基于空间分数阶偏微分方程图像去噪的隐式差分方法

Implicit Difference Numerical Method of Image Denoising Based on Space Fractional PDE

摘要: 图像去噪的空间分数阶偏微分方程方法是图像去噪领域中的一个重要方向，对于它的数值方法研究有重要的理论意义和实用价值。本文研究基于空间分数阶偏微分方程的图像去噪方法，对空间分数阶图像去噪模型构造隐式差分格式，分析格式解的存在唯一性和格式的稳定性、收敛性，并给出精度分析。理论分析和数值试验证实：隐式差分格式对求解空间分数阶偏微分方程是可行的，且去噪效果优良。

Abstract: Image denoising numerical methods based on space fractional Partial Differential Equations is an important direction of image denoising field, and its study of numerical methods has important theoretical significance and practical value. This paper constructs implicit difference scheme for solving the space fractional partial differential equation. Through theoretical analysis and numer-ical experiments, we found that implicit difference scheme for solving space fractional partial dif-ferential equations is feasible, it can ensure good denoising effect.