The use of tikhonov regularization theory was to solve ill - posed problem of image reconstruction and the use of sirt algorithm was to improve the quality of the final reconstructed image 为了克服图像重建中的不适定性问题，利用tikhonov正则化原理进行初始图像重建。 sirt算法则用来对初始重建图像进行迭代改善以获得最终重建图像，改善了重建图像的质量。
The ill - posed problems include the ill - conditioned and the rank - deficient ones in geodesy , which exist widely in gps data processing , deformation analysis , geodesy inversion , gravity field continuation downward , and so on 大地测量中的不适定问题包括病态问题和秩亏问题，它广泛存在于gps数据处理、形变分析、大地测量反演、重力场向下延拓等领域。
Based on tikhonov regularization method and considering sufficiently the practice of geodesy , the main thread of the choice of the regularizer and the determination of the smoothing parameters is grasped and the in - depth research on the ill - posed problems in geodesy is carried out . a framework of the theory and methods of systematically processing the ill - posed problems has been established and tikhonov regularization method has been evolved in this paper 本文基于tikhonov正则化方法和欧吉坤研究员提出的选权拟合的研究思路，充分考虑大地测量实际，抓住正则化矩阵的选取和正则化参数的确定这条主线，对大地测量中的不适定问题进行了深入研究，建立起了一套较系统的不适定问题处理理论及方法的框架，进一步发展了tikhonov正则化方法。
Based on this ill - posed problem of edge detection , the edge types that exist in real images are described as mathematical models and the edge models that smoothed by gaussian function are regarded as the research objects . the paper systematically analyzes the characteristics of the different edge types and the relations between the localization of the different edge types and the smoothing scale while using the numerical differentiation as the method to detect edges 本文从边缘检测的“两难”问题出发，对实际图像中可能出现的边缘类型进行了数学模型描述，然后把高斯平滑后的边缘模型作为研究对象，系统地分析了采用微分法检测边缘时，不同的边缘类型表现出来的特性，以及不同类型的边缘定位与平滑尺度的关系。
On one hand , from the technique of constrained least squares and limited energy of additive noise , an effective restored approach by adopting regularization method to overcoming ill - posed problem , solving an equation with a single variable , and using space iterative algorithm is proposed ; on the other hand , aiming at the restoration of blurred image , another effective restoration approach based on least - square algorithm is also proposed in this paper . this method firstly adopts increment iterative algorithm to improve convergence and meanwhile applies regularization technique to overcome ill - posed problem . in the computations , the regularized parameter has its adaptive character , which can be determined in terms of the restored image at each iteration step therefore automatically correct to the appropriate value 一是从约束最小二乘出发,在加性噪声能量有界的前提下,采用正则化方法来克服病态问题,通过解一个单变量方程,并利用空域迭代运算实现了一种有效的图像复原;二是针对模糊图像的复原问题,从最小二乘算法出发,采用增量迭代的方法改善算法的收敛性,同时结合正则化技术克服问题的病态性质,并引入自适应的正则化参数,使其与图像复原的迭代运算同步进行并自动修正到最优值。
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。
