Showing papers on "Iterative method published in 1990"

Gridding with continuous curvature splines in tension

Abstract: A gridding method commonly called minimum curvature is widely used in the earth sciences. The method interpolates the data to be gridded with a surface having continuous second derivatives and minimal total squared curvature. The minimum-curvature surface has an analogy in elastic plate flexure and approximates the shape adopted by a thin plate flexed to pass through the data points. Minimum-curvature surfaces may have large oscillations and extraneous inflection points which make them unsuitable for gridding in many of the applications where they are commonly used. These extraneous inflection points can be eliminated by adding tension to the elastic-plate flexure equation. It is straightforward to generalize minimum-curvature gridding algorithms to include a tension parameter; the same system of equations must be solved in either case and only the relative weights of the coefficients change. Therefore, solutions under tension require no more computational effort than minimum-curvature solutions, and any algorithm which can solve the minimum-curvature equations can solve the more general system. We give common geologic examples where minimum-curvature gridding produces erroneous results but gridding with tension yields a good solution. We also outline how to improve the convergence of an iterative method of solution for the gridding equations.

Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method

Abstract: The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations are performed using the DBIM and the method proposed previously by the authors (Int. J. Imaging Syst. Technol., vol.1, no.1, p.100-8, 1989) called the Born iterative method (BIM) for several cases in which the conditions for the first-order Born approximation are not satisfied. The results show that each method has its advantages; the DBIM shows faster convergence rate compared to the BIM, while the BIM is more robust to noise contamination compared to the DBIM. >

Iterative methods for image deblurring

Abstract: The authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be assumed to be degraded by pointwise nonlinearities such as film saturation and additive noise. Iterative algorithms allow for the incorporation of various types of prior knowledge about the class of feasible solutions, can be used to remove nonstationary blurs, and are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms after a finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed. >

Sensor Placement for On-Orbit Modal Identification and Correlation of Large Space Structures

Abstract: A method is presented for the selection of a set of sensor locations from a larger candidate set for the purpose of on-orbit identification and correlation of Large Space Structures. The method ranks the candidate sensor locations according to their contribution to the linear independence of the target modal partitions. In an iterative maner, the locations which do not contribute significantly are removed. The final sensor configuration tends to maximize determinant of the corresponding Fisher Information Matrix.

Diffractive optical elements: iterative calculation of quantized, blazed phase structures

Abstract: A procedure to calculate a highly quantized, blazed phase structure is presented. Characteristics that are concentrated on are a high diffraction efficiency and a large signal-to-noise ratio. The calculation techniques are based on iterative Fourier-transform algorithms. Stagnation problems are discussed, and methods to overcome them are described.

Super resolution from image sequences

Abstract: An iterative algorithm to increase image resolution is described. Examples are shown for low-resolution gray-level pictures, with an increase of resolution clearly observed after only a few iterations. The same method can also be used for deblurring a single blurred image. The approach is based on the resemblance of the presented problem to the reconstruction of a 2-D object from its 1-D projections in computer-aided tomography. The algorithm performed well for both computer-simulated and real images and is shown, theoretically and practically, to converge quickly. The algorithm can be executed in parallel for faster hardware implementation. >

Continuous probabilistic solutions to the biomagnetic inverse problem

Abstract: A general method for obtaining continuous solutions to the biomagnetic inverse problem is outlined and illustrated with a wide range of test cases, in a variety of experimental geometries. Magnetic sources are discussed briefly, but the main emphasis is on ionic flows, both in free space and in a homogeneous conducting sphere. The authors describe a way of obtaining depth information from measurements taken in a single plane and show how instrumental noise affects the quality of the reconstructions. An iterative scheme is introduced, capable of pinpointing a number of localised sources with a minimum of prior assumptions. However, the method is most naturally adapted to distributed sources. A number of inversions of distributed sources demonstrate that the method is powerful, accurate and convenient.

