非局部特征方向图像插值方法研究

提出了一种非局部的特征方向图像插值方法,有效地保持了插值图像轮廓的光滑,抑制了图像边缘的模糊.这种方法把非局部Hessian矩阵的特征向量视为图像特征方向,使图像能量泛函沿这个方向进行扩散,其扩散强度由图像局部Hessian矩阵特征值参与控制.它克服了传统方法以梯度方向指示图像特征方向的局部性,使图像能量泛函沿正确方向扩散,避免了对图像特征的模糊.数值实验结果显示,该方法既能很好地重建插值图像的边缘,又不会在插值图像中产生伪影或图像边缘失真.     

Newton type algorithm on Riemannian manifolds applied to robot vision, and suggestions for improvement of its performance

In visual servo control of a robot, we often encounter the structure-from-motion problem. To study the structure-from-motion problem, we are led to finding a minimum of a real valued function defined on a product Riemannian manifold, e.g., special orthogonal groups and unit sphere. To take advantage of its Riemannian structure, we consider the Newton algorithm on this manifold. In particular, we focus on improving the algorithm to be more robust and faster than the existing Newton algorithm on Riemannian manifolds. For this, we exploit the sparseness of the Hessian matrix and suggest how to choose the step size during the optimisation procedure, which can be considered as extensions of those for vector space optimisation algorithms.     

改进的迭代算法在图像恢复正则化模型中的应用

根据图像成像过程容易受泊松噪声的影响,提出用Kullback-Leibler距离描述保真项,用平方根复合函数描述正则项,建立具有自适应权系数的能量泛函正则化模型.由于模型的梯度退化和海森矩阵的规模较大,使得无法应用牛顿迭代算法.本文利用退化梯度幅值作为约束集,建立可对角化和容易求逆的海森矩阵,提出改进的牛顿投影迭代算法.仿真表明,该方法取得较小的相对误差、偏差,较高的信噪比和良好的视觉效果.     

一种新的机载SAR回波高阶多项式相位误差提取方法

当载机在SAR回波方位子孔径时间内运动较复杂时,二次相位误差模型不能准确描述载机运动造成的相位误差。针对此情况,该文借鉴PACE算法的思想,提出了一种提取SAR回波中时域高阶多项式相位误差的TPACE算法。TPACE算法将图像对比度函数作为目标函数,以时域高阶多项式相位误差模型系数作为自变量,通过最优化方法提取时域误差系数。文中详细推导了对比度函数关于误差模型系数的梯度表达式,分析了TPACE与以往提取时域高阶多项式相位误差的算法计算量之差别。实际超宽带SAR回波数据处理结果表明,TPACE能有效提取时域高阶多项式误差,是一种计算量相对较小的SAR自聚焦算法。     

Recursive formulae for ladder-network optimisation

The analysis, the gradient and the Hessian matrix of a ladder-network structure may be derived precisely from a family recursive formulae. The method is well suited to computer programming and extremely efficient computationally. The formulae might be included in a c.a.d. programme as a self-contained block and may be used to solve optimisation problems of certain ladder networks employing Newton-Raphson techniques.     

Goal-seeking problem in discrete event systems simulation

For most complex stochastic systems such as microelectronic systems, the Mean Time To Failure (MTTF) is not available in analytical form. We resort to Monte-Carlo Simulation (MCS) to estimate MTTF function for some specific values of underlying density function parameter(s). MCS models, although simpler than a real-world system, are still a very complex way of relating input parameter(s) to MTTF. This study develops a polynomial model to be used as an auxiliary to a MCS model. The estimated metamodel is a Taylor expansion of the MTTF function in the neighborhood of the nominal value for the parameter(s). The Score Function methods estimate the needed sensitivities (i.e. gradient, Hessian, etc.) of the MTTF function with respect to the input parameter in a single simulation run. The explicit use of this metamodel is the target-setting problem in Taguchi's product design concept: given a desired target MTTF value, find the input parameter(s). A stochastic approximation algorithm of the Robbins-Monro type uses a linear metamodel to estimate the necessary controllable input parameter within a desired accuracy. The potential effectiveness is demonstrated by simulating a reliability system with a known analytical solution.     

基于耦合梯度神经网络的光学层析图像重建

为克服光学层析图像重建的病态性,通常在重建过程中加入先验信息.本文采用含有二值线过程的Gibbs分布作为图像的先验模型,该模型具有保留清晰边缘的全局平滑特性.由于重建目标函数是连续变量和二值离散变量的混合体,常规的优化算法无法实现.为此,提出了一种基于耦合梯度神经网络的优化方法.优化过程中,能量函数关于光学参数的梯度计算是关键,本文提出一种基于梯度树的梯度求解方法.对吸收系数和散射系数的重建结果表明:该方法可高效地重建光学层析图像;线过程的引入可以改善重建的病态特性,提高图像的重建质量.     

