A time-splitting local meshfree approach for time-fractional anisotropic diffusion equation: application in image denoising

被引:2
作者
Mazloum, Jalil [1 ]
Siahkal-Mahalle, Behrang Hadian [1 ]
机构
[1] Shahid Sattari Aeronaut Univ Sci & Technol, Dept Elect Engn, Tehran, Iran
来源
ADVANCES IN CONTINUOUS AND DISCRETE MODELS | 2022年 / 2022卷 / 01期
关键词
Meshless methods; Fractional calculus; Image denoising; Operator splitting; Perona-Malik; EDGE-DETECTION; SIMULATION; MODELS;
D O I
10.1186/s13662-022-03728-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Image denoising approaches based on partial differential modeling have attracted a lot of attention in image processing due to their high performance. The nonlinear anisotropic diffusion equations, specially Perona-Malik model, are powerful tools that improve the quality of the image by removing noise while preserving details and edges. In this paper, we propose a powerful and accurate local meshless algorithm to solve the time-fractional Perona-Malik model which has an adjustable fractional derivative making the control of the diffusion process more convenient than the classical one. In order to overcome the complexities of the problem, a suitable combination of the compactly supported radial basis function method and operator splitting technique is proposed to convert a complex time-fractional partial differential equation into sparse linear algebraic systems that standard solvers can solve. The numerical results of classical and fractional models are explored in different metrics to demonstrate the proposed scheme's effectiveness. The numerical experiments confirm that the method is suitable to denoise digital images and show that the fractional derivative increases the model's ability to remove noise in images.
引用
收藏
页数:19
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