Identification and restoration of noisy blurred images using the expectation-maximization algorithm

Abstract: A maximum-likelihood approach to the blur identification problem is presented. The expectation-maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way. In order to improve the performance of the identification algorithm, low-order parametric image and blur models are incorporated into the identification method. The resulting iterative technique simultaneously identifies and restores noisy blurred images. >

Direct analytical methods for solving Poisson equations in computer vision problems

Abstract: Direct analytical methods are discussed for solving Poisson equations of the general form Delta u=f on a rectangular domain. Some embedding techniques that may be useful when boundary conditions (obtained from stereo and occluding boundary) are defined on arbitrary contours are described. The suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms. Applications to shape from shading, lightness and optical flow problems are also discussed. A proof for the existence and convergence of the flow estimates is given. Experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations. >

Shape from interreflections

Abstract: An iterative algorithm is presented that simultaneously recovers the actual shape and the actual reflectance from the pseudo estimates. The recovery algorithm works on Lambertian surfaces of arbitrary shape with possibly varying and unknown reflectance. The general behavior of the algorithm and its convergence properties are discussed. Both simulation and experimental results are included to demonstrate the accuracy and stability of the algorithm. >

Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction

Abstract: A three-dimensional iterative reconstruction algorithm which incorporates models of the geometric point response in the projector-backprojector is presented for parallel, fan, and cone beam geometries. The algorithms have been tested on an IBM 3090-600S supercomputer. The iterative EM reconstruction algorithm is 50 times longer with geometric response and photon attenuation models than without modeling these physical effects. An improvement in image quality in the reconstruction of projection data collected from a single-photon-emission computed tomography (SPECT) imaging system has been observed. Significant improvements in image quality are obtained when the geometric point response and attenuation are appropriately compensated. It is observed that resolution is significantly improved with attenuation correction alone. Using phantom experiments, it is observed that the modeling of the spatial system response imposes a smoothing without loss of resolution. >

Continuous-spontaneous-reduction model involving gravity

Abstract: A continuous-reduction model implying the dynamical suppression of linear superpositions of macroscopically distinguishable states, presented recently by Di\`osi [Phys. Rev. A 40, 1165 (1989)], is investigated. The model exhibits appealing features; in particular, it relates reduction to gravity and contains no constants besides Newton's gravitational constant G. It turns out, however, that the model is not fully consistent. A slight modification of this model is proposed, which overcomes the difficulties and retains partially its appealing features. The resulting model deals with systems containing distinguishable or identical constituents, allows the derivation from microdynamics of wave-packet reduction, and accounts for the emergence of definite macroscopic properties for macro-objects. Reduction is related to gravity in the same way as in Di\`osi's model, but a fundamental length must be introduced to avoid inconsistencies.

Structure from motion using line correspondences

Abstract: A theory is presented for the computation of three-dimensional motion and structure from dynamic imagery, using only line correspondences. The traditional approach of corresponding microfeatures (interesting points-highlights, corners, high-curvature points, etc.) is reviewed and its shortcomings are discussed. Then, a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views. The theory is compared with previous ones that are based on nonlinear equations and iterative methods.

A backprojection algorithm for electrical impedance imaging

Abstract: The authors study a two-dimensional reconstruction algorithm due to D. C. Barber and B. H. Brown, applied to a linearized electrostatic inverse problem. First, the authors demonstrate how this algorithm fits within the framework of inverses of generalized Radon transforms studied by G. Beylkin. Second, an iterative improvement of the Barber–Brown algorithm is constructed based on the conjugate residual method. Several numerical results obtained with this iterative algorithm are presented.

