A new two-step variational model for multiplicative noise removal with applications to texture images  

作　　者：ZHANG Long-hui YAO Wen-juan SHI Sheng-zhu GUO Zhi-chang ZHANG Da-zhi 

机构地区：[1]School of Mathematics,Harbin Institute of Technology,Harbin 150001,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第3期486-501,共16页高校应用数学学报（英文版）（B辑）

摘　　要：Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

关 键 词：multiplicative noise removal texture images total variation two-step variational method aug-mented Lagrangian method 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]