一种鲁棒的总体最小二乘自适应辨识算法

针对输入输出观测数据均含有噪声的系统辨识问题，提出了一种鲁棒的总体最小二乘自适应辨识算法．该算法在对总体最小二乘问题与向量的瑞利商及其性质研究的基础上，以被辨识系统的增广权向量的瑞利商(RQ)作为损失函数，利用梯度最陡下降原理导出权向量的自适应迭代算法，并利用随机离散学习规律对权向量模的分析修正了算法梯度，提高了算法的噪声鲁棒性，构成了一种噪声鲁棒的总体最小二乘自适应辨识算法．文中研究了该算法的收敛性能．仿真实验结果表明该算法的鲁棒抗噪性能和稳态收敛精度明显高于其它同类方法，而且可使用较大的学习因子，在较高的噪声环境下仍然保持良好的收敛性．     

有序子集最小二乘OS—LS图像重建迭代算法

为推导一种新的快速图像迭代重建方法，首先将有序子集(ordered subsets，OS)技术应用到最小二乘图像重建迭代算法(least square reconstruction，LS)；然后对仿真Phantom模型数据和实际医用正电子发射断层成像仪(PET)数据进行重建，并研究了在不同子集划分下的重建结果，同时分析比较了不同子集的选取对OS—LS重建罔像质量以及重建收敛速度的影响。重建结果表明，这种基于有序子集的最小二乘图像重建迭代算法(OS—LS)具有较高的重建图像质量和较短的计算时间，相对于传统LS算法的重建，OS—LS的收敛速度加速了约L倍(L为子集个数)．其重建图像质量也好于传统的滤波反投影(FBP)方法的重建．町应用在PET图像重建中。     

一种具有迭代约束的最小二乘 ECT图像重建算法 *

针对电容层析成像系统中的 “软场 ”效应和病态问题 ,将最小二乘法和迭代法相结合 ,提出了一种最小二乘约束迭代的图像重建算法。给出了算法的数学模型 ,完成了算法的收敛性分析和证明 ,算法在图像重建中使迭代步长在保证收敛的情况下达到最优。仿真和实验结果表明 ,该方法与最小二乘法相比 ,具有更稳定、成像效果好等特点 ,为 ECT图像重建提供了一种新的有效方法。     

l1鲁棒辨识:最小二乘算法及试验设计

现有的l^1鲁棒辨识方法依赖于观测数据窗的起始时刻因而不能用来辨识时变系统,针对该问题基于最小二乘法提出了一种l^1鲁棒辨识算法．该算法与观测窗的起始时刻无关,可用于时变系统的辨识．证明了当试验输入为持续激励信号时所提出的算法为本质最优算法,进一步证明了周期持续激励序列为最优试验信号,并给出了辨识误差紧界的计算公式．最后利用提出的算法研究了慢时变系统的l^1鲁棒辨识问题．     

RBF网络的鲁棒最小二乘学习算法

首先,针对径向基函数(RBF)神经网络参数学习中最小二乘法(LS)难以获得较高鲁棒性的问题,假定训练数据扰动上界可知,并基于鲁棒最小二乘原理,提出一种RBF网的最优鲁棒参数学习算法;然后分析指出,扰动上界可依据训练数据集自适应学习估计;最后通过实验分析结果表明了所提算法具有较高的参数鲁棒学习能力.与LS相似,新算法无额外参数,易于实际应用.     

鲁棒最小二乘孪生支持向量机及其稀疏算法

最小二乘孪生支持向量机通过求解两个线性规划问题来代替求解复杂的二次规划问题,具有计算简单和训练速度快的优势。然而,最小二乘孪生支持向量机得到的超平面易受异常点影响且解缺乏稀疏性。针对这一问题,基于截断最小二乘损失提出了一种鲁棒最小二乘孪生支持向量机模型,并从理论上验证了模型对异常点具有鲁棒性。为使模型可处理大规模数据,基于表示定理和不完全Cholesky分解得到了新模型的稀疏解,并提出了适合处理带异常点的大规模数据的稀疏鲁棒最小二乘孪生支持向量机算法。数值实验表明,新算法比已有算法分类准确率、稀疏性、收敛速度分别提高了1.97%~37.7%、26~199倍和6.6~2 027.4倍。     

一类非平坦函数的多核最小二乘支持向量机的鲁棒回归算法

给出了标准最小二乘支持向量机的数学回归模型,并提出了多核最小二乘支持向量机算法,用于提高非平坦函数的回归精度.运用谱系聚类方法解决多核最小二乘支持向量机的解缺乏稀疏性的问题.利用偏最小二乘回归方法对多核最小二乘支持向量机进行了鲁棒回归.通过仿真实例证实了所提方法的有效性.     

M-估计耦合双边滤波的正则化超分辨率重建

在正则化超分辨率重建框架下,基于M-估计理论和双边滤波思想,建立了一种鲁棒的超分辨率重建统一能量泛函。该能量泛函融合了M-估计的鲁棒性处理机制和双边滤波的双重异性加权机制,提高了算法的鲁棒性和边缘保持特性。鉴于采用最小二乘估计的CLS算法和采用最小一乘估计的Farsiu重建算法在边缘保持特性方面存在的不足,在算法实现时选用了Huber稳健M-估计。不论是视觉效果还是峰值信噪比(PSNR),实验结果都表明该算法的有效性。     

