多帧图像的Tikhonov正则化重建算法研究*

介绍了Tikhonov正则化超分辨率重建算法的基本原理和特点,在原有正则化空域图像复原方法的基础上,根据多帧序列图像之间的互补信息,提出一种改进的正则化空域图像复原的新方法,该算法直接将正则化函数作用于图像超分辨率重建算法的条件概率项内,提高了正则化项的校正效率,并用共轭梯度运算来改善算法的收敛性,节省了图像重建所需的时间。实验和仿真结果表明,与传统方法相比,该算法不仅减轻了图像边缘纹理的模糊性,提高了图像的清晰度,而且收敛速度快。     

Iterative solvers for Tikhonov regularization of dense inverse problems

According to the special demands arising from the development of science and technology, in the last decades appeared a special class of problems that are inverse to the classical direct ones. Such an inverse problem is concerned with the opposite way, usually followed by a direct one: finding the cause of a given effect or finding the law of evolution given the cause and effect. Very frequently, such inverse problems are modelled by Fredholm first-kind integral equations that give rise after discretization to (very) ill-conditioned linear systems, in classical or least squares formulation. Then, an efficient numerical solution can be obtained by using the Tikhonov regularization technique. In this respect, in the present paper, we propose three Kovarik-like algorithms for numerical solution of the regularized problem. We prove convergence for all three methods and present numerical experiments on a mathematical model of an inverse problem concerned with the determination of charge distribution generating a given electric field.     

A method for regularization of evolutionary polynomial regression

While many applications require models that have no acceptable linear approximation, the simpler nonlinear models are defined by polynomials. The use of genetic algorithms to find polynomial models from data is known as evolutionary polynomial regression (EPR). This paper introduces evolutionary polynomial regression with regularization, an algorithm extending EPR with a regularization term to control polynomial complexity. The article also describes a set of experiences to compare both flavors of EPR against other methods including linear regression, regression trees and support vector regression. These experiments show that evolutionary polynomial regression with regularization is able to achieve better fitting and needs less computation time than plain EPR.     

近似最优正则化参数方法在电容成像图像重建中的应用

将基于近似最优正则化参数的Tikhonov方法应用于电容成像(Electrical capacitance tomography,ECT)图像重建以解决其中存在的病态性问题,并利用几种典型分布对该方法进行仿真测试。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。在重建结果方面,基于近似最优参数的Tikhonov方法在不同的介电常数分布下与目前普遍采用的线性反投影算法(Linear back projection,LBP)各有优势。结果表明,该方法尚不能完全取代LBP算法,但能在一定程度上弥补LBP算法的不足。     

A general learning framework using local and global regularization

In this paper, we propose a general learning framework based on local and global regularization. In the local regularization part, our algorithm constructs a regularized classifier for each data point using its neighborhood, while the global regularization part adopts a Laplacian regularizer to smooth the data labels predicted by those local classifiers. We show that such a learning framework can easily be incorporated into either unsupervised learning, semi-supervised learning, and supervised learning paradigm. Moreover, many existing learning algorithms can be derived from our framework. Finally we present some experimental results to show the effectiveness of our method.     

热传导方程反问题的Tikhonov正则化法

为了分析热传导方程反问题所涉及的初始条件.论文把这一类问题转化成第一类Fredholm积分方程,运用Tikhonov正则化的反演法和牛顿法获取正则化参数,得到这一问题的数值解.通过数值实验,验证了这一算法在实际应用中的有效性.     

Segmentation of ARX-models using sum-of-norms regularization

Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. Here it is formulated as a least-squares problem with sum-of-norms regularization over the state parameter jumps, a generalization of ?₁-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade-off fit and the number of segments.     

An Algorithm for Image Denoising with Automatic Noise Estimate

In this paper, we propose a general algorithm for image denoising when no a priori information on the noise is available. The image denoising problem is formulated as an inequality constrained minimization problem where the objective is a general convex regularization functional and the right-hand side of the constraint depends on the noise norm and is not known. The proposed method is an iterative procedure which, at each iteration, automatically computes both an approximation of the noise norm and an approximate solution of the minimization problem. Experimental results demonstrate the effectiveness of the proposed automatic denoising procedure.

