Total fractional-order variation and bilateral filter for image denoising
| dc.citation.epage | 653 | |
| dc.citation.issue | 3 | |
| dc.citation.journalTitle | Математичне моделювання та обчислення | |
| dc.citation.spage | 642 | |
| dc.contributor.affiliation | Університет Хасана ІІ у Касабланці | |
| dc.contributor.affiliation | Hassan II University of Casablanca | |
| dc.contributor.author | Аддуш, Р. | |
| dc.contributor.author | Муссаід, Н. | |
| dc.contributor.author | Гуаснуан, О. | |
| dc.contributor.author | Бен-Логфірі, А. | |
| dc.contributor.author | Addouch, R. | |
| dc.contributor.author | Moussaid, N. | |
| dc.contributor.author | Gouasnouane, O. | |
| dc.contributor.author | Ben-Loghfyry, A. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2026-04-22T06:48:46Z | |
| dc.date.created | 2024-02-24 | |
| dc.date.issued | 2024-02-24 | |
| dc.description.abstract | Усунення шумів на зображенні є основною метою обробки зображень. Однак багато існуючих методів стикаються з проблемами збереження таких особливостей, як кути та краї зображення, одночасно видаляючи шум. У статті досліджується та оцінюється похідна дробового порядку на основі моделі варіації загального α-порядку (TV) і моделі двосторонньої загальної варіації (BTV). Цей вибір обумовлений доведеною ефективністю моделі TV у видаленні шумів і збереженні країв, а модель BTV додатково використовується для покращення відновлення дрібних і складних деталей. Експериментальні результати підтверджують ефективність запропонованої моделі, що підтверджується об’єктивними кількісними показниками та суб’єктивними оцінками візуального вигляду. | |
| dc.description.abstract | Image denoising stands out as a primary goal in image processing. However, many existing methods encounter challenges in preserving features such as corners and edges of an image while deleting the noise. This study investigates and evaluates a fractional-order derivative based on the total α-order variation (TV) model and the bilateral total variation (BTV) model. This choice is motivated by the proven effectiveness of the TV model in noise removal and edge preservation, with the BTV model further utilized to enhance the restoration of fine and intricate details. The experimental results affirm the efficacy of the proposed model, supported by objective quantitative metrics and subjective assessments of visual appearance. | |
| dc.format.extent | 642-653 | |
| dc.format.pages | 12 | |
| dc.identifier.citation | Total fractional-order variation and bilateral filter for image denoising / R. Addouch, N. Moussaid, O. Gouasnouane, A. Ben-Loghfyry // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 3. — P. 642–653. | |
| dc.identifier.citationen | Total fractional-order variation and bilateral filter for image denoising / R. Addouch, N. Moussaid, O. Gouasnouane, A. Ben-Loghfyry // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 3. — P. 642–653. | |
| dc.identifier.doi | doi.org/10.23939/mmc2024.03.642 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/125003 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та обчислення, 3 (11), 2024 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 3 (11), 2024 | |
| dc.relation.references | [1] Ben-Loghfyry A., Hakim A. A total variable-order variation model for image denoising. AIMS Mathematics. 4 (5), 1320–1335 (2019). | |
| dc.relation.references | [2] Zhu M., Wright S. J., Chan T. F. Duality-based algorithms for total-variation-regularized image restoration. Computational Optimization and Applications. 47 (3), 377–400 (2010). | |
| dc.relation.references | [3] 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 | [4] Laghrib A., Hakim A., Raghay S. A combined total variation and bilateral filter approach for image robust super resolution. EURASIP Journal on Image and Video Processing. 2015, 19 (2015). | |
| dc.relation.references | [5] El Mourabit I., El Rhabi M., Hakim A. Blind deconvolution using bilateral total variation regularization: a theoretical study and application. Applicable Analysis. 101 (16), 5660–5673 (2022). | |
| dc.relation.references | [6] 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.references | [7] Ben-Loghfyry A., Hakim A., Laghrib A. A denoising model based on the fractional Beltrami regularization and its numerical solution. Journal of Applied Mathematics and Computing. 69 (2), 1431–1463 (2023). | |
| dc.relation.references | [8] Ben-Loghfyry A., Hakim A. Time-fractional difusion equation for signal and image smoothing. Mathematical Modeling and Computing. 9 (2), 351–364 (2022). | |
| dc.relation.references | [9] Ben-Loghfyry A., Hakim A. Robust-time-fractional diffusion filtering for noise removal. Mathematical Methods in the Applied Sciences. 45 (16), 9719–9735 (2022). | |
| dc.relation.references | [10] Ben-Loghfyry A., Charkaoui A. Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising. Chaos, Solitons & Fractals. 175 (1), 113925 (2023). | |
| dc.relation.references | [11] Gouasnouane O., Moussaid N., Boujena S. A nonlinear fractional partial equation differential for image denoising. 2021 Third International Conference on Transportation and Smart Technologies (TST), Tangier, Morocco. 59–64 (2021). | |
| dc.relation.references | [12] Gouasnouane O., Moussaid N., Boujena S., Kabli K. A nonlinear fractional partial differential equation for image inpainting. Mathematical Modeling and Computing. 9 (3), 536–546 (2022). | |