Iterative Identification and Restoration of Images

Abstract: The blur identification problem is formulated as a constrained maximum-likelihood problem. The constraints directly incorporate a priori known relations between the blur (and image model) coefficients, such as symmetry properties, into the identification procedure. The resulting nonlinear minimization problem is solved iteratively, yielding a very general identification algorithm. An example of blur identification using synthetic data is given. >

A Petrov-Galerkin type method for solving Axk=b, where A is symmetric complex

Abstract: Discretization of steady-state eddy-current equations may lead to linear system Ax=b in which the complex matrix A is not Hermitian, but may be chosen symmetric. In the positive definite Hermitian case, an iterative algorithm for solving this system can be defined. The residual vectors can be made mutually orthogonal by means of a two-term recursion relation which leads to the well-known conjugate gradient (CG) method. The proposed method is illustrated by comparing it with other methods for some eddy current examples. >

A study of incremental-iterative strategies for non-linear analyses

Abstract: The paper describes a study of incremental-iterative solution techniques for geometrically non-linear analyses. The solution methods documented are based on a modified Newton-Raphson approach, meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations. A consistent mathematical notation is employed in the description of the iterative and load incrementation strategies, enabling the simple inclusion of several solution options in a computer program. The iterative strategies investigated are iteration at constant load, iteration at constant displacement, iteration at constant ‘arc-length’, iteration at constant external work, iteration at minimum unbalanced displacement norm, iteration at minimum unbalanced force norm and iteration at constant ‘weighted response’. The load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step, strategies based on the ‘current stiffness parameter’ and a strategy based on a parabolic approximation to the load-deflection response. Criteria for detecting when the applied external load increment should reverse sign are described. A challenging example of a circular arch exhibiting snap-through (load limit point) behaviour and snap-back (displacement limit point) behaviour is solved using several different iterative and load incrementation strategies. The performance of the solution schemes is evaluated and conclusions are drawn.

Secular perturbation theory and computation of asteroid proper elements

Abstract: A new theory for the calculation of proper elements is presented This theory defines an explicit algorithm applicable to any chosen set of orbits and accounts for the effect of shallow resonances on secular frequencies The proper elements are computed with an iterative algorithm and the behavior of the iteration can be used to define a quality code

Interactive interpolation and approximation by Be´zier polynomials

Abstract: One of the main problems in computer-aided design is how to input shape information to the computer. The paper describes a method developed for the interactive interpolation and approximation of curves which has been found in practice to provide a natural interface between the mathematically unsophisticated user and the computer.

Convergence of nested classical iterative methods for linear systems

Abstract: Classical iterative methods for the solution of algebraic linear systems of equations proceed by solving at each step a simpler system of equations. When this system is itself solved by an (inner) iterative method, the global method is called a two-stage iterative method. If this process is repeated, then the resulting method is called a nested iterative method. We study the convergence of such methods and present conditions on the splittings corresponding to the iterative methods to guarantee convergence forany number of inner iterations. We also show that under the conditions presented, the spectral radii of the global iteration matrices decrease when the number of inner iterations increases. The proof uses a new comparison theorem for weak regular splittings. We extend our results to larger classes of iterative methods, which include iterative block Gauss-Seidel. We develop a theory for the concatenation of such iterative methods. This concatenation appears when different numbers of inner interations are performed at each outer step. We also analyze block methods, where different numbers of inner iterations are performed for different diagonal blocks.

Comments on Picture thresholding using an iterative selection method

Abstract: T.W. Ridler and E.S. Calvard (ibid., vol.SMC-8, p.630-2, Aug. 1978) presented a method of picture thresholding that was further mathematically developed by H.J. Trussel (ibid., vol.SMC-9, p.311, 1979). The principle of this method is to evaluate the unique threshold T for any image with a bimodal histogram. The present paper reinterprets the procedure as an algorithm designed to optimize the conversion of a multiple gray-level picture to a bimodel picture while maintaining as closely as possible the average luminance of the picture. >

