Partial differential and Stochastic Equations in image processing, applications to medica images

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dc.contributor.authorHALILOU, Radhia
dc.date.accessioned2026-04-16T08:20:58Z
dc.date.available2026-04-16T08:20:58Z
dc.date.issued2026
dc.description.abstractThis thesis is devoted to the study and application of stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) for image denoising. The pro- porsed mathematical models are designed to reduce noise in corrupted images while preserving essential structural features. These models incorporate drift and diffusion terms inspired by both classical and contemporary approaches, notably the Perona-Malik model, Barbu-type drift, and Borkowski’s diffusion formulation. A rigorous mathematical analysis is conducted to establish the existence and uniqueness of weak solutions for each model. In the case of SDEs, this analysis is based on the framework of stochastic calculus developed by Øksendal. For SPDEs, the well-posedness of the problem is ensured by imposing appropriate conditions and hypotheses, following the theoretical contributions of Bensoussan. From a numerical perspective, the SDE-based models are discretized using the Euler–Maruyama scheme com-bined with Monte Carlo simulations, while SPDEs are solved using finite difference methods to ensure both stability and accuracy. The performance of the proposed models is evaluated on both grayscale and color images contaminated with noise. Quantitative assessments using standard image quality metrics such as Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) demonstrate the effectiveness of the stochastic models in restoring image quality. The results confirm that introducing stochasticity into the denoising process offers a robust and flexible framework for image restoration.
dc.formatPDF
dc.identifier.urihttps://dspace.univ-annaba.dz//handle/123456789/4664
dc.language.isoen
dc.publisherUniversité Badji Mokhtar Annaba
dc.subjectStochastic Differential Equations (SDEs); Stochastic Partial Differential Equa- tions (SPDEs); Denoising and Restoring Images
dc.titlePartial differential and Stochastic Equations in image processing, applications to medica images
dc.title.alternativeEquations aux dérivées partielles et Stochastiques en traitement d’Image, applications aux images médicales
dc.typeThesis
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