Optimal control problem with nonlinear fractional system constraint applied to image restoration

被引:0
作者
Atlas, Abdelghafour [1 ]
Attmani, Jamal [1 ]
Karami, Fahd [2 ,3 ]
Meskine, Driss [2 ]
机构
[1] Univ Cadi Ayyad, Ecole Natl Sci Appl Marrakech, Marrakech, Morocco
[2] Univ Cadi Ayyad, Ecole Super Technol Essaouira, Lab Math Informat & Modelisat Syst Complexes, Essaouira, Morocco
[3] Univ Cadi Ayyad, Ecole Super Technol Essaouira, Lab Math Informat & Modelisat Syst Complexes, BP 383, Essaouira, Morocco
关键词
constrained PDE; fractional-order PDE; image denoising; nonlinear diffusion; SEMILINEAR OPTIMAL-CONTROL; PARABOLIC-SYSTEMS; EDGE-DETECTION; DECOMPOSITION; SPACE;
D O I
10.1002/mma.9998
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This study aims to investigate a novel nonlinear optimization problem that incorporate a partial differential equation (PDE) constraint for image denoising in the context of mixed noise removal. Based on H-s$$ {H} circumflex {-s} $$-norm and decomposition approach, we develop a nonlinear system that involves the fractional Laplacian operator. Based on Schauder's fixed point theorem, we establish the existence and uniqueness of weak solution for the direct problem. Furthermore, we study the well-posedness of the optimal control, and we also prove the existence of the weak solutions for the adjoint problem by using Galerkin's method. In order to numerically compute the solution of the proposed model, we introduce the numerical discretization scheme and the primal-dual algorithm used to solve our problem. Finally, we provide comparative numerical experiments to evaluate the efficiency and effectiveness of our proposed model.
引用
收藏
页码:7714 / 7741
页数:28
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