二维有耗介质目标重建的Newtoin迭代方法

本文给出了一种由已知的散射场数据重建二线非均匀有耗目标的复介电常数的迭代算法。由积分方程出发，利用点匹配技术导出了依赖于未知参数的解析逆散射公式。由此可以以解析的形式计算场量对未知参数的导数（Jacobian和Hessian矩阵）。本文采用Newton优化方法迭代末解道散射问题，具有二次收敛特性。为了克服逆散射中解的不适定性，连续采用多个方向的TM波照射目标，并采集目标区域外的散射场数据，以及采用共轭梯度法（CGM）求解逆问题．数值结果表明了本文所提方法的可行性和灵活性。     

Optimal segmentation of cell images

An optimal segmentation algorithm for light microscopic cell images is presented. The image segmentation is performed by thresholding a parametric image approximating the original image. Using the mean squared error between the original and the constructed image as the cost function, the segmentation problem is transformed into an optimisation process where parametric parameters are determined that minimise the defined cost function. The cost function is iteratively minimised using an unsupervised learning rule to adjust the parameters, and a parametric image is constructed at each iteration, based on the obtained parameters. The cell region is extracted by thresholding the final parametric image, where the threshold is one of the image parameters. Application results to real cervical images are provided to show the performance of the proposed segmentation approach. Experimental segmentation results are presented for the proposed optimal algorithm for synthetic cell images corrupted by variant levels of noise; these results are compared with the K-means clustering method and Bayes classifier in terms of classification errors     

Connectivity of projected high dimensional data charts on one-dimensional curves

We propose a principal curve tracing algorithm, which uses the gradient and the Hessian of a given density estimate. Curve definition requires the local smoothness of data density and is based on the concept of subspace local maxima. Tracing of the curve is handled through the leading eigenvector where fixed step updates are used. We also propose an image segmentation algorithm based on the original idea and show the effectiveness of the proposed algorithm on a Brainbow dataset. Lastly, we showed a simple approach to define connectivity in complex topologies, by providing a tree representation for the bifurcating synthetic data.     

Improved Newton-type algorithm for adaptive implementation ofPisarenko's harmonic retrieval method and its convergence analysis

Pisarenko's harmonic retrieval (PHR) method is probably the first eigenstructure based algorithm for estimating the frequencies of sinusoids corrupted by additive white noise. To develop an adaptive implementation of the PHR method, one group of authors has proposed a least-squares type recursive algorithm. In their algorithm, they made approximations for both gradient and Hessian. The authors derive an improved algorithm, where they use exact gradient and a different approximation for the Hessian and analyze its convergence rigorously. Specifically, they provide a proof for the local convergence and detailed arguments supporting the local instability of undesired stationary points. Computer simulations are used to verify the convergence performance of the new algorithm. Its performance is substantially better than that exhibited by its counterpart, especially at low SNR's     

抑制特定区间距离旁瓣的恒模波形设计方法

 该文提出在特定的距离旁瓣区间具有极低相关幅值的恒模波形设计方法。该类波形可应用于具有发射自适应能力的雷达、声呐和通信系统,以抑制距离旁瓣遮蔽和多路径等干扰。该文使用0-1加权的积分旁瓣电平构造目标函数,将波形设计转化为无约束优化问题。针对目标函数的特点,基于功率谱拟合的思想提出了初始点选择算法,推导了目标函数梯度和Hessian矩阵的解析表达式,并利用子空间信赖域算法求解该优化问题,提高了优化过程的计算效率。计算机仿真表明,对于连续区间和多个离散点的距离旁瓣抑制,均能提供较好的效果。     

Camera-pose estimation via projective Newton optimization on the manifold

Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.     

基于实数编码遗传算法的稀布阵列综合

针对有孔径和阵元总数约束的线性阵列,提出了一种基于实数编码遗传算法的稀布阵列综合方法。算法中每条染色体基因主要由阵元间距和激励幅度共同组成,采用双变量组合优化的方式为阵列性能优化提供了更多的自由度。采用十进制实数量化编码的方式,省去了二进制编码过程中的解码运算,使算法程序更为简洁,效率更高。以降低阵列方向图的峰值旁瓣电平为目标函数,运用提出的改进遗传算法针对几种不同的线性阵列进行优化仿真,在同等约束条件下将该算法与其他改进遗传算法进行了优化对比,结果表明该算法表现更为出色。     

