1. 南京信息工程大学电子与信息工程学院南京210044;2. 南京信息工程大学江苏省大气环境与装备技术协同创新中心南京210044
TP391.41；TN911.7
国家自然科学基金(61601229,11202106)、江苏省"信息与通信工程"优势学科建设项目、江苏省青蓝工程和江苏省高校自然科学研究项目(16KJB510022)资助
Wu Denghui
1. College of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China; 2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaZhou Xianchun
1. College of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China; 2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China1. College of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China; 2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China
为了更好的实现图像模糊消除和有效地去除斑点噪声，提出了一种新的基于偏微分方程的图像去噪方法,它是基于非线性四阶扩散模型。首先提出了该非线性偏微分方程的方案，然后对微分模型进行数学处理，研究它的适定性，最后证明了此模型在一定条件下是适定的，并且存在了弱解，所得到的弱解近似于基于有限差分数值离散格式。实验结果表明，新模型在图像去噪和保边缘等细节信息方面都达到较好的效果，峰值信噪比有了大幅提高，去噪性能较经典模型更具优越性。
To provide a better image deblurring and remove successfully the speckle noise, a novel PDEbased image denoising approach is proposed in this paper. It is based on a nonlinear fourthorder diffusion model. The nonlinear PDE scheme is described first. Then, a mathematical treatment is provided for this differential model, its wellposedness being investigated. It is proved that the model is wellposed in some certain conditions and admits a weak solution. The weak solution of the obtained PDE is approximated by developing an explicit finitedifference based numerical discretization scheme. The experimental results show that the new model proposed in this paper can achieve good results in image denoising and preserving edges and other details. Compared with the classical model, the peak signal to noise ratio is greatly improved and the denoising performance is more better.
吴登辉,周先春,陈铭.基于四阶非线性偏微分方程的图像去噪算法[J].电子测量与仪器学报,2017,31(6):839-843
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