Fast numerical scheme for gradient vector flow computation using a multigrid method

The gradient vector flow (GVF) deformable model was introduced by Xu and Prince as an effective approach to overcome the limited capture range problem of classical deformable models and their inability to progress into boundary concavities. It has found many important applications in the area of medical image processing. The simple iterative method proposed in the original work on GVF, however, is slow to converge. A new multigrid method is proposed for GVF computation on 2D and 3D images. Experimental results show that the new implementation significantly improves the computational speed by at least an order of magnitude, which facilitates the application of GVF deformable models in processing large medical images     

Proximal gradient method for huberized support vector machine

The support vector machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with \(\ell _1\)-regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the proximal gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show that our algorithm converges linearly. In addition, we give a finite convergence result about the support of the solution, based on which we further accelerate the algorithm by a two-stage method. We present extensive numerical experiments on both synthetic and real datasets which demonstrate the superiority of our methods over some state-of-the-art methods for both binary- and multi-class SVMs.     

B样条快速求值算法及其在数控插补中的应用

通过对B样条的de Boor-Cox定义式分析,给出了一种基于向量扩展的B样条基函数快速求值算法。该算法能够将k次B样条非零值计算效率提高2k+1倍。该算法用于数控实时插补中的B样条曲线求值求导运算时,可获得比de Boor算法更高的计算效率。     

基于近端梯度的快速字典学习方法的研究

基于稀疏表示的图像处理技术近年来成为研究热点,多种字典学习算法如K-SVD,OLM(Online dictionary learning Method)等予以提出;这类算法使用重叠的图像块来构建字典进行稀疏表示,产生了大量稀疏系数,致使计算过缓,且不能确保收敛。针对此问题开展研究,提出了基于近端梯度的快速字典学习算法;该算法结合了多凸优化求解,采用近端梯度算法求解字典学习过程中涉及的优化问题,有效地降低了每次迭代的复杂度,减少了迭代开销,同时能够确保收敛。合成数据上的实验表明,相较于其它经典算法,该算法进行字典学习速度更快,所耗时间较短,获得的字典更好;且在图像稀疏去噪的应用中,该算法的去噪效果表现优异。     

Comparing scalar and vector forms of the finite element method by example of an elliptic cylinder

An algorithm for constructing the stiffness matrix of a quadrangular curvilinear finite element in the form of a fragment of the middle surface of an elliptic cylinder with 18 degrees of freedom in the node is given. Implementation of the finite-difference procedure includes two variants of approximation of the sought variables, i.e., a scalar one and a vector one. Numerical examples are given and prove that the vector approximation has principal advantages over the scalar approximation for arbitrary shells with significant gradients of curvature of the lines of the middle surface or allowing for displacement as a rigid body.     

Block jacobi preconditioning of the conjugate gradient method on a vector processor

The preconditioned conjugate gradient method is well established for solving linear systems of equations that arise from the discretization of partial differential equations. Point and block Jacobi preconditioning are both common preconditioning techniques. Although it is reasonable to expect that block Jacobi preconditioning is more effective, block preconditioning requires the solution of triangular systems of equations that are difficult to vectorize. We present an implementation of block Jacobi for vector computers, especially for the Cray Y-MP/264, and discuss several techniques to improve vectorization. We present these in a progression to show the effect on performance. For the model problem, resulting from a self-adjoint operator, the final implementation of one block Jacobi step uses almost the same amount of time as one point Jacobi step on the Cray Y-MP/264 despite the solution of triangular systems.     

Fast FOCUSS method based on bi-conjugate gradient and its application to space-time clutter spectrum estimation

The focal underdetermined system solver (FOCUSS) is a powerful tool for sparse representation in complex underdetermined systems. This paper presents the fast FOCUSS method based on the bi-conjugate gradient (BICG), termed BICG-FOCUSS, to speed up the convergence rate of the original FOCUSS. BICGFOCUSS was specifically designed to reduce the computational complexity of FOCUSS by solving a complex linear equation using the BICG method according to the rank of the weight matrix in FOCUSS. Experimental results show that BICG-FOCUSS is more efficient in terms of computational time than FOCUSS without losing accuracy. Since FOCUSS is an efficient tool for estimating the space-time clutter spectrum in sparse recoverybased space-time adaptive processing (SR-STAP), we propose BICG-FOCUSS to achieve a fast estimation of the space-time clutter spectrum in mono-static array radar and in the mountaintop system. The high performance of the proposed BICG-FOCUSS in the application is demonstrated with both simulated and real data.     

