Fractional partial differential equation denoising models for texture image

• Published in: Science China. Information sciences Vol. 57; no. 7; pp. 180 - 198
• Main Authors: Pu, YiFei, Siarry, Patrick, Zhou, JiLiu, Liu, YiGuang, Zhang, Ni, Huang, Guo, Liu, YiZhi
• Format: Journal Article
• Language: English
• Published: Heidelberg Science China Press 01.07.2014; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Descent; Information Systems and Communication Service; Mathematical models; Noise reduction; Partial differential equations; Research Paper; Stability; Stability analysis; Surface layer; Texture; 偏微分方程; 分数; 去噪; 微分方程式; 拉格朗日公式; 最速下降法; 模型; 纹理图像; fractional Green formula; fractional steepest descent approach; fractional total variation; fractional differential mask; fractional extreme points; fractional Euler-Lagrange equation
• ISSN: 1674-733X; 1869-1919
• DOI: 10.1007/s11432-014-5112-x

In this paper,a set of fractional partial differential equations based on fractional total variation and fractional steepest descent approach are proposed to address the problem of traditional drawbacks of PM and ROF multi-scale denoising for texture image.By extending Green,Gauss,Stokes and Euler-Lagrange formulas to fractional field,we can find that the integer formulas are just their special case of fractional ones.In order to improve the denoising capability,we proposed 4 fractional partial differential equation based multiscale denoising models,and then discussed their stabilities and convergence rate.Theoretic deduction and experimental evaluation demonstrate the stability and astringency of fractional steepest descent approach,and fractional nonlinearly multi-scale denoising capability and best value of parameters are discussed also.The experiments results prove that the ability for preserving high-frequency edge and complex texture information of the proposed denoising models are obviously superior to traditional integral based algorithms,especially for texture detail rich images.