calculus and Applied Analysis. 19 (5), 1306 (2016). | |
| dc.relation.references | [23] Chang A., Sun H. Time-space fractional derivative models for CO2 transport in heterogeneous media. Fractional Calculus and Applied Analysis. 21 (1), 151–173 (2018). | |
| dc.relation.references | [24] Zhao X., Sun Z. Z. Time-fractional derivatives. Numerical Methods. 3, 23–48 (2019). | |
| dc.relation.references | [25] Oliveira D. S., de Oliveira E. C. On a Caputo-type fractional derivative. Advances in Pure and Applied Mathematics. 10 (2), 81–91 (2019). | |
| dc.relation.references | [26] Li C., Qian D., Chen Y. On Riemann-Liouville and Caputo derivatives. Discrete Dynamics in Nature and Society. 2011, 562494 (2011). | |
| dc.relation.references | [27] Weickert J. Anisotropic diffusion in image processing. Vol. 1. Teubner Stuttgart (1998). | |
| dc.relation.references | [28] Zhang J., Chen K. A total fractional-order variation model for image restoration with nonhomogeneous boundary conditions and its numerical solution. SIAM Journal on Imaging Sciences. 8 (4), 2487–2518 (2015). | |
| dc.relation.references | [29] Rudin L. I., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena. 60 (1–4), 259–268 (1992). | |
| dc.relation.referencesen | [1] Ben-loghfyry A., Hakim A. Robust time-fractional diffusion filtering for noise removal. Mathematical Methods in the Applied Sciences. 1–17 (2022). | |
| dc.relation.referencesen | [2] El Alaoui El Fels A., Ben-loghfyry A., El Ghorfi M. Performance of denoising algorithms in the improvement of lithological discrimination. Modeling Earth Systems and Environment. 1–8 (2022). | |
| dc.relation.referencesen | [3] Hakim A., Ben-Loghfyry A. A total variable-order variation model for image denoising. AIMS Mathematics. 4 (5), 1320–1335 (2019). | |
| dc.relation.referencesen | [4] Pan H., Wen Y. W., Zhu H. M. A regularization parameter selection model for total variation based image noise removal. Applied Mathematical Modelling. 68, 353–367 (2019). | |
| dc.relation.referencesen | [5] Laghrib A., Ben-Loghfyry A., Hadri A., Hakim A. A nonconvex fractional order variational model for multiframe image super-resolution. Signal Processing: Image Communication. 67, 1–11 (2018). | |
| dc.relation.referencesen | [6] Hakim M., Ghazdali A., Laghrib A. A multi-frame super-resolution based on new variational data fidelity term. Applied Mathematical Modelling. 87, 446–467 (2020). | |
| dc.relation.referencesen | [7] Baloochian H., Ghaffary H. R., Balochian S. Enhancing fingerprint image recognition algorithm using fractional derivative filters. Open Computer Science. 7 (1), 9–16 (2017). | |
| dc.relation.referencesen | [8] Ferrah I., Chaou A. K., Maadjoudj D., Teguar M. Novel colour image encoding system combined with ANN for discharges pattern recognition on polluted insulator model. IET Science, Measurement & Technology. 14, 718–725 (2020). | |
| dc.relation.referencesen | [9] Nasreddine K., Benzinou A., Fablet R. Signal and image registration: Application to decrypt marine biological archives. Traitement du Signal. 26 (4), 255–268 (2009). | |
| dc.relation.referencesen | [10] Frohn-Schauf C., Henn S., Witsch K. Multigrid based total variation image registration. Computing and Visualization in Science. 11 (2), 101–113 (2008). | |
| dc.relation.referencesen | [11] Alaa H., Alaa N. E., Aqel F., Lefraich H. A new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement. Mathematical Modeling and Computing. 9 (2), 187–202 (2022). | |
| dc.relation.referencesen | [12] Alaa K., Atouni M., Zirhem M. Image restoration and contrast enhancement based on a nonlinear reactiondiffusion mathematical model and divide & conquer technique. Mathematical Modeling and Computing. 8 (3), 549–559 (2021). | |