Open-loop neuro-fuzzy speed estimator applied to vector and scalar induction motor drives

Scalar and vector drives have been the cornerstones of control of industrial motors for decades. In both the elimination of mechanical speed sensor consists in a trend of modern drives. This work proposes the development of an adaptive neuro-fuzzy inference system (ANFIS) angular rotor speed estimator applied to vector and scalar drives. A multi-frequency training of ANFIS is proposed, initially for a V/f scheme and after that a vector drive with magnetizing flux oriented control is proposed. In the literature ANFIS has been commonly proposed as a speed controller in substitution of the classical PI controller of the speed control loop. This paper investigates the ANFIS as an open-loop speed estimator instead. The subtractive clustering technique was used as strategy for generating the membership functions for all the incoming signal inputs of ANFIS. This provided a better analysis of the training data set improving the comprehension of the estimator. Additionally the subtractive cluster technique allowed the training with experimental data corrupted by noise improving the estimator robustness. Simulations to evaluate the performance of the estimator considering the V/f and vector drive system were realized using the Matlab/Simulink^® software. Finally experimental results are presented to validate the ANFIS open loop estimator.     

The deconvolution problem: Fast algorithms including the preconditioned conjugate-gradient to compute a MAP estimator

Different aspects of the deconvolution problem are discussed and a solution by the MAP estimator using the a priori knowledge of smoothness and nonnegativity of the unknown signal is proposed. Several fast algorithms are examined and the conjugate-gradient (CG) method is show to have several advantages: it allows computation of a constrained solution and when used with a preconditioning technique it can be faster than other algorithms for general near-to-Toeplitz systems, in particular, for Toeplitz-block-Toeplitz systems.     

一种快速稀疏最小二乘支持向量回归机

将Jiao法直接应用于最小二乘支持向量回归机上的效果并不理想,为此采用不完全抛弃的策略,提出了改进的Jiao法,并将其应用于最小二乘支持向量回归机.数据集测试的结果表明,基于改进Jiao法的稀疏最小二乘支持向量回归机,无论在支持向量个数和训练时间上都取得了一定的优势.与其他剪枝算法相比,在不丧失回归精度的情况下,改进的Jiao法可大大缩短训练时间.另外,改进的Jiao法同样适用于分类问题.     

基于二维特征向量的快速分形编码方法

编码时间过长是目前分形图像压缩存在的主要问题,对图像块进行分类是解决这一问题的一类重要方法,然而在诸多分类方法中,编码时间的减少通常是以牺牲图像解码质量为代价的。为此,本文提出了一种基于二维特征向量的自适应分类方法。并把图像的1、2阶矩不变量作为图像的主副特征得到了一种能够较好地保证图像解码质量的快速分形编码方法。     

Dynamic gradient approaches to compute the closest unstable equilibrium point for stability region estimate and their computational limitations

The reflected gradient method and the Newton trajectory method are approaches to compute the closest unstable equilibrium point (UEP) for stability region estimation. We address the computational issues involved in these methods. We first suggest a dynamic gradient approach as a unified and extended version of these methods. Then, we show that computing the closest UEP using the dynamic gradient approach can be infeasible.     

基于重编码的快速标量乘算法

采用回溯法设计出一种重编码算法。该算法只需对标量序列进行一次变换、至多四个中间变量,以及只需基于比特位比较赋值操作,效率更高,利于硬件实现标量乘法,并证明了所得结果具有正则序列的性质。该算法应用到计算数字签名中常用的gP+hQ时,得到g、h的具有最小联合重量序列。     

Analytical formulation to compute QFT bounds: The envelope method

This paper describes an analytical formulation to compute quantitative feedback theory (QFT) bounds in one‐degree‐of‐freedom feedback control problems. The new approach is based on envelope curves and shows that a QFT control specification can be expressed as a family of circumferences. Then, the controller bound is defined by the envelope curve of this family and can be obtained as an analytical function. This offers the possibility of studying the QFT bounds in an analytical way with several useful properties. Gridding methods are avoided, resulting in a lower computational effort procedure. The new formulation improves the accuracy of previous methods and allows the designer to calculate multivalued bounds. Copyright © 2009 John Wiley & Sons, Ltd.     

