Abstract: This paper presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac-b/sup 2/=1 the new method incorporates the ellipticity constraint into the normalization factor. The new method combines several advantages: 1) it is ellipse-specific so that even bad data will always return an ellipse; 2) it can be solved naturally by a generalized eigensystem, and 3) it is extremely robust, efficient and easy to implement. We compare the proposed method to other approaches and show its robustness on several examples in which other nonellipse-specific approaches would fail or require computationally expensive iterative refinements.

Abstract: Total variation (TV) methods are very effective for recovering “blocky,” possibly discontinuous, images from noisy data. A fixed point algorithm for minimizing a TV penalized least squares functional is presented and compared with existing minimization schemes. A variant of the cell-centered finite difference multigrid method of Ewing and Shen is implemented for solving the (large, sparse) linear subproblems. Numerical results are presented for one- and two-dimensional examples; in particular, the algorithm is applied to actual data obtained from confocal microscopy.

Abstract: Iterative deblurring methods using the expectation maximization (EM) formulation and the algebraic reconstruction technique (ART), respectively, are adapted for metal artifact reduction in medical computed tomography (CT). In experiments with synthetic noise-free and additive noisy projection data of dental phantoms, it is found that both simultaneous iterative algorithms produce superior image quality as compared to filtered backprojection after linearly fitting projection gaps. Furthermore, the EM-type algorithm converges faster than the ART-type algorithm in terms of either the I-divergence or Euclidean distance between ideal and reprojected data in the authors' simulation. Also, for a given iteration number, the EM-type deblurring method produces better image clarity but stronger noise than the ART-type reconstruction. The computational complexity of EM- and ART-based iterative deblurring is essentially the same, dominated by reprojection and backprojection. Relevant practical and theoretical issues are discussed.

Abstract: We develop an algorithm for the minimum Lp-norm solution to the two-dimensional phase unwrapping problem. Rather than its being a mathematically intractable problem, we show that the governing equations are equivalent to those that describe weighted least-squares phase unwrapping. The only exception is that the weights are data dependent. In addition, we show that the minimum Lp-norm solution is obtained by embedding the transform-based methods for unweighted and weighted least squares within a simple iterative structure. The data-dependent weights are generated within the algorithm and need not be supplied explicitly by the user. Interesting and useful solutions to many phase unwrapping problems can be obtained when p< 2. Specifically, the minimum L0-norm solution requires the solution phase gradients to equal the input data phase gradients in as many places as possible. This concept provides an interesting link to branch-cut unwrapping methods, where none existed previously.

Abstract: Spherically symmetric volume elements with smooth tapering of the values near their boundaries are alternatives to the more conventional voxels for the construction of volume images in the computer. Their use, instead of voxels, introduces additional parameters which enable the user to control the shape of the volume element (blob) and consequently to control the characteristics of the images produced by iterative methods for reconstruction from projection data. For images composed of blobs, efficient algorithms have been designed for the projection and discrete back-projection operations, which are the crucial parts of iterative reconstruction methods. The authors have investigated the relationship between the values of the blob parameters and the properties of images represented by the blobs. Experiments show that using blobs in iterative reconstruction methods leads to substantial improvement in the reconstruction performance, based on visual quality and on quantitative measures, in comparison with the voxel case. The images reconstructed using appropriately chosen blobs are characterized by less image noise for both noiseless data and noisy data, without loss of image resolution.

Abstract: This paper develops a fast maximum likelihood method for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. The resulting method consists of two iterative steps, where each step minimizes a quadratic function. The two-step maximum likelihood (TSML) method is shown to be high-SNR efficient, i.e., attaining the Cramer-Rao lower bound (CRB) at high SNR. The TSML method exploits a novel orthogonal complement matrix of the generalized Sylvester matrix. Simulations show that the TSML, method significantly outperforms the cross-relation (CR) method and the subspace (SS) method and attains the CRB over a wide range of SNR. This paper also studies a Fisher information (FI) matrix to reveal the identifiability of the M-channel system. A strong connection between the FI-based identifiability and the CR-based identifiability is established.

Abstract: This paper presents a new stochastic decomposition method well-suited to deal with large-scale unit commitment problems. In this approach, random disturbances are modeled as scenario trees. Optimization consists in minimizing the average generation cost over this "tree-shaped future". An augmented Lagrangian technique is applied to this problem. At each iteration, nonseparable terms introduced by the augmentation are linearized so as to obtain a decomposition algorithm. This algorithm may be considered as a generalization of price decomposition methods, which are now classical in this field, to the stochastic framework. At each iteration, for each unit, a stochastic dynamic subproblem has to be solved. Prices attached to nodes of the scenario trees are updated by the coordination level. This method has been applied to a daily generation scheduling problem. The use of an augmented Lagrangian technique, provides satisfactory convergence properties to the decomposition algorithm. Moreover, numerical simulations show that compared to a classical deterministic optimization with reserve constraints, this new approach achieves substantial savings.

