本文在求解波动方程反问题的GR（梯度正则化法）方法基础上提出一种一维波动问题的分层反演方法。
The author puts forward the layer-by-layer inversion method for one-dimensional wave problem, which is based on the gradient regularization(GR)method for wave equation inversion.
数值结果表明，在先验知识满足的条件下，近似最优参数法所找到的正则化参数是对最优正则化参数的较合理近似。
Numerical results show that 'near optimal' parameter can be considered as an acceptable approximation of optimal regularization parameter with available priori information.
第一章为绪论，简单描述了熵正则化方法与罚函数法的研究现状；
The first chapter is the introduction for the entropy regularization method and penalty function method.
本文综述了作者提出的免除噪声正则化条纹法的原理和多种方法。
Noise free normalized fringe method (NFNF) that is also named pure fringe gray level method is one of the effective methods.
基于TIK - HONOV正则化原理，选择了一种具有物理意义的正则化矩阵，以减弱法矩阵的病态性。
Based on TIKHONOV regularization theorem, a new regularizer, which has explicitly physical meaning, is chosen to mitigate the ill-condition of the normal matrix.
本文综述了作者提出的免除噪声正则化条纹法的原理和多种方法。
In this paper, the noise free normalized fringe method that was proposed and developed by the author is reviewed and summarized briefly.
本文根据常微分方程参数反问题的数学理论，将正交化方法同有限差分法结合用于确定水质模型参数，并与正则化方法、最速下降法和共轭梯度法作了比较。
The comparison of the calculation results show that orthogonal rule method is fast, simple and reliable, and is applicable to the calculation of the water quality modeling parameters.
因此许多学者提出了各种求解反问题的方法，比如脉冲谱方法，最佳摄动量法，蒙特卡罗方法，各种优化方法和正则化方法等。
So various methods are proposed by scholars to solve these problems, such as pulse spectrum method, the best perturbation method, Monte Carlo method, optimized and regularization method.
本文在讨论反演基本问题的基础上，用共轭梯度法实现了核磁共振的一维正则化反演。
After discussing the basic inversion problem, this paper achieve the 1d SNMR Tikhonov regularization inverse by conjugate gradient method.
在两步计算中，均采用L曲线法来确定正则化参数α。
This paper utilizes L-curve method to determine the regularization parameter in the (above) two computation steps.
在两步计算中，均采用L曲线法来确定正则化参数α。
This paper utilizes L-curve method to determine the regularization parameter in the (above) two computation steps.
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