Regularization theory in image restoration-the stabilizing functional approach

Abstract: Several aspects of the application of regularization theory in image restoration are presented. This is accomplished by extending the applicability of the stabilizing functional approach to 2-D ill-posed inverse problems. Inverse restoration is formulated as the constrained minimization of a stabilizing functional. The choice of a particular quadratic functional to be minimized is related to the a priori knowledge regarding the original object through a formulation of image restoration as a maximum a posteriori estimation problem. This formulation is based on image representation by certain stochastic partial differential equation image models. The analytical study and computational treatment of the resulting optimization problem are subsequently presented. As a result, a variety of regularizing filters and iterative regularizing algorithms are proposed. A relationship between the regularized solutions proposed and optimal Wiener estimation is identified. The filters and algorithms proposed are evaluated through several experimental results. >

A model for coupled magnetic-electric circuits in electric machines with skewed slots

Abstract: A model permitting the simulation of skewed-slot saturated machines associated with nonlinear external circuits is proposed. To take the slot effects into account, the magnetic circuit is modeled through the combined two-dimensional calculations along the machine axis. In this simulation the electric circuit equation is directly coupled with the magnetic one. The solution of the resulting nonlinear time-dependent equation is obtained using step-by-step numerical integration and the Newton-Raphson iterative procedure. The model is used for the simulation of a 4.6-N-m permanent-magnet synchronous machine in various modes of operation. >

Dynamic adaptive windows for high speed data networks: theory and simulations

Abstract: Recent results on the asymptotically optimal design of sliding windows for virtual circuits in high speed, geographically dispersed data networks in a stationary environment are exploited here in the synthesis of algorithms for adapting windows in realistic, non-stationary environments. The algorithms proposed here require each virtual circuit's source to measure the round trip response times of its packets and to use these measurements to dynamically adjust its window. Our design philosophy is quasi-stationary: we first obtain, for a complete range of parameterized stationary conditions, the relation, called the “design equation”, that exists between the window and the mean response time in asymptotically optimal designs; the adaptation algorithm is simply an iterative algorithm for tracking the root of the design equation as conditions change in a non-stationary environment. A report is given of extensive simulations of networks with data rates of 45 Mbps and propagation delays of up to 47 msecs. The simulations generally confirm that the realizations of the adaptive algorithms give stable, efficient performance and are close to theoretical expectations when these exist.

Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration

Abstract: This article describes three approximation methods I used to solve the growth model (Model 1) studied by the National Bureau of Economic Research's nonlinear rational-expectations-modeling group project, the results of which were summarized by Taylor and Uhlig (1990). The methods involve computing exact solutions to models that approximate Model 1 in different ways. The first two methods approximate Model 1 about its nonstochastic steady state. The third method works with a version of the model in which the state space has been discretized. A value function iteration method is used to solve that model.

Evaluating elementary functions in a numerical coprocessor based on rational approximations

Abstract: A different approach to hardware evaluation of elementary functions for high-precision floating-point numbers (in particular, the extended double precision format of the IEEE standard P754) is examined. The evaluation is based on rational approximations of the elementary functions, a method which is commonly used in scientific software packages. A hardware model is presented of a floating-point numeric coprocessor consisting of a fast adder and a fast multiplier, and the minimum hardware required for evaluation of the elementary functions is added to it. Next, rational approximations for evaluating the elementary functions and testing the accuracy of the results are derived. The calculation time of these approximations in the proposed numeric processor is then estimated. It is concluded that rational approximations can successfully complete with previously used methods when execution time and silicon area are considered. >

Iterative methods for cyclically reduced non-self-adjoint linear systems

Abstract: We study iterative methods for solving linear systems of the type arising from two-cyclic discretizations of non-self-adjoint two-dimensional ellip- tic partial differential equations. A prototype is the convection-diffusion equa- tion. The methods consist of applying one step of cyclic reduction, resulting in a "reduced system" of half the order of the original discrete problem, com- bined with a reordering and a block iterative technique for solving the reduced system. For constant-coefficient problems, we present analytic bounds on the spectral radii of the iteration matrices in terms of cell Reynolds numbers that show the methods to be rapidly convergent. In addition, we describe numerical experiments that supplement the analysis and that indicate that the methods compare favorably with methods for solving the "unreduced" system.