分块二维保局投影方法及其在人脸识别中的应用

提出了一种基于图像分块的二维保局投影(分块2DLPP)的人脸识别方法.先对原始图像矩阵进行分块,然后对分块子图像施行2DLPP方法,再将各个分块按照一定的次序整合起来进行特征提取,从而实现图像降维.该方法能有效地提取图像的局部特征.实验表明:该方法在识别性能上优于2DLPP方法.     

基于图像分块的二维投影特征提取能力研究

人脸识别研究的主要目的是提高识别率,关键技术在于提取有效的人脸特征。提出了分块多投影和分块双向多投影二维特征提取方法。分块多投影特征提取方法,针对现有分块单投影特征提取方法中每一子图均采用相同投影矩阵,而对人脸局部信息不加以区别,利用二维主成分分析方法,构造了分块多投影矩阵,使不同的子图投影到不同的子空间,与传统二维主成分方法和分块单投影方法相比,有效地利用人脸局部信息,降低了特征维数,提高了识别率,在ORL人脸库上实验表明了其有效性。     

二维主成分分析方法的推广及其在人脸识别中的应用

提出了分块二维主成分分析(分块2DPCA)的人脸识别方法。分块2DPCA方法先对图像矩阵进行分块,对分块得到的子图像矩阵直接进行鉴别分析。其特点是:能方便地降低鉴别特征的维数;可以完全避免使用矩阵的奇异值分解,特征抽取方便;与2DPCA方法相比,使用低维的鉴别特征矩阵,而达到较高(至少是不低)的正确识别率。此外,2DPCA是分块2DPCA的特例。在ORL和NUST603人脸库上的试验结果表明,所提出的方法在识别性能上优于2DPCA方法。     

一种基于局部排序PCA的线性鉴别算法

主分量分析(Principal Component Analysis,PCA)是模式识别领域中一种重要的特征抽取方法,该方法通过K-L展开式来抽取样本的主要特征。基于此,提出一种拓展的PCA人脸识别方法,即分块排序PCA人脸识别方法(MSPCA)。分块排序PCA方法先对图像矩阵进行分块,对所有分块得到的子图像矩阵利用PCA方法求出矩阵的所有特征值所对应的特征向量并加以标识;然后找出这些所有的特征值中k个最大的特征值所对应的特征向量,用这些特征向量分别去抽取所属的子图像的特征;最后,在MSPCA的基础上,将抽取子图像所得到的特征矩阵合并,把这个合并后的特征矩阵作为新的样本进行PCA+LDA。与PCA和PCA+LDA方法相比,分块排序PCA由于使用子图像矩阵,可以避免使用奇异值分解理论,从而更加简便。在ORL人脸库上的实验结果表明,所提出的方法在识别性能上明显优于经典的PCA和PCA+LDA方法。     

嵌入率可调和低修改率的二值图像密写算法

为了提供大而可调的二值图像信息隐藏容量和保持载密二值图像良好的视觉质量,提出一种基于分块和矩阵编码的二值图像信息隐藏算法.将二值图像划分为互不相交的2×2的图像子块,随机选择黑白相间的边缘子块作为可嵌子块,应用(1,n,k)矩阵编码实现最多只改变n块可嵌子块中一块的1个像素即可嵌入k比特信息,以及修改像素的规则.选择不同的矩阵编码方案,可以得到不同的嵌入率和像素修改率.理论分析和实验结果表明,本文算法具有信息嵌入量大,效率高,修改率低,安全性好;其信息嵌入率选择具有高度弹性,可以根据实际要求选择在嵌入率和载密图像质量都很理想的密写方案.     

模块二维主成分分析——人脸识别新方法

提出了模块二维主成分分析(M2DPCA)线性鉴别分析方法。M2DPCA方法先对图像矩阵进行分块，对分块得到的子图像矩阵直接进行鉴别分析。其特点是：能有效地降低模式原始特征的维数；可以完全避免使用矩阵的奇异值分解，特征抽取方便；此外，2DPCA是M2DPCA的特例。在ORL人脸库上试验结果表明，M2DPCA方法在识别性能上优于PCA，比2DPCA更具有鲁棒性。     

基于分块二维线性鉴别分析的人脸识别

基于2DLDA方法,提出了一种基于图像分块的二维线性鉴别分析(M2DLDA)的人脸识别方法。该方法首先对原始人脸图像进行必要的预处理后进行分块,再对分块后的子图像分别采用2DLDA方法进行特征提取,最后用最小距离分类器进行识别。该方法的优点：分块后能有效的抽取人脸图像的局部特征有利于分类;降低了2DLDA方法提取的特征矩阵的维数;特征提取是基于图像矩阵的,抽取方便快速。在ORL人脸数据库上的实验结果表明：该方法在识别性能上优于2DLDA方法。     

推广的PCA及其在人脸识别中的应用

基于传统的PCA方法,提出了推广的PCA人脸识别方法.推广的PCA方法先对训练图像矩阵集进行分块,再利用传统PCA对分块得到的子训练矩阵集进行分析,得到多个变换矩阵,通过这些变换矩阵将训练图片和测试图片投影到特征空间进行鉴别.与传统PCA方法相比,提高了主元的维数,有效地增加了识别的精度.在FERET人脸库上的试验结果表明,所提出的方法在识别性能上明显优于传统的PCA方法,识别率得到了提高.     