| dc.relation.references | [13] 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 | [14] Podlubny I., Chechkin A., Skovranek T., Chen Y., Vinagre-Jara B.M. Matrix approach to discrete fractional calculus II: Partial fractional differential equations. Journal of Computational Physics. 228 (1), 3137–3153 (2009). | |
| dc.relation.references | [15] Wang H., Du N. Fast solution methods for space-fractional diffusion equations. Journal of Computational and Applied Mathematics. 255, 376–383 (2014). | |
| dc.relation.references | [16] Sayah A., Moussaid N., Gouasnouane O. Finite difference method for Perona-Malik model with fractional derivative and its application in image processing. 2021 Third International Conference on Transportation and Smart Technologies (TST), Tangier, Morocco. 101–106 (2021). | |
| dc.relation.references | [17] Zosso D., Bustin R. A Primal-Dual Projected Gradient algorithm for efficient Beltrami regularization. UCLA CAM Report. 14–52 (2014). | |
| dc.relation.references | [18] Zeidler E. Nonlinear functional analysis and its Applications. III. Variational methods and optimization. Springer-Verlag, New York (1985). | |
| dc.relation.referencesen | [1] Ben-Loghfyry A., Hakim A. A total variable-order variation model for image denoising. AIMS Mathematics. 4 (5), 1320–1335 (2019). | |
| dc.relation.referencesen | [2] Zhu M., Wright S. J., Chan T. F. Duality-based algorithms for total-variation-regularized image restoration. Computational Optimization and Applications. 47 (3), 377–400 (2010). | |
| dc.relation.referencesen | [3] 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 | [4] Laghrib A., Hakim A., Raghay S. A combined total variation and bilateral filter approach for image robust super resolution. EURASIP Journal on Image and Video Processing. 2015, 19 (2015). | |
| dc.relation.referencesen | [5] El Mourabit I., El Rhabi M., Hakim A. Blind deconvolution using bilateral total variation regularization: a theoretical study and application. Applicable Analysis. 101 (16), 5660–5673 (2022). | |
| dc.relation.referencesen | [6] 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 | [7] Ben-Loghfyry A., Hakim A., Laghrib A. A denoising model based on the fractional Beltrami regularization and its numerical solution. Journal of Applied Mathematics and Computing. 69 (2), 1431–1463 (2023). | |
| dc.relation.referencesen | [8] Ben-Loghfyry A., Hakim A. Time-fractional difusion equation for signal and image smoothing. Mathematical Modeling and Computing. 9 (2), 351–364 (2022). | |
| dc.relation.referencesen | [9] Ben-Loghfyry A., Hakim A. Robust-time-fractional diffusion filtering for noise removal. Mathematical Methods in the Applied Sciences. 45 (16), 9719–9735 (2022). | |
| dc.relation.referencesen | [10] Ben-Loghfyry A., Charkaoui A. Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising. Chaos, Solitons & Fractals. 175 (1), 113925 (2023). | |
| dc.relation.referencesen | [11] Gouasnouane O., Moussaid N., Boujena S. A nonlinear fractional partial equation differential for image denoising. 2021 Third International Conference on Transportation and Smart Technologies (TST), Tangier, Morocco. 59–64 (2021). | |
| dc.relation.referencesen | [12] Gouasnouane O., Moussaid N., Boujena S., Kabli K. A nonlinear fractional partial differential equation for image inpainting. Mathematical Modeling and Computing. 9 (3), 536–546 (2022). | |
| dc.relation.referencesen | [13] 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 | [14] Podlubny I., Chechkin A., Skovranek T., Chen Y., Vinagre-Jara B.M. Matrix approach to discrete fractional calculus II: Partial fractional differential equations. Journal of Computational Physics. 228 (1), 3137–3153 (2009). | |
| dc.relation.referencesen | [15] Wang H., Du N. Fast solution methods for space-fractional diffusion equations. Journal of Computational and Applied Mathematics. 255, 376–383 (2014). | |
| dc.relation.referencesen | [16] Sayah A., Moussaid N., Gouasnouane O. Finite difference method for Perona-Malik model with fractional derivative and its application in image processing. 2021 Third International Conference on Transportation and Smart Technologies (TST), Tangier, Morocco. 101–106 (2021). | |
| dc.relation.referencesen | [17] Zosso D., Bustin R. A Primal-Dual Projected Gradient algorithm for efficient Beltrami regularization. UCLA CAM Report. 14–52 (2014). | |
| dc.relation.referencesen | [18] Zeidler E. Nonlinear functional analysis and its Applications. III. Variational methods and optimization. Springer-Verlag, New York (1985). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2024 | |
| dc.subject | зменшення шуму зображення | |
| dc.subject | регулярізація | |
| dc.subject | похідні дробового порядку | |
| dc.subject | загальна варіація α-порядку | |
| dc.subject | двостороння загальна варіація | |
| dc.subject | image denoising | |
| dc.subject | regularization | |
| dc.subject | fractional-order derivatives | |
| dc.subject | total α-order variation | |
| dc.subject | bilateral total variation | |
| dc.title | Total fractional-order variation and bilateral filter for image denoising | |
| dc.title.alternative | Загальна варіація дробового порядку та двосторонній фільтр для зменшення шуму зображення | |
| dc.type | Article |
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