Abstract: Scatter compensation using iterative reconstruction results in improved image quality and quantitative accuracy compared to subtraction-based methods, However, this requires knowledge of the spatially-varying, object-dependent scatter response function (SRF), We have previously developed a method, slab derived scatter estimation (SDSE) for estimating the SRF. However, this method has reduced accuracy for nonuniform attenuators and Tl-201 imaging. In this paper we present a new method which provides better modeling of the SRF for Tl-201 SPECT, and should provide improved accuracy for nonuniform attenuators. The method requires 3 image space convolutions and an attenuated projection for each viewing angle. Implementation in a projector-backprojector pair for use with an iterative reconstruction algorithm would require 2 image space Fourier transforms and 6 image space inverse Fourier transforms per iteration. We observed good agreement between SRFs and projection data estimated using this new model compared to those obtained using Monte Carlo simulations.

Abstract: The paper deals with certain adaptive multilevel methods at the confluence of nested multigrid methods and iterative methods based on the cascade principle of [10]. From the multigrid point of view, no correction cycles are needed; from the cascade principle view, a basic iteration method without any preconditioner is used at successive refinement levels. For a prescribed error tolerance on the final level, more iterations must be spent on coarser grids in order to allow for less iterations on finer grids. A first candidate of such a cascadic multigrid method was the recently suggested cascadic conjugate gradient method of [9], in short CCG method, whichused the CG method as basic iteration method on each level. In [18] it has been proven, that the CCG method is accurate with optimal complexity for elliptic problems in 2D and quasi-uniform triangulations. The present paper simplifies that theory and extends it to more general basic iteration methods like the traditional multigrid smoothers. Moreover, an adaptive control strategy for the number of iterations on successive refinement levels for possibly highly non-uniform grids is worked out on the basis of a posteriori estimates. Numerical tests confirm the efficiency and robustness of the cascadic multigrid method.

Abstract: We introduce a methodology for automated production planning of semiconductor manufacturing based on iterative linear programming (LP) optimization and discrete-event simulation calculations. The LP formulation incorporates epoch dependent parameters for flow times from lot release up to each operation on each manufacturing route. LP-derived release schedules are used as input to the simulation model, from which statistics on flow times are collected and used to reformulate the LP model for a revised planning calculation. Iteration continues until satisfactory agreement between simulation and LP models is obtained. We demonstrate in experiments on an industry data set that a relatively small number of iterations is required to develop a production plan correctly characterizing future flow times as a function of factory load and product mix. The methodology makes possible automated production planning of semiconductor manufacturing on an engineering work station.

Abstract: In this paper, we develop an iterative solution to the coupled Gel'Fand-Levitan-Marchenko integral equations. It will be proved that this new technique outstands other methods such as the exact GLM solution or the Fourier method. As one of its many applications, the synthesis of fiber gratings for dispersion equalization will be tackled.

Abstract: A class of globally convergent iterative methods for solving nonlinear projection equations is provided under a continuity condition of the mappingF. WhenF is pseudomonotone, a necessary and sufficient condition on the nonemptiness of the solution set is obtained.

Abstract: An iterative solution method is presented and illustrated to analyse the dynamic response of bridge–vehicle systems. The method consists in dividing the whole system into 2 subsystems at the interface of the bridge and vehicles; these 2 subsystems are solved separately; their compatibility at the interface is achieved by an iterative procedure with under-relaxation or with Aitken acceleration. The characteristics of this method are explained on a simplified system with 2 degrees of freedom (DOF). The numerical results for a simple example demonstrate the high performances of the proposed method: good convergence rate and high accuracy. Finally, the method is applied to a practical example: the linear dynamic response of the Yangtze-River Bridge at Wuhan under a moving train with 2 locomotives and 4 freight cars. The efficiency is attained because neither formation nor factorisation of the coefficient matrices for the equations of the system are needed at every time step in linear analysis. The Aitken acceleration technique is more efficient in systems with multi-degrees of freedom than the relaxation technique. The proposed method will be even more efficient in non-linear dynamic response because, in this case, the iterations are necessary whether the system is solved as a whole or not.

Abstract: In this paper, we investigate some effects of errors in the initial conditions as a learning control algorithm is iteratively applied. We show that the pure error term in the learning control law can be positively utilized to improve the system performance, making it robust against varying initial conditions. For better performance in the face of variable initial conditions, we propose a method of ‘iterative learning control with multi-modal input’. In this proposed control method, an input is synthesized based on the state of initial condition. Numerical examples are given to show the effectiveness of the proposed learning control algorithm.

