L_1-L_2范数联合约束的鲁棒目标跟踪

针对稀疏原型跟踪方法中未考虑正交模板系数的密集性的问题,本文提出一种L1-L2范数联合约束的鲁棒目标跟踪。首先,该方法建立基于L1-L2范数联合约束的目标表示模型,对PCA基模板系数和琐碎模板系数分别进行L2范数和L1范数正则化约束,不仅提高了跟踪的准确性,而且保证了对目标遮挡的鲁棒性;其次,针对目标表示模型的优化问题,运用岭回归和软阈值收缩方法快速迭代求解PCA基模板系数和琐碎模板系数;最后以粒子滤波为框架,利用目标未被遮挡部分的重构误差和稀疏噪声项建立观测模型,并结合提出的L1-L2范数联合约束的算法实现目标跟踪。实验结果表明,与5个现有的跟踪算法相比,本文的跟踪算法具有更好的准确性和鲁棒性。

基于极限学习机的非线性内模控制

针对非线性的内模控制的逆模难以求解的问题,该文提出一种基于改进极限学习机(MELM)的非线性内模控制方法。在基本的极限学习机模型中加入L1和L2范数罚函数,然后将改进极限学习机算法用于建立非线性系统的内模型和逆模型。仿真实验中,选取4种典型信号进行跟踪,并检验了系统的抗干扰能力和系统参数发生变化时的鲁棒性,通过将MELM和最小二乘支持向量机(SVM)以及极限学习机算法进行对比,表明基于MELM的内模控制方法对非线性系统具有更好的控制性能、较强的抗干扰能力和鲁棒性能。

利用稀疏约束非平稳多项式回归去除地震噪声及拾取初至

非平稳多项式拟合是L2范数下的优化问题,尽管考虑了信号的时变特征,但是仍然假设残差呈随机分布,当地震数据中存在较强非随机噪声时,常规的基于L2范数的非平稳多项式拟合不再适用。为此,研究了稀疏约束非平稳多项式回归理论与方法。首先回顾了非平稳多项式回归的基本原理;针对复杂稀疏分布残差问题,在反问题正则化理论框架下,结合非平稳多项式回归和L1范数约束,采用整形正则化和L1范数联合约束策略,利用共轭梯度和投影算法联合求解多约束反问题,同时估计具有时变光滑特征的多项式回归系数和具有稀疏分布特征的回归残差,可克服稀疏分布强噪声对反演的影响,并给出了算法基本流程和参数分析。模拟和实际数据应用结果表明,稀疏约束非平稳多项式回归方法在地震噪声压制和初至拾取等方面具有较好的应用效果。

基于L2范数的局部保持投影算法

针对传统局部保持投影算法对外点敏感的问题,提出了一种基于L2范数的局部保持投影算法。该算法通过采用L2范数定义目标函数并重新定义了权值矩阵,多次迭代计算投影矩阵得到局部最小值,直至达到收敛条件,进而获得最终的最优投影矩阵;通过利用最优投影矩阵将原始数据投影到最优的投影子空间,降低高维数据维度,同时能够保持原有数据特征。合成数据实验结果表明,与传统局部保持投影算法相比,所提基于L2范数的局部保持投影算法能够有效地降低数据维度,改善了算法对外点的敏感问题,提高了算法的鲁棒性。人脸识别实验结果表明,该算法能够取得较高且较为稳定的人脸识别率,人脸识别率可达80%。

一种自适应超分辨率图像重建方法研究

针对图像去噪的问题,提出了一种自适应范数及正则化参数的图像重建方法。首先,考虑到退化图像不仅含有高斯噪声,而且含有拉普拉斯噪声,利用最大似然估计的思想估计高斯噪声和拉普拉斯噪声的标准差;其次,由于在图像重建过程中,噪声分布会发生变化,为此,构造基于统计量的高斯和拉普拉斯权重函数,整合L_1、L_2范数,设计一种自适应加权函数;最后,结合自适应正则化参数方法,设计了一种自适应L_1、L_2范数及正则化参数的图像重建方法。实验结果表明,提出的方法对含有混合噪声的不同图像具有比较理想的重建效果。

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

An improved Gaussian frequency domain sparse inversion method based on compressed sensing

The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.

不可压缩核废料污染问题的变网格有限元法

在求解过程中对不同时刻的空间区域采用不同的有限元网格 ,提出并分析了一类变网格有限元格式 ,并在相当一般的情况下得到了最佳的L2 模误差估计 .

