This thesis introduces and analyses in detail the research and application of regularization in image restoration , the main contributions and creativities are listed as follows : firstly , on the basis of the regularization technique for dealing with ill - posed problems , starting from the mathematical theories about regularization , analyzing the degraded model and the ill - posed character of image restoration , this paper mainly discusses the regularized parameter and regularized item , and the solution approaches and fast algorithms are also summarized , therefore perfects the essential theories about regularization in image restoration 本文针对图像复原中正则化方法的研究及应用进行了广泛深入的探讨与分析,主要工作和创新点如下:第一,在正则化技术解决病态问题的基础上,从正则化方法数学理论入手,分析了图像的退化模型和图像复原的病态特征,重点讨论了正则化参数和正则项的选取,并总结了其求解算法及快速实现方法,完善了正则化方法图像复原的基本理论。
The rapid development and the increasing achievements on these areas during the past two decades lay a solid foundation for the fault diagnosis of complicated systems . wavelet analysis is a novel mathematical theory and method proposed in 1980s . it is regarded as a breakthrough of fourier analysis because it has many wonderful characteristics 小波分析( waveletanalysis )即小波变换是80年代中期发展起来的一门新兴的数学理论和方法,它被认为是傅立叶分析方法的突破性进展,它具有许多优良的特性。