基于谱逼近的瞬态极化雷达最优波形设计

针对瞬态极化雷达(IPR)两路极化波形相关度较高而导致的目标极化参数估计误差大的问题,该文提出纯相位谱逼近算法(POSAA)来设计具有低相关水平的波形对。首先,以积分旁瓣电平准则构建目标函数;然后利用相关与谱的傅里叶变换对关系,基于谱逼近的思想,推导了目标函数的频域表示;最后获得目标函数的梯度和Hess矩阵,并采用信赖域方法优化求解目标函数以获得理想波形。仿真结果表明优化后的波形对具有极低的相关水平,且利用该优化波形获得的目标参数误差远小于当前常见波形。     

A new 2-D image reconstruction algorithm based on FDTD and design sensitivity analysis

This paper proposes a numerical algorithm that reconstructs the complex permittivity profile of unknown scatterers by the design sensitivity analysis (DSA) and topology optimization technique. By introducing the DSA and adjoint-variable method, the derivatives of the error function with respect to the complex permittivity variables can be calculated, and the material property in each cell can be changed simultaneously using sensitivity information. The steepest descent method is used as an optimization technique. The proposed method is validated by applying it to reconstructions of unknown two-dimensional scatterers that are illuminated by TM/sup z/ with a Gaussian-pulsed plane wave.     

基于微分搜索的高光谱图像非线性解混算法

针对线性混合模型在实际高光谱图像解混过程中的局限性,提出一种新的基于微分搜索的非线性高光谱图像解混算法.在广义双线性模型的基础上采用重构误差作为解混的目标函数,将非线性解混问题转化为最优化问题.将目标函数中的待求参数映射为微分搜索过程中的位置变量,利用微分搜索算法对目标函数进行优化求解.在求解过程中,通过执行搜索范围控制等机制满足高光谱图像解混的约束要求,进而求得丰度系数和非线性参数,实现非线性高光谱图像解混.仿真数据和真实遥感数据实验结果表明,所提出的非线性解混算法可以有效克服线性模型下解混算法的局限性,避免了由于使用梯度类优化方法而易陷入局部收敛的问题,较之其它高光谱图像解混算法具有更好的解混精度.     

Complex Adaptive ICA Employing the Conjugate Gradient Technique for Signal Separation in Time-Varying Flat Fading Channels

The conjugate gradient method is a prominent technique for solving systems of linear equations and unconstrained optimization problems, including adaptive filtering. Since it is an iterative method, it can be particularly applied to solve sparse systems which are too large to be handled by direct methods. The main advantage of the conjugate gradient method is that it employs orthogonal search directions with optimal steps along each direction to arrive at the solution. As a result, it has a much faster convergence speed than the steepest descent method, which often takes steps in the same direction as earlier steps. Furthermore, it has lower computational complexity than Newton’s iteration approach. This unique tradeoff between convergence speed and computational complexity gives the conjugate gradient method desirable properties for application in numerous mathematical optimization problems. In this paper, the conjugate gradient principle is applied to complex adaptive independent component analysis (ICA) for maximization of the kurtosis function, to achieve separation of complex-valued signals. The proposed technique is called the complex block conjugate independent component analysis (CBC-ICA) algorithm. The CBC-ICA derives independent conjugate gradient search directions for the real and imaginary components of the complex coefficients of the adaptive system employed for signal separation. In addition, along each conjugate direction an optimal update is generated separately for the real and imaginary components using the Taylor series approximation. Simulation results confirm that in dynamic flat fading channel conditions, the CBC-ICA demonstrates excellent convergence speed and accuracy, even for large processing block sizes.     

Analytical form of globally optimal solution of weighted sum of intraclass separation and interclass separation

The Fisher linear discriminant analysis (FLDA)-based method is a common method for jointly optimizing the intraclass separation and the interclass separation of the projected feature vectors by defining the objective function as the ratio of the intraclass separation over the interclass separation. To address the eigenproblem of the FLDA, a quadratic equality constraint is imposed on the square of the \(l_{2}\) norm of the decision vector. However, the constrained optimization problem is highly nonconvex. This paper proposes to reformulate the objective function as a weighted sum of the intraclass separation and the interclass separation subject to the same quadratic equality constraint on the square of the \(l_{2}\) norm of the decision vector. Although both the objective function and the feasible set of the optimization problem are still nonconvex, this paper shows that the global minimum of the objective functional value is equal to the minimum singular value of the Hessian matrix of the objective function. Also, the globally optimal solution of the optimization problem is in the null space of the Hessian matrix minus this singular value multiplied by the identity matrix. As it is only required to find the singular value of the Hessian matrix, no numerical optimization-based computer aided design tool is required to find the globally optimal solution. Therefore, the globally optimal solution can be found in real time. Experimental results demonstrate the effectiveness of our proposed method.