有监督的二维分块局部相似与差异算法

为提高人脸识别算法的鲁棒性,提出一种有监督的二维分块局部相似与差异的人脸识别算法.该算法对原图像矩阵分块后,利用局部相似和差异算法中定义的2个权值矩阵,求解分块矩阵中的投影矩阵,将得到的投影矩阵按次序整合得出特征矩阵,以达到使原图像降维的目的.实验结果表明,该算法在降低计算难度的同时,能保持图像的局部信息,取得良好的识...     

分块二维主成分分析鉴别特征抽取能力研究

基于二维主成分分析(2DPCA),文章提出了分块二维主成分分析(M2DPCA)人脸识别方法。M2DPCA从模式的原始数字图像出发,先对图像进行分块,对分块得到的子图像矩阵采用2DPCA方法进行特征抽取,从而实现模式的分类。新方法的特点是能有效地抽取图像的局部特征,正是这些特征使此类模式区别于彼类。在ORL人脸数据库上测试了该方法的鉴别能力。实验的结果表明,M2DPCA在鉴别性能上优于通常的2DPCA和PCA方法,也优于基于Fisher鉴别准则的鉴别分析方法:Fisherfaces方法、F-S方法和J-Y方法。     

连续时间线性等式约束LQ控制的混合能消元算法

将连续时间LQ控制问题的微分方程离散化后,建立了连续时间线性等式约束LQ控制 问题的混合能消元算法,可有效求解约束条件下的Riccati方程.文中给出了相应的算例.     

Characterizing all optimal controls for an indefinite stochasticlinear quadratic control problem

This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite-time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation is introduced and all the possible optimal controls, including the ones in state feedback form, of the underlying LQ problem are explicitly obtained in terms of the two Riccati equations     

线性离散奇异系统的不定二次最优控制问题: Krein空间方法

The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter. Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.     

Optimal control of coupled parabolic–hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic–hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.     

Linear matrix inequalities, Riccati equations, and indefinitestochastic linear quadratic controls

This paper deals with an optimal stochastic linear-quadratic (LQ) control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables. In contrast to the deterministic case, we allow the control and state weighting matrices in the cost functional to be indefinite. This leads to an indefinite LQ problem, which may still be well posed due to the deep nature of uncertainty involved. The problem gives rise to a stochastic algebraic Riccati equation (SARE), which is, however, fundamentally different from the classical algebraic Riccati equation as a result of the indefinite nature of the LQ problem. To analyze the SARE, we introduce linear matrix inequalities (LMIs) whose feasibility is shown to be equivalent to the solvability of the SARE. Moreover, we develop a computational approach to the SARE via a semi-definite programming associated with the LMIs. Finally, numerical experiments are reported to illustrate the proposed approach     

Nonsymmetric Riccati equations: Partitioned algorithms

Generalized partitioned solutions (GPS) of nonsymmetric matric Riccati equations are presented in terms of forward and backward time differential equations that are of theoretical interest and also are computationally powerful. The GPS are the natural framework for the effective change of initial conditions, and the transformation of backward Riccati equation to forward Riccati equation and vice versa.Based on the GPS, computationally effective algorithms are obtained for the numerical solution of Riccati equations. These partitioned numerical algorithms have a decomposed or “partitioned” structure. They are given exactly in terms of a set of elemental solutions which are completely decoupled, and as such computable in either a parallel or serial processing mode. The overall solution is given exactly in terms of a simple recursive operation on the elemental solutions. Except for a subinterval of the total computation interval, the partitioned numerical algorithms are integration-free for the Riccati equation with constant or periodic matrices.Most importantly based on the GPS, a computationally attractive numerical algorithm is obtained for the computation of the steady-state solution of time-invariant Riccati equations. By making use of the GPS and some simple iterative operations, the Riccati solution is obtained in an interval which is twice as long as the previous interval requiring integration only in the initial subinterval.     

Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon

This paper is concerned with a stochastic linear-quadratic (LQ) problem in an infinite time horizon with multiplicative noises both in the state and the control. A distinctive feature of the problem under consideration is that the cost weighting matrices for the state and the control are allowed to be indefinite. A new type of algebraic Riccati equation – called a generalized algebraic Riccati equation (GARE) – is introduced which involves a matrix pseudo-inverse and two additional algebraic equality/inequality constraints. It is then shown that the well-posedness of the indefinite LQ problem is equivalent to a linear matrix inequality (LMI) condition, whereas the attainability of the LQ problem is equivalent to the existence of a “stabilizing solution” to the GARE. Moreover, all possible optimal controls are identified via the solution to the GARE. Finally, it is proved that the solution to the GARE can be obtained via solving a convex optimization problem called semidefinite programming.     

Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.