Abstract: This paper considers an inverse potential problem which seeks to recover the shape of an obstacle separating two different densities by measurements of the potential. A representation for the domain derivative of the corresponding operator is established and this allows the investigation of several iterative methods for the solution of this ill-posed problem.

Abstract: Iterative learning control (ILC) is a powerful feedback methodology that iteratively improves the transient behaviour of processes that are repetitive in nature Although most of the published ILC schemes are heuristic in nature, some initial research has been performed on the formulation of the ILC problem in the H/sub /spl infin// mathematical framework However, so far only the performance and robustness analysis of the ILC schemes has been performed for a given learning controller In this paper it is shown how the synthesis of an iterative learning controller can be generalized to the synthesis of an H/sub /spl infin// (sub)optimal controller It is shown how a general learning control problem can be reformulated in the so-called 'standard plant' format, by choosing an appropriate weighting function for learning performance Moreover, the process uncertainty can be included explicitly in the ILC design, by choosing appropriate weighting functions related to this uncertainty It turns out that convergence and learning performance of this ILC scheme can be obtained for all systems in the uncertainty set, by solving a /spl mu/-synthesis problem The practical usefulness of the scheme is verified on a wafer stage experimental setup

Abstract: An iterative algorithm for constructing fully continuous phase screens for tailoring far-field intensity profiles is presented. The algorithm is robust, stable, and, if run properly, maintains the continuous nature of the phase throughout the iterative process. The iterative procedure is applied to generate continuous phase screens to produce a 12th-power super-Gaussian far-field intensity profile.

Abstract: The free-form surface matching problem is important in several practical applications, such as reverse engineering. An accurate, robust and fast solution is, therefore, of great significance. Recently genetic algorithms have attracted great interest for their ability to robustly solve hard optimization problems. In this work we investigate the performance of such an approach for finding the initial guess of the transformation, a translation and a rotation, between the object and the model surface. This is followed by a local gradient descent method, such as iterative closest point, to refine the estimate. Promising results are demonstrated on accurate real data.

Abstract: This paper proposes a technique of iterative dynamic programming to plan minimum energy consumption trajectories for robotic manipulators. The dynamic programming method is modified to perform a series of dynamic programming passes over a small reconfigurable grid covering only a portion of the solution space at any one pass. Although strictly no longer a global optimization process, this iterative approach retains the ability to avoid some poor local minima while avoiding the curse of dimensionality associated with a pure dynamic programming approach. The algorithm has an inherent parallel structure, allowing for reduced computation time on parallel architecture computers. No limiting assumptions are made about the performance index, or function to be optimized. As such, extremely complex functions and constraints are easily handled. Joint actuator and time constraints are considered in this work. The modified dynamic programming approach is verified experimentally by planning and executing a minimum energy consumption path for a Reis V15 industrial manipulator.

Abstract: A nonoverlapping domain decomposition method is proposed for the finite element solution of the scattering problem by electrically large, inhomogeneous, infinite cylinders of arbitrary cross section. To minimize the size of the total computational domain, a second-order-absorbing boundary condition (ABC) is applied upon an outer boundary of arbitrary shape which may be conformal to the surface of the scatterer. This domain is then partitioned into concentric subdomains circumscribing the object. A second-order transmission condition, derived from the ABC, is prescribed upon the interfaces between two adjacent subdomains. This particular configuration is responsible for the fast convergence of the domain decomposition iterative algorithm, which is parallelizable. Numerical results obtained with a nonparallelized computer code are presented, which emphasize the superiority of this technique in terms of memory storage requirements and computing times over the standard finite element approach, as well as over the rigorous hybrid finite element-integral equation formulation.

Abstract: Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.

Abstract: Speech enhancement using iterative Wiener filtering has been shown to require interframe and intraframe constraints in all-pole parameter estimation We show that a clean speech VQ codebook is more effective in providing intraframe constraints and, hence, better convergence of the iterative filtering scheme Satisfactory speech enhancement results are obtained with a small codebook of 128, and the algorithm is effective for both white noise and pink noise up to 0 dB SNR

Abstract: The source separation problem has been addressed in many ways during the last decade, and one of its instances gave birth to Independent Component Analysis (ICA). Iterative methods can be opposed to algebraic ones for the computation of the ICA, and seem to reveal very interesting research tracks. This paper attempts to give an outline of some of the works that have been carried out in the latter area, without pretending to survey exhaustively or objectively the subject. Bibliographical pointers hopefully compensate for this drawback.