改进的鲁棒总体最小二乘无源定位算法

针对机载无源定位易受异常误差影响的问题,提出一种基于角度信息的鲁棒递推总体最小二乘定位（RRTLS）算法。建立机载无源定位模型,得出总体最小二乘（TLS）解,根据机载定位的实时性、低复杂度要求将其转化为加权递推形式;根据广义M估计原理构建鲁棒TLS极值准则,利用其性质将RRTLS定位问题转化为等价权函数的设计问题;验证了利用残差识别异常误差的合理性,在此基础上建立了等价权函数。仿真结果表明,不存在异常误差时,递推总体最小二乘（RTLS）算法和RRTLS算法均能较好收敛;存在异常误差时,递推最小二乘（RLS）和RTLS定位结果受到扭曲,而RRTLS算法能够获得理想的估值,具有较强的鲁棒性。     

在线鲁棒最小二乘支持向量机回归建模

鉴于工业过程的时变特性以及现场采集的数据通常具有非线性特性且包含离群点,利用最小二乘支持向量机回归（least squares support vector regression,LSSVR）建模易受离群点的影响.针对这一问题,结合鲁棒学习算法（robust learning algorithm,RLA）,本文提出了一种在线鲁棒最小二乘支持向量机回归建模方法.该方法首先利用LSSVR模型对过程输出进行预测,与真实输出相比较得到预测误差;然后利用RLA方法训练LSSVR模型的权值,建立鲁棒LSSVR模型;最后应用增量学习方法在线更新鲁棒LSSVR模型,从而得到在线鲁棒LSSVR模型.仿真研究验证了所提方法的有效性.     

Robust reweighted MAP motion estimation

This paper proposes a motion estimation algorithm that is robust to motion discontinuity and noise. The proposed algorithm is constructed by embedding the least median squares (LMedS) of robust statistics into the maximum a posteriori (MAP) estimator. Difficulties in accurate estimation of the motion field arise from the smoothness constraint and the sensitivity to noise. To cope robustly with these problems, a median operator and the concept of reweighted least squares (RLS) are applied to the MAP motion estimator, resulting in the reweighted robust MAP (RRMAP). The proposed RRMAP motion estimation algorithm is also generalized for multiple image frame cases. Computer simulation with various synthetic image sequences shows that the proposed algorithm reduces errors, compared to three existing robust motion estimation algorithms that are based on M-estimation, total least squares (TLS), and Hough transform. It is also observed that the proposed algorithm is statistically efficient and robust to additive Gaussian noise and impulse noise. Furthermore, the proposed algorithm yields reasonable performance for real image sequences     

Implicitly Weighted Methods in Robust Image Analysis

This paper is devoted to highly robust statistical methods with applications to image analysis. The methods of the paper exploit the idea of implicit weighting, which is inspired by the highly robust least weighted squares regression estimator. We use a correlation coefficient based on implicit weighting of individual pixels as a highly robust similarity measure between two images. The reweighted least weighted squares estimator is considered as an alternative regression estimator with a clear interpretation. We apply implicit weighting to dimension reduction by means of robust principal component analysis. Highly robust methods are exploited in tasks of face localization and face detection in a database of 2D images. In this context we investigate a method for outlier detection and a filter for image denoising based on implicit weighting.     

Robust adaptive segmentation of range images

We propose a novel image segmentation technique using the robust, adaptive least kth order squares (ALKS) estimator which minimizes the kth order statistics of the squares of residuals. The optimal value of k is determined from the data, and the procedure detects the homogeneous surface patch representing the relative majority of the pixels. The ALKS shows a better tolerance to structured outliers than other recently proposed similar techniques. The performance of the new, fully autonomous, range image segmentation algorithm is compared to several other methods     

Estimation of 2D Displacement Field Based on Affine Geometric Invariance and Scene Constraints

In the paper, a novel approach using affine transfer and scene constraint for estimation of 2D displacement field was developed. In this approach, we derived a system of 5 linear equations for computing corresponding point of any image point via the utilisation of affine invariant. Subsequently, the characteristics of such a linear system was thoroughly studied, and the way to obtain a reliable solution of the system via robust least squares (RLS) approach, in conjunction with total least squares technique, was proposed. In addition, through the interpretation of the approach from both geometric point of view and numerical point of view, we gave the limitation of the algorithm. The limitation was then relaxed to a certain extent by using full fundamental matrix. These findings were further verified through the experimental results.     

LMSMVE: a program for least median of squares regression and robust distances.

The program LMSMVE performs robust regression analysis by using the method of the least median of squares. It also computes robust distances to locate leverage points, that is, outliers with respect to the set of independent variables. LMSMVE constructs plots of least median of squares residuals against robust distances. Both methods can tolerate up to half the data being outliers before they fail to give results that describe the bulk of the data. A complete system that operates directly on SYSTAT files is available for the IBM PC and compatibles; it includes a utility that converts ASCII files to SYSTAT format.     

A novel image encryption algorithm based on piecewise linear chaotic maps and least squares approximation

In this paper, we propose a novel image encryption algorithm based on chaotic maps and least squares approximations. The proposed algorithm consists of two main phases, which are applied sequentially in several rounds, namely a shuffling phase and a masking phase. Both phases are based on 1–dimensional piecewise linear chaotic maps and act on the rows/columns of the input plain image. Least squares approximations are used to strengthen the security of the proposed algorithm by providing strong mixing between the rows/columns of the image. Simulation results show that the proposed image encryption algorithm is robust against common statistical and security attacks. We present thorough comparison of the proposed algorithm with some existing image encryption algorithms.

     

航向保持鲁棒最小二乘支持向量机控制

考虑到船舶航向控制中,存在的大量不确定因素及对控制系统的实时性要求,提出一种基于鲁棒最小二乘支持向量机(RLSSVM)的船舶航向保持控制方案.该控制策略充分利用最小二乘支持向量机良好的非线性映射能力、自学习适应能力和并行信息处理能力,并与H~2/H~∞鲁棒控制算法相结合,优势互补,形成闭环控制.仿真结果表明,该系统对海情的变化有良好的自适应能力,鲁棒性强,实现了航向保持精确控制.     

Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.