Application of finite difference method in solving a second- and fourth-order PDE blending denoising model

被引：2

作者：

Eslahchi, M. R. ^{[1
]}

Esmaili, Sakine ^{[1
]}

Namaki, Neda ^{[1
]}

Salehi, Rezvan ^{[1
]}

机构：

[1] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, POB 14115-134, Tehran, Iran

来源：

MATHEMATICAL SCIENCES | 2023年 / 17卷 / 01期

关键词：

Finite difference method; Heat equation; Perona and Malik model; Total variation model; YK model; Partial Differential equation; Image denoising; IMAGE; EQUATIONS;

D O I：

10.1007/s40096-021-00444-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a modified blending model (MBM) based on a weighted combination of total variation model, isotropic diffusion model, Perona and Malik model (which is an anisotropic diffusion model), YK model, and two fourth-order partial differential equation models. MBM is a PDE model with two main parts. One part is made of famous denoising models and the other one includes the fourth-order PDE models. Each one is involved in the model to use the advantages of that part and overcome the shortcomings of another part. Finite difference method, which is one of the tools to solve PDEs, is applied to approximate the output image using the proposed blending denoising model. Applying a criteria named PSNR and showing some images, it can be seen that MBM is more efficient compared with the models mentioned above.

引用

页码：93 / 106

页数：14

共 22 条

[1] A high order PDE-constrained optimization for the image denoising problem [J].