A projection method based on the splitting Bregman iteration for the image denoising

By analyzing the connection between the projection operator and the shrink operator, we propose a projection method based on the splitting Bregman iteration for image denoising problem in this paper. Compared with the splitting Bregman method, the proposed method has a more compact form so that it is more fast and efficient. Following from the operator theory, the convergence of the proposed method is proved. Some numerical comparisons between the proposed method and the splitting Bregman method are arranged for solving two basic image denoising models.     

Implicit difference approximation for the time fractional heat equation with the nonlocal condition

In this work, a method for solving inhomogeneous nonlocal fractional heat equations is proposed. The method is based on the modified Gauss elimination method. It is proved by using matrix stability approach that the method is unconditionally stable. Numerical results are provided to illustrate the accuracy and efficiency of the proposed method.     

The estimation of the strength of the heat source in the heat conduction problems

A general method is proposed to determine the strength of the heat source in the Fourier and non-Fourier heat conduction problems. A finite difference method, the concept of the future time and a modified Newton–Raphson method are adopted in the problem. The undetermined heat source at each time step is formulated as an unknown variable in a set of equations from the measured temperature and the calculated temperature. Then, an iterative process is used to solve the set of equations. No selected function is needed to represent the undetermined function in advance. Three examples are used to demonstrate the characteristics of the proposed method. The validity of the proposed method is confirmed by the numerical results. The results show that the proposed method is an accurate and stable method to determine the strength of the heat source in the inverse hyperbolic heat conduction problems. Furthermore, the result shows that more future times are needed in the hyperbolic equation than that of parabolic equation. Moreover, the robustness and the accuracy of the estimated results in the non-Fourier problem are not as well as those of the Fourier problem.     

Parametric spline functions for the solution of the one time fractional Burgers’ equation

This paper aims to present a general framework of the cubic parametric spline functions to develop a numerical method for obtaining an approximate solution for the time fractional Burgers’ equation. The truncation error of the method is theoretically analyzed. Using Von Neumann method, the proposed method is also shown to be conditionally stable. Two numerical examples are then included to illustrate the practical implementation of the proposed method. The obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.     

Armijo线性搜索下Hager-Zhang共轭梯度法的全局收敛性

Hager和Zhang^[4]提出了一种新的非线性共轭梯度法(简称 HZ 方法), 并证明了该方法在 Wolfe搜索和 Goldstein 搜索下求解强凸问题的全局收敛性.但是HZ方法在标准Armijo 搜索下求解非凸问题是否全局收敛尚不清楚.该文提出了一种保守的HZ共轭梯度法,并且证明了这种方法在 Armijo 线性搜索下求解非凸优化问题的全局收敛性.此外,作者给出了一些 数值结果以检验该方法的有效性.     

A domain decomposition method based on the iterative operator splitting method

In this article a new approach is proposed for constructing a domain decomposition method based on the iterative operator splitting method. The convergence properties of such a method are studied. The main feature of the proposed idea is the decoupling of space and time. We present a multi-iterative operator splitting method that combines iteratively the space and time splitting. We confirm with numerical applications the effectiveness of the proposed iterative operator splitting method in comparison with the classical Schwarz waveform relaxation method as a standard method for domain decomposition. We provide improved results and convergence rates.     

Cardinal functions for Legendre pseudo-spectral method for solving the integro-differential equations

In this article, we present a new numerical method to solve the integro-differential equations (IDEs). The proposed method uses the Legendre cardinal functions to express the approximate solution as a finite series. In our method the operational matrix of derivatives is used to reduce IDEs to a system of algebraic equations. To demonstrate the validity and applicability of the proposed method, we present some numerical examples. We compare the obtained numerical results from the proposed method with some other methods. The results show that the proposed algorithm is of high accuracy, more simple and effective.     

A Staged Continuous Tabu Search Algorithm for the Global Optimization and its Applications to the Design of Fiber Bragg Gratings

A novel staged continuous Tabu search (SCTS) algorithm is proposed for solving global optimization problems of multi-minima functions with multi-variables. The proposed method comprises three stages that are based on the continuous Tabu search (CTS) algorithm with different neighbor-search strategies, with each devoting to one task. The method searches for the global optimum thoroughly and efficiently over the space of solutions compared to a single process of CTS. The effectiveness of the proposed SCTS algorithm is evaluated using a set of benchmark multimodal functions whose global and local minima are known. The numerical test results obtained indicate that the proposed method is more efficient than an improved genetic algorithm published previously. The method is also applied to the optimization of fiber grating design for optical communication systems. Compared with two other well-known algorithms, namely, genetic algorithm (GA) and simulated annealing (SA), the proposed method performs better in the optimization of the fiber grating design.     

Nonlinear multigrid method for solving the anisotropic image denoising models

In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L ¹-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formulation of the general model by augmented Lagrangian method. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we apply the proposed method to the anisotropic ROF model and the anisotropic LLT model. We also give the local Fourier analysis (LFAs) of the Chambolle’s dual iterations and a modified smoother for solving these two models, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images.     

An improved method for the computation of the Moore-Penrose inverse matrix

In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better accuracy than the already proposed methods, while works for full and sparse matrices.     

从模糊现象中识别物理机制的证据论方法

本文提出了一种新的模糊模式识别方法。这种方法第一步是从已有的物理现象中，提取出支持不同类物理机制的“证据”，证据的提取采用了文中提出的模糊数学方法。第二步是去比较支持不同物理机制的证据，最后一步是给出模糊模式识别结果。本文把证据论和数学成功地结合起来，建立新的模糊识别方法。虽然，新方法可望在广泛的领域中得到应用，最后，本文用所提方法研究了炉霍地震（１９７３，Ｍｓ＝７．９）的破裂机制。     

Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the taylor expansion method

This paper presents a new and an efficient method for determining solutions of the linear second kind Volterra integral equations system. In this method, the linear Volterra integral equations system using the Taylor series expansion of the unknown functions transformed to a linear system of ordinary differential equations. For determining boundary conditions we use a new method. This method is effective to approximate solutions of integral equations system with a smooth kernel, and a convolution kernel. An error analysis for the proposed method is provided. And illustrative examples are given to represent the efficiency and the accuracy of the proposed method.     

