基于偏微分方程的图像修复算法研究

近些年来，随着科学技术的发展，数字图像处理技术在人们的日常生活各个方面都有所体现。因此，这就成为科学家们研究的重点邻域，而数字图像处理技术中的最重要的一方面便是图像修复技术。图像修复主要应用于珍贵文物的修复，影视作品中特定文字的去除、物体的隐藏等。
本文以偏微分方程为主线，重点介绍了整体变分（TV）模型和曲率驱动扩散（CDD）模型。运用matlab软件实现对图像的修复，通过实验数据我们发现两者在修复较小的破损区域时，会有很好的修复效果。TV模型数值实现简单，算法迭代效率高，收敛速度快，而且边缘信息保持的很好。CDD模型可以去除阶梯效应，满足人的“连通性准则”。最后从主观和客观两个方面给出了图像质量的评价标准。

关键词：图像修复；TV模型；CDD模型；峰值信噪比
Image Restoration Algorithm Based on Partial Differential
Equation
 
Abstract:In recent years, with the development of science and technology, digital image processing technology is reflected in all aspects of people's daily life. It makes digital image processing technology become the focus of research scientists, and image restoration technology is an important aspect of digital image processing techniques. It is mainly used precious cultural relics restoration, removal of specific characters in film and television works, hidden object and other fields .
    In this paper, the image of partial differential equations repair is the main line, focus on total variation (TV) model and curvature-driven diffusion (CDD) model. Using matlab software for image restoration,we found both in the repair of damaged image smaller areas, there will be a very good result. The TV model numerical implementation is simple, efficient iterative algorithm, convergence speed and edge information well maintained. The CDD model can be removed step effect, meet the people's "Connectivity Guidelines." Finally, the evaluation criteria of image quality from a subjective and objective aspects.

Key words: Image restoration; TV model;CDD model;PSNR

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