1,721,058 research outputs found
A boundary integral equation approach to wave propagation over a trench
No full textAn analysis is presented for the propagation of water waves with oblique incidence past a submarine trench. The boundary integral equation deduced from the differential formulation of the problem allows the study of submarine trenches of arbitrary geometries. A numerical solution is obtained at discrete points on the boundary and numerical examples are reported. © 1983
Primal-dual variational problems by boundary and finite elements
No full textIn this paper the primal-dual (or mixed) formulation is studied for self-adjoint elliptic problems coupled with a boundary integral equation. It is shown that, after introducing a suitable complementary variational principle, the problem is reduced to finding a stationarity point of a constrained functional. Some numerical examples are reported for a second-order differential equation on unbounded domains. © 1985
A weak formulation of boundary integral equations for time dependent parabolic problems
No full textA weak formulation for 'direct' boundary methods for time dependent parabolic problems, deduced from distribution theory, is presented. The present approach seems particularly valuable when dealing with problems with non-integrable singularities and solutions with an exponential growth. Numerical examples are also reported for plane diffusion. © 1985
Semi-implicit finite volume scheme for image processing in 3D cylindrical geometry
No full textNowadays, 3D echocardiography is a well-known technique in medical diagnosis. Inexpensive echocardiographic acquisition devices are applied to scan 2D slices rotated along a prescribed direction. Then the discrete 3D image information is given on a cylindrical grid. Usually, this original discrete image intensity function is interpolated to a uniform rectangular grid and then numerical schemes for 3D image processing operations (e.g. nonlinear smoothing) in the uniform rectangular geometry are used. However, due to the generally large amount of noise present in echocardiographic images, the interpolation step can yield undesirable results. In this paper, we avoid this step and suggest a 3D finite volume method for image selective smoothing directly in the cylindrical image geometry. Specifically, we study a semi-implicit 3D cylindrical finite volume scheme for solving a Perona-Malik-type nonlinear diffusion equation and apply the scheme to 3D cylindrical echocardiographic images. The L∞-stability and convergence of the scheme to the weak solution of the regularized Perona-Malik equation is proved. © 2003 Elsevier B.V. All rights reserved
A regularizing L-curve Lanczos method for underdetermined linear systems
No full textMany real applications give rise to the solution of underdetermined linear systems of equations with a very ill conditioned matrix A, whose dimensions are so large as to make solution by direct methods impractical or infeasible. Image reconstruction from projections is a well-known example of such systems. In order to facilitate the computation of a meaningful approximate solution, we regularize the linear system, i.e., we replace it by a nearby system that is better conditioned. The amount of regularization is determined by a regularization parameter. Its optimal value is, in most applications, not known a priori. A well-known method to determine it is given by the L-curve approach. We present an iterative method based on the Lanczos algorithm for inexpensively evaluating an approximation of the points on the L-curve and then determine the value of the optimal regularization parameter which lets us compute an approximate solution of the regularized system of equations. © 2001 Elsevier Science Inc
Chebyshev approximation of recursive digital filters having specified amplitude and phase characteristics
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Parallel algorithms for the iterative solution of sparse least-squares problems
No full textIn this paper, we are concerned with a generalized Gauss-Seidel approach to sparse linear least-squares problems. Two algorithms, related to those given by Schechter (1959), for the solution of linear systems are presented and their parallel implementation is discussed. In these procedures, which can be viewed as an alternative ordering of the variables in the SOR methods, the variables are divided into nondisjoint groups. Numerical results, obtained on CRAY X-MP/48, are presented and discussed. © 1990
'ILL-CONDITIONED' VOLTERRA INTEGRAL EQUATION RELATED TO THE RECONSTRUCTION OF IMAGES FROM PROJECTIONS
No full textA Volterra integral equation, which relates the Fourier coefficients of the projection (in polar coordinates) with the corresponding coefficients of the unknown density function, is deduced. The same equation holds for both divergent and parallel beam projections. The problem is shown to be 'ill-conditioned'. A numerical solution, based on the recursive evaluation of certain integrals, is proposed and a Tikhonov regularization procedure is applied to the discete problem. Numerical examples are also reported
An high order finite co-volume scheme for denoising using radial basis functions
No full textIn this work we investigate finite co-volume methods for solving Partial Differential Equation (PDE) based diffusion models for noise removal in functional surfaces. We generalized the model proposed by Tai et al. [1][2] based on the reconstruction of a noise-reduced surface from the smoothed normal field, considering a curvature preserving term. The discretization of the PDE model by basic finite co-volume schemes on unstructured grids is investigated. The accuracy of the numerical model is then improved by using an higher order optimal recovery based on Radial Basis Functions (RBF). Preliminary numerical results demonstrate the effectiveness of the new numerical approach. © Springer-Verlag Berlin Heidelberg 2007
A Workstation-Based System for 2-D Echocardiography Visualization and Image Processing
No full textParameters of cardiac function can be drawn from the analysis of echocardiographic image sequences, especially the motion of the ventricular wall, heart wall thickness, and shape parameters. Automatic image analysis and visualization allows reduced manual operations and, above all, ensures objectivity and repetition of analysis, which is essential when one wishes to calculate parameters based on variations, i.e., on image sequence analysis. In this paper, a system and the related software package for interactive echocardiographic image analysis and visualization are illustrated and discussed. Furthermore, the full model for smoothing, edge enhancement, and contour detection is discussed and a new technique based on the heat anisotropic diffusion model is presented. The results of automatic detection of the left ventricle contours are presented and discussed. © 1990 IEE
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