基于偏微分方程的自适应图像去噪模型
Adaptive Image Denoising Model Based on Partial Differential Equation
DOI: 10.12677/PM.2022.1211214, PDF,   
作者: 王鹏飞：成都理工大学数理学院，四川 成都；成都理工大学数学地质四川省重点实验室，四川 成都
关键词: 图像去噪；AFOD模型；P-Laplace；差分曲率；Image Denoising； AFOD Model； P-Laplace； Differential Curvature
摘要: 四阶各项异性扩散模型(AFOD)的提出有效解决了各向同性扩散模型(Y-K)的斑点效应、收敛速度慢等和边缘信息丢失等问题。但图像梯度作为边缘指示器，区分斜坡区域和边缘区域的能力弱，会使得去噪图像在斜坡区域产生阶梯效应。本文利用差分曲率能有效区分图像边缘区域和斜坡区域的特点，将AFOD模型和P-Laplace结合，使得模型能在保护图像边缘的同时，有效抑制阶梯效应。实验结果与几种相关方法进行比较，证明了该模型稳定良好的性能。
Abstract: The Anisotropic Fourth-Order Diffusion Filter (AFOD) is proposed to effectively solve the problems of speckle effect, slow convergence speed and loss of edge information of isotropic Diffusion Filter (Y-K). However, as an edge indicator, the image gradient has a weak ability to distinguish the slope area from the edge area, which will cause the denoised image to produce a staircase effect in the slope area. In this paper, the difference curvature can effectively distinguish the edge area and the slope area of the image, and the AFOD model is combined with P-Laplace, so that the model can effectively suppress the step effect while protecting the image edge. The experimental results are compared with several related methods, which demonstrate the stable and good performance of the model.
文章引用：王鹏飞. 基于偏微分方程的自适应图像去噪模型[J]. 理论数学, 2022, 12(11): 1981-1988. https://doi.org/10.12677/PM.2022.1211214

参考文献

[1] Catté, F., Lions, P.-L., Morel, J.-M. and Coll, T. (1992) Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. SIAM Journal on Numerical Analysis, 29, 182-193. [Google Scholar] [CrossRef] 
[2] Rudin, L.I., Osher, S. and Fatemi, E. (1992) Nonlinear Total Variation Based Noise Removal Algorithms. Physica D: Nonlinear Phenomena, 60, 259-268. [Google Scholar] [CrossRef] 
[3] Lysaker, M., Lundervold, A. and Tai, X.C. (2003) Noise Removal Using Fourth-Order Partial Differential Equation with Applications to Medical Mag-netic Resonance Images in Space and Time. IEEE Transactions on Image Processing, 12, 1579-1590. [Google Scholar] [CrossRef] 
[4] Hajiaboli, M.R. (2011) An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal. International Journal of Computer Vision, 92, 177-191. [Google Scholar] [CrossRef] 
[5] Chen, Q., Montesinos, P., Sun, Q.S., et al. (2010) Adaptive Total Variation Denoising Based on Difference Curvature. Image and Vision Computing, 28, 298-306. [Google Scholar] [CrossRef] 
[6] 徐书方, 刘婧, 沈立新. 一种基于偏微分方程的图像去噪方法[J]. 大连海事大学学报, 2010, 36(4): 107-110.
[7] Chang, Q.S., Tai, X.C. and Xing, L. (2009) A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations. Numerical Mathematics: Theory, Methods and Applications, 2, 353-376. [Google Scholar] [CrossRef] 
[8] Wang, Y.Q., Guo, J.C., Chen, W.F. and Zhang, W.X. (2013) Image Denoising Using Modified Perona-Malik Model Based on Directional Laplacian. Signal Processing, 93, 2548-2558. [Google Scholar] [CrossRef] 
[9] 李丹, 仲崇权, 王世强, 陈祖军. 基于全变差和P-Laplace模型的混合图像修复算法[J]. 大连理工大学学报, 2014, 54(6): 676-681.
[10] Deng, L., Zhu, H., Yang, Z., et al. (2019) Hessian Matrix-Based Fourth-Order Anisotropic Diffusion Filter for Image Denoising. Optics & Laser Technology, 110, 184-190. [Google Scholar] [CrossRef] 
[11] 贺亚茹. 图像恢复的PDE方法研究[D]: [硕士学位论文]. 西安: 西安理工大学, 2018.
[12] Baravdish, G., Cheng, Y., Svensson, O., et al. (2015) Extension of p-Laplace Operator for Image Denoising. IFIP Conference on System Modeling and Optimization, Springer, Cham, Vol. 494, 107-116. [Google Scholar] [CrossRef] 

为你推荐