数学与统计学院知识库

图像恢复是一类众所周知的不适定性的问题.解决这类问题的一个有效方法是在保证恢复图像的均方误差最小的基础上加入处罚项，即正则化方法.然而，对一些具有代表性的正则化方法，比如Wiener滤波、Tikhonov正则化和TV模型，很少有工作通过比较详细叙述这些算法的优劣.这些算法的构造思想非常经典，是此后众多方法衍生、改进和复合的基础.因此，深入地了解它们的理论以及优缺点对图像恢复理论的发展是非常有意义的.除了一些经典的正则化方法之外，本文还选取了一些前沿算法，比如IDD-BM3D和ARSD法，这些方法从新颖的角度来解决问题的不适定性.

本文对这五种方法的理论进行系统阐述，分析其特征以及优缺点.最后设计数值实验来比较的它们恢复效果.

Image restoration is a kind of well-known ill-posed problems. An effective way to solve this problem is through regularization methods, which introduce penalty items based on the minimum of mean square error caused by restored images. However, few jobs focus on detailed discussing the advantages and disadvantages of typically regularization methods, such as Wiener filtering, Tikhonov regularization and TV model. These classical ideas of these algorithms for image reconstruction play important roles in the derivation, improvement and composition of subsequent numerous approaches. Therefore, this study is very meaningful for exploration of image restoration theories through introductions and comparisons of these methods. In addition, this paper introduces several advanced algorithms which attempt to address this ill-posed problem in a novel strategy, such as IDD-BM3D and ARSD.

This thesis systematically describes theories of five methods mentioned above and analyzes their properties, advantages and disadvantages. In the end, the results are presented via comparing in designed numerical experiments.