| dc.relation.referencesen | [13] Guichard F., Moisan L., Morel J. M. A review of PDE models in image processing and image analysis. Journal de Physique IV. 12 (1), 137–154 (2002). | |
| dc.relation.referencesen | [14] Chan T. F., Shen J., Vese L. Variational PDE models in image processing. Notices of the American Mathematical Society. 50 (1), 14–26 (2003). | |
| dc.relation.referencesen | [15] Aubert G., Kornprobst P. Mathematical problems in image processing: partial differential equations and the calculus of variations. Vol. 147. Springer Science & Business Media (2006). | |
| dc.relation.referencesen | [16] Perona P., Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on pattern analysis and machine intelligence. 12 (7), 629–639 (1990). | |
| dc.relation.referencesen | [17] Catt´e F., Lions P. L., Morel J. M., Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical analysis. 29 (1), 182–193 (1992). | |
| dc.relation.referencesen | [18] Weickert J. Applications of nonlinear diffusion in image processing and computer vision. Acta Math. Univ. Comenianae. 70 (1), 33–50 (2001). | |
| dc.relation.referencesen | [19] Sabatier J., Agrawal O. P., Machado J. T. Advances in fractional calculus. Vol. 4. Springer (2007). | |
| dc.relation.referencesen | [20] Machado J. T., Kiryakova V. The chronicles of fractional calculus. Fractional Calculus and Applied Analysis. 20 (2), 307–336 (2017). | |
| dc.relation.referencesen | [21] Yang Q., Chen D., Zhao T., Chen Y. Fractional calculus in image processing: a review. Fractional Calculus and Applied Analysis. 19 (5), 1222–1249 (2016). | |
| dc.relation.referencesen | [22] Uchaikin V. V. On time-fractional representation of an open system response. Fractional Calculus and Applied Analysis. 19 (5), 1306 (2016). | |
| dc.relation.referencesen | [23] Chang A., Sun H. Time-space fractional derivative models for CO2 transport in heterogeneous media. Fractional Calculus and Applied Analysis. 21 (1), 151–173 (2018). | |
| dc.relation.referencesen | [24] Zhao X., Sun Z. Z. Time-fractional derivatives. Numerical Methods. 3, 23–48 (2019). | |
| dc.relation.referencesen | [25] Oliveira D. S., de Oliveira E. C. On a Caputo-type fractional derivative. Advances in Pure and Applied Mathematics. 10 (2), 81–91 (2019). | |
| dc.relation.referencesen | [26] Li C., Qian D., Chen Y. On Riemann-Liouville and Caputo derivatives. Discrete Dynamics in Nature and Society. 2011, 562494 (2011). | |
| dc.relation.referencesen | [27] Weickert J. Anisotropic diffusion in image processing. Vol. 1. Teubner Stuttgart (1998). | |
| dc.relation.referencesen | [28] Zhang J., Chen K. A total fractional-order variation model for image restoration with nonhomogeneous boundary conditions and its numerical solution. SIAM Journal on Imaging Sciences. 8 (4), 2487–2518 (2015). | |
| dc.relation.referencesen | [29] Rudin L. I., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena. 60 (1–4), 259–268 (1992). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | знешумлення зображення | |
| dc.subject | дробова похідна | |
| dc.subject | похідна дробового порядку за часом | |
| dc.subject | тензор дифузії | |
| dc.subject | image denoising | |
| dc.subject | fractional derivative | |
| dc.subject | time-fractional order derivative | |
| dc.subject | tensor diffusion | |
| dc.title | Time-fractional diffusion equation for signal and image smoothing | |
| dc.title.alternative | Рівняння дифузії з дробовою часовою похідною для згладжування сигналу та зображення | |
| dc.type | Article |
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