基于AHP方法计算电信用户信用度

AHP（Analytical Hierarchy Process）方法是一种定性分析与定量分析相结合的多目标决策分析方法。AHP方法将决策者的经验判断给予量化,当目标结构复杂或者缺乏必要的数据情况下,采用此方法较为实用有效。针对电信行业这一特殊的应用背景,抽取用户相关信息,构建数学模型,进行信用度计算。基于AHP方法的技术特点,在实际计算过程中,合理地构造了判别矩阵并进行了一致性检验。最后给出相应的数值实验,验证了这种计算技巧的有效性。     

Performance of SOR methods on modern vector and scalar processors

The building-cube method (BCM) is a new generation algorithm for CFD simulations. The basic idea of BCM is to simplify the algorithm in all stages of flow computation to achieve large-scale simulations. Calculation of a pressure field using the Successive Over Relaxation (SOR) method consumes most of the total execution time required for BCM. In this paper, effective implementations on modern vector and scalar processors are investigated. NEC SX-9 and Intel Nehalem-EX are the latest vector and scalar processors. Those processors have much higher peak performances than their previous-generation processors. However, their memory bandwidth improvement cannot catch up with the performance improvement of processors. This is the so-called memory wall problem. In our paper, we discuss optimization techniques for implementation of the SOR method based on architectural characteristics of these modern processors, and evaluate their effects on the sustained performances of these processors for BCM.     

A nested Krylov subspace method to compute the sign function of large complex matrices

We present an acceleration of the well-established Krylov–Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov–Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite large, which makes the method too costly. The new idea is to make a further projection on an even smaller, nested Krylov subspace. If additionally an intermediate preconditioning step is applied, this projection can be performed without affecting the accuracy of the approximation, and a substantial gain in efficiency is achieved for both Hermitian and non-Hermitian matrices. The numerical efficiency of the method is demonstrated on lattice configurations of sizes ranging from 4⁴ to 10⁴, and the new results are compared with those obtained with rational approximation methods.     

Multigrid gradient vector flow computation on the GPU

Gradient vector flow (GVF) is a feature-preserving spatial diffusion of image gradients. It was introduced to overcome the limited capture range in traditional active contour segmentation. However, the original iterative solver for GVF, using Euler’s method, converges very slowly. Thus, many iterations are needed to achieve the desired capture range. Several groups have investigated the use of graphic processing units (GPUs) to accelerate the GVF computation. Still, this does not reduce the number of iterations needed. Multigrid methods, on the other hand, have been shown to provide a much better capture range using considerable less iterations. However, non-GPU implementations of the multigrid method are not as fast as the Euler method when executed on the GPU. In this paper, a novel GPU implementation of a multigrid solver for GVF written in OpenCL is presented. The results show that this implementation converges and provides a better capture range about 2–5 times faster than the conventional iterative GVF solver on the GPU.     

Video object tracking based on improved gradient vector flow snake and intra-frame centroids tracking method

Accurately tracking the video object in video sequence is a crucial stage for video object processing which has wide applications in different fields. In this paper, a novel video object tracking algorithm based on the improved gradient vector flow (GVF) snake model and intra-frame centroids tracking algorithm is proposed. Unlike traditional gradient vector flow snake, the improved gradient vector flow snake adopts anisotropic diffusion and a four directions edge operator to solve the blurry boundary and edge shifting problem. Then the improved gradient vector flow snake is employed to extract the object contour in each frame of the video sequence. To set the initial contour of the gradient vector flow snake automatically, we design an intra-frame centroids tracking algorithm. Splitting the original video sequence into segments, for each segment, the initial contours of first two frames are set by change detection based on t-distribution significance test. Then, utilizing the redundancy between the consecutive frames, the subsequent frames’ initial contours are obtained by intra-frame motion vectors. Experimental results with several test video sequences indicate the validity and accuracy of the video object tracking.