查询词典 regularization

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

Potential theory is used to transfer the exterior boundary value problem into the boundary integral equation of the first kind. A iterated Tikhonov regularization and a modified Tikhonov regularization are presented to solve the integral equation.

利用位势理论将外边值问题转化为第一类边界积分方程，再分别利用迭代的Tikhonov正则化方法和改进的Tikhonov正则化方法求解积分方程。

Gradient regularization method ; Frechet derivative ; regularization parameters ; parameter identification ; ill posedness ; elliptic operator equation

梯度正则化方法； Frechet导数；正则参数；参数识别；不适定；椭圆算子方程

To solve the ill-posed problem of the super-resolution image regularization reconstruction, an energy function based on p harmonic mapping regularization and super-resolution image observed model was drawn.

针对超分辨率图像重建过程中的正则化约束问题，本文提出采用p调和映射进行正则化重建，根据超分辨率图像观察模型及正则约束，给出相应的能量泛函，并采用动态偏微分方程演化来求解能量泛函。

Maximum Clique Problem; Information Theory Method; Homotopy Method; Entropy Regularization; D-function Regularization

基础科学，数学，代数、数论、组合理论最大团问题；信息论方法；同伦方法；熵正则化； D函数正则化

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

In the study based on noise-distribution, an approach to compute local regularization parameter and design local regularization operator adaptively is proposed according to the distribution of the noise.

在基于噪声分布的方法中，提出根据噪声分布自适应计算正则化参数及设计正则化算子的方法。

An applied method was put forward to select regularization parameters in the iterative process of gradient regularization method.

并给出了该方法在计算过程中求正则解时一种实用正则参数选取方法。

The use of regularization method for the restoration of blurred images of the algorithm, resulting in an image, and then adding noise to the input of specific parameters of regularization to restore its image.

详细说明：利用正则化方法对模糊图像进行恢复的算法，产生一幅图象，然后加入噪声后对特定的输入正则化参数其进行图象恢复。

All the Tikhonov regularization theory, regularization operator and regularization parameter are given a complete analysis and discussion. The differentiability of Morozov discrepancy equation is investigated. And the image noise, as the knowledge a prior, is estimated and the equation is modified.

图像复原计算方法的研究是一个反卷积的病态性求解问题，本文用反问题正则解的基本理论，对经典的图像复原方法依正则化思想进行了细致的分析与研究。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。