Double-Talk Detection Algorithm Based on the l_2 Norm

Echo canceller generally needs a double-talk detector which is used to keep the adaptive filter from diverging in the appearance of near-end speech. In this paper we adopt a new double-talk detection algorithm based onl 2 norm to detect the existence of near-end speech in an acoustic echo canceller. We analyze this algorithm from the point of view of functional analysis and point out that the proposed double-talk detection algorithm has the same performance as the classic one in a finite Banach space. The remarkable feature of this algorithm is its higher accuracy and better computation complexity. The fine properties of this algorithm are confirmed by computer simulation and the application in a multimedia communication system. Key words acoustic echo cancellation - double-talk, detection - l 2 norm - adaptive FIR CLC number TN 911 Foundation item: Supported by the the National High Technology Development of China (863-306-ZT05)Biography: Wang Shao-wei (1975-) male, Ph. D candidate, research direction: multimedia communication.

An ADI Finite Volume Element Method for a Viscous Wave Equation with Variable Coefficients

Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.

An Estimation for the Average Error of the Quasi-Griinwald Interpolation in the Wiener Space

We obtain an upper bound for the average error of the quasi-Griinwald interpolation based on the zeros of Chebyshev polynomial of the second kind in the Wiener space.

Blind Deblurring Based on L_0 Norm from Salient Edges

Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.

A novel algorithm for explicit optimal multi-degree reduction of triangular surfaces

This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials and Jacobi polynomials, we naturally deduce a novel algorithm for multi-degree reduction of triangular B^zier surfaces. This algorithm possesses four characteristics： ability of error forecast, explicit expression, less time consumption, and best precision. That is, firstly, whether there exists a multi-degree reduced surface within a prescribed tolerance is judged beforehand; secondly, all the operations of multi-degree reduction are just to multiply the column vector generated by sorting the series of the control points of the original surface in lexicographic order by a matrix; thirdly, this matrix can be computed at one time and stored in an array before processing degree reduction; fourthly, the multi-degree reduced surface achieves an optimal approximation in the norm L2. Some numerical experiments are presented to validate the effectiveness of this algorithm, and to show that the algorithm is applicable to information processing of products in CAD system.

DENSENESS OF RADIAL-BASIS FUNCTIONS IN L^2(Rn) AND ITS APPLICATIONS IN NEURAL NETWORKS

The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks.

THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM

In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？

A Mixed-finite Volume Element Coupled with the Method of Characteristic Fractional Step Difference for Simulating Transient Behavior of Semiconductor Device of Heat Conductor And Its Numerical Analysis

The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids （coarse partition and refined partition）, piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L2-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.

The research on method of interlayer modeling based on seismic inversion and petrophysical facies

Currently,the three-dimensional distribution of interlayer is realized by stochastic modeling.Traditionally,the three-dimensional geological modeling controlled by sedimentary facies models is built on the basis of logging interpretation parameters and geophysical information.Because of shallow gas-cap,the quality of three-dimensional seismic data vertical resolution in research area cannot meet the interlayer research that is below ten meters.Moreover,sedimentary facies cannot commendably reveal interlayer distribution and the well density is very sparse in research area.So,it is difficult for conventional technology to finely describe interlayers.In this document,it uses L1-L2 combined norm constrained inversion to enhance the recognition capability of interlayer in seismic profile and improve the signal to noise ratio,the wave group characteristics and the vertical resolution of three-dimensional data and classifies petrophysical facies of interlayer based on core,sedimentary facies and logging interpretation.The interlayer model which is based on seismic inversion model and petrophysical facies can precisely simulate the distribution of reservoir and interlayer.The results show that the simulation results of this new methodology are consistent with the dynamic production perfectly which provide a better basis for producing and mining remaining oil and a new interlayer modeling method for sparse well density.

On the Convergence of Broyden-Like Methods

The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ≥ 1 a natural number）.

Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method

In this work,the Benjamin-Bona-Mahony-Burgers(BBMB)equation is solved using an improvised cubic B-spline collocation technique.This equation describes the propagation of small amplitude waves in a non-linear dispersive medium,in the modeling of unidirectional planar waves.Due to the higher smoothness and sparse nature of matrices corresponding to splines,cubic B-splines are chosen as the basis function in the collocation method.But,the optimal accuracy and order of convergence cannot be achieved using the standard B-spline collocation method.So to overcome this,improvised cubic B-splines are formed by making posteriori corrections to cubic B-spline interpolant and its higher-order derivatives.The Crank-Nicolson scheme is used to discretize the temporal domain along with the quasilinearization process to deal with the nonlinear terms.The spatial domain discretization is carried out using the improvised cubic B-spline collocation method(ICSCM).The stability analysis of the technique is performed using the von-Neumann scheme.Several test problems are solved numerically and obtained results are compared with the results available in the literature.The aim of the paper is to show that such improvised techniques which were earlier used to solve ODEs,can be applied to solve the BBMB equation also,with excellent accuracy in results.