一种求解救灾物资运输问题的改进解法

本文通过对B运输问题建立数学模型,提出了一种求解B运输问题的改进解法。改进解法首先通过最小元素法求出初始解,然后进行变量闭回路法调整,直到求出最优解,并给出了一个计算实例证明了解法的有效性。文章还对改进解法和另外两种现有的算法进行了综合的分析,由于改进解法计算过程中采用的变量闭回路法省略了求检验数的环节,使得新算法比两种现有的算法更简便。     

Split Bregman method for the modified lot model in image denoising

In this paper a split Bregman iteration is proposed for the modified LOT model in image denoising. We first use the split Bregman method to solve the ROF model which can be seen as an approximate form of the first step of the original LOT model. Then we use a modified split Bregman method to fit the second step of the LOT model and give the convergence of the proposed split Bregman method. Several numerical examples are arranged to show the effectiveness of the proposed method.     

Direct and inverse solutions of the two-dimensional hyperbolic heat conduction problems

A sequential method is proposed to estimate boundary condition of the two-dimensional hyperbolic heat conduction problems. An inverse solution is deduced from a finite difference method, the concept of the future time and a modified Newton–Raphson method. The undetermined boundary condition at each time step is denoted as an unknown variable in a set of non-linear equations, which are formulated from the measured temperature and the calculated temperature. Then, an iterative process is used to solve the set of equations. No selected function is needed to represent the undetermined function in advance. The example problem is used to demonstrate the characteristics of the proposed method. In the example, a well-known problem is used to demonstrate the validity of the proposed direct method and then the inverse solutions are evaluated. In the second example, the larger value of the relaxation time is implemented in the direct solutions and the inverse solutions. The close agreement between the exact values and the estimated results is made to confirm the validity and accuracy of the proposed method. The results show that the proposed method is an accurate and stable method to determine the boundary conditions in the two-dimensional inverse hyperbolic heat conduction problems.     

A Hybrid Algorithm for the Non-Guillotine Cutting Problem

In this article, a meta-heuristic method to solve the non-guillotine cutting stock problem is proposed. The method is based on a combination between the basic principles of the constructive and evolutive methods. With an adequate management of the parameters involved, the method allows regulation of the solution quality to computational effort relationship. This method is applied to a particular case of cutting problems, with which the computational behaviors is evaluated. In fact, 1000 instances of the problem have been classified according to their combinatorial degree and then the efficiency and robustness of the method have been tested. The final results conclude that the proposed method generates an average error close to 2.18% with respect to optimal solutions. It has also been verified that the method yields solutions for all of the instances examined; something that has not been achieved with an exact constructive method, which was also implemented. Comparison of the running times demonstrates the superiority of the proposed method as compared with the exact method.     

A Modification of the Projection Method for Integral Equation of the First Kind

A modification of the projection method is proposed for an integral equation of the first kind with a Fourier core on an interval. The proposed method replaces the eigenvectors corresponding to a multiple eigenvalue with odd Hermite functions — the eigenfunctions of the Fourier sine transform on the half-line.     

Puncture alloplasty of the tendon-capsule part of the external rotators of the shoulder and subacromial bursa by fast-setting polyurethane SKU-PFL in tendonitis and chronic lacerations of the tendon of the musculus supraspinatus (clinical-biomechanical investigation)

A method is proposed for alloplastic restoration of the dynamic stability of the shoulder joint with the use of fast-setting polyurethane SKU-PFL in the most common injuries of the tendoncapsule apparatus of the shoulder joint — tendonitis and lacerations of the musculus supraspinatus. A biomechanical substantiation of the proposed method of treatment is given.     

H2 optimal model order reduction on the Stiefel manifold for the MIMO discrete system by the cross Gramian

ABSTRACT

In this paper, the H₂ optimal model order reduction method for the large-scale multiple-input multiple-output (MIMO) discrete system is investigated. First, the MIMO discrete system is resolved into a number of single-input single-output (SISO) subsystems, and the H₂ norm of the original MIMO discrete system is expressed by the cross Gramian of each subsystem. Then, the retraction and the vector transport on the Stiefel manifold are introduced, and the geometric conjugate gradient model order reduction method is proposed. The reduced system of the original MIMO discrete system is generated by using the proposed method. Finally, two numerical examples show the efficiency of the proposed method.     

A multilevel image thresholding using the honey bee mating optimization

Image thresholding is an important technique for image processing and pattern recognition. Many thresholding techniques have been proposed in the literature. Among them, the maximum entropy thresholding (MET) has been widely applied. In this paper, a new multilevel MET algorithm based on the technology of the honey bee mating optimization (HBMO) is proposed. This proposed method is called the maximum entropy based honey bee mating optimization thresholding (MEHBMOT) method. Three different methods such as the particle swarm optimization (PSO), the hybrid cooperative-comprehensive learning based PSO algorithm (HCOCLPSO) and the Fast Otsu’s method are also implemented for comparison with the results of the proposed method. The experimental results manifest that the proposed MEHBMOT algorithm can search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method. In comparison with the other three thresholding methods, the segmentation results using the MEHBMOT algorithm is the best and its computation time is relatively low. Furthermore, the convergence of the MEHBMOT algorithm can rapidly achieve and the results validate that the proposed MEHBMOT algorithm is efficient.