基于动态参数的Tikhonov方法在电容成像图像重建中的应用

该文针对电容成像(ECT)图像重建问题的病态性,采用Tikhonov正则化方法进行图像重建,并选用三种方法动态选择正则化参数。仿真结果表明对某些流型分布,用文中所述方法得到的重建结果优于目前普遍使用的线性反投影(LBP)算法。该方法为提高ECT图像重建质量提供了新的途径。     

Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization

Some regularization methods, including the group lasso and the adaptive group lasso, have been developed for the automatic selection of grouped variables (factors) in conditional mean regression. In many practical situations, such a problem arises naturally when a set of dummy variables is used to represent a categorical factor and/or when a set of basis functions of a continuous variable is included in the predictor set. Complementary to these earlier works, the simultaneous and automatic factor selection is examined in quantile regression. To incorporate the factor information into regularized model fitting, the adaptive sup-norm regularized quantile regression is proposed, which penalizes the empirical check loss function by the sum of factor-wise adaptive sup-norm penalties. It is shown that the proposed method possesses the oracle property. A simulation study demonstrates that the proposed method is a more appropriate tool for factor selection than the adaptive lasso regularized quantile regression.     

应用谱回归和图正则最小二乘回归的数据降维

数据降维对于提高高维数据处理的效率具有重要意义,稀疏编码是目前受到广泛关注的主流降维方法。针对该方法在降维过程中不能保持样本空间几何结构信息的不足,提出一种基于谱回归和图正则最小二乘回归的改进方案,以2个图像数据集和2个基因表达数据集为样本的实验表明该方法优于未加改进的稀疏编码降维法。     

A new investigation into regularization techniques for the method of fundamental solutions

This study examines different regularization approaches to investigate the solution stability of the method of fundamental solutions (MFS). We compare three regularization methods in conjunction with two different regularization parameters to find the optimal stable MFS scheme. Meanwhile, we have investigated the relationship among the condition number, the effective condition number, and the MFS solution accuracy. Numerical results show that the damped singular value decomposition under the parameter choice of the generalized cross-validation performs the best in terms of the MFS stability analysis. We also find that the condition number is a superior criterion to the effective condition number.     

基于低频唤醒和极限学习机的无线定位系统

设计了一种基于低频(LF)唤醒技术和极限学习机(ELM)分类算法的无线定位系统.实现了低频唤醒、射频应答的电路结构和通信回路,实现了有源应答器的超低待机监听.通过比较各类型的多种射频定位算法,选用基于ELM分类的定位算法,对低频唤醒接收信号强度指示(RSSI)数据进行分类并实现定位,有效降低了定位算法在线阶段的计算量,在单片机系统中实现了实时定位计算.测试结果表明:定位系统在有效范围内定位精度可达15 cm,定位正确率可达95％以上,在定位精度和稳定性方面明显优于超高频(UHF)频段射频定位系统.     

贝叶斯框架下的LSSVM和贝叶斯网络及其应用

贝叶斯理论能够利用样本信息和先验知识,简化预测模型,优化参数.主要介绍了贝叶斯框架下的最小二乘支持向量机算法和贝叶斯正则化神经网络,贝叶斯框架下的最小二乘支持向量机能确定正则化参数和核参数,贝叶斯正则化网络能够自适应的调整网络的复杂度和网络的隐节点个数.以轻柴油的凝点、闪点、95%馏出温度3个关键指标输出为例分别建立了这两种预测模型,并且对结果进行了比较,仿真结果表明贝叶斯框架下的最小二乘支持向量机比贝叶斯正则化网络有更强的泛化能力,而且程序运行速度快,运算精度高.     

基于信息熵优化的极限学习机研究及应用

为了提高极限学习机对化工过程的高维数据进行建模的能力,提出了一种基于信息熵优化的学习算法。利用互信息方法判断输入变量与输出变量之间的相关性,通过去除部分与输出变量相关性较弱的输入变量来过滤冗余信息,从而达到降维的目的。然后利用熵权法对输入数据进行加权优化,从而降低输入数据中的离散点对极限学习机模型精确度的影响。因此本文提出了一种基于信息熵的ELM算法。该算法以UCI标准数据集进行测试,并以PTA工业系统数据进行实际验证。实验结果表明,与传统ELM算法相比,优化后的学习算法在处理高维数据时具有稳定性强、建模精度高的特点。从而拓展了神经网络技术在化工领域里的应用。     

Inference of building occupancy signals using moving horizon estimation and Fourier regularization

We study the problem of estimating time-varying occupancy and ambient air flow signals using noisy carbon dioxide and flow sensor measurements. A regularized moving horizon estimation formulation is proposed that constrains time-varying signals to smooth Fourier expansions. We demonstrate that the regularization approach makes the estimator robust to high levels of noise. In addition, it requires minimal information about the shape of the signals. Computational experiments with simulated and real data demonstrate the effectiveness of the approach.     

基于FAM-ELM股票价格预测研究

研究股票价格准确预测问题.股票价格预测是股票交易者最关心的问题,直接影响着股票交易者的收益.由于股票受经济发展的影响,价格波动较大,在股票价格预测中采用传统神经网络方法存在训练速度慢,易陷入局部极小值,隐含层节点数人为指定等问题,导致泛化能力受到影响,预测不准.为了提高股票价格预测的精度,提出基于因子分析法的极限学习机股票价格预测模型.首先使用因子分析法综合股票价格影响指标;接着使用隐含层神经元数量寻优算法搜索最优隐含层神经元数量值;然后使用极限学习机对综合后的股票价格影响指标进行学习,建立股票价格预测模型;最后通过实验对模型性能进行测试.试验结果证明,基于因子分析法的极限学习机提高了股票价格的预测精度和运行效率.     

Super-resolution image reconstruction techniques: Trade-offs between the data-fidelity and regularization terms

Stochastic regularized methods are quite advantageous in super-resolution (SR) image reconstruction problems. In the particular techniques, the SR problem is formulated by means of two terms, the data-fidelity term and the regularization term. The present work examines the effect of each one of these terms on the SR reconstruction result with respect to the presence or absence of noise in the low-resolution (LR) frames. Experimentation is carried out with the widely employed L₂, L₁, Huber and Lorentzian estimators for the data-fidelity term. The Tikhonov and Bilateral (B) Total Variation (TV) techniques are employed for the regularization term. The extracted conclusions can, in practice, help to select an effective SR method for a given sequence of LR frames. Thus, in case that the potential methods present common data-fidelity or regularization term, and frames are noiseless, the method which employs the most robust regularization or data-fidelity term should be used. Otherwise, experimental conclusions regarding performance ranking vary with the presence of noise in frames, the noise model as well as the difference in robustness of efficiency between the rival terms. Estimators employed for the data-fidelity term or regularizations stand for the rival terms.     

Robust variable selection using least angle regression and elemental set sampling

The problem of selecting variables or features in a regression model in the presence of both additive (vertical) and leverage outliers is addressed. Since variable selection and the detection of anomalous data are not separable problems, the focus is on methods that select variables and outliers simultaneously. For selection, the fast forward selection algorithm, least angle regression (LARS), is used, but it is not robust. To achieve robustness to additive outliers, a dummy variable identity matrix is appended to the design matrix allowing both real variables and additive outliers to be in the selection set. For leverage outliers, these selection methods are used on samples of elemental sets in a manner similar to that used in high breakdown robust estimation. These results are compared to several other selection methods of varying computational complexity and robustness. The extension of these methods to situations where the number of variables exceeds the number of observations is discussed.     

基于PCA和ELM的模拟电路故障诊断

针对模拟电路的故障诊断和健康管理（PHM）的应用,提出了结合主成分分析（PCA）和极限学习机（ELM）的故障诊断方法。该方法用Sallen-Key带通滤波器来获取故障样本,并通过PCA进行故障特征提取。根据故障样本对ELM进行训练来获得故障诊断模型。实验结果表明,该实现方法识别率高、鲁棒性好,在工程实际中具有研究和应用价值。