Special Weight Functions Research Articles

心拍動によるモーションアーチファクト軽減のための高時間分解能再構成アルゴリズム

Cardiac pulsation is the most important cause of serious image degradation on high resolution CT(HRCT) images of lung adjacent to heart and cardiac images. The purpose of this study was to propose a special high temporal resolution reconstruction(HTRR) algorithm, and to assess the effects on the reduction in motion artifacts caused by cardiac pulsation on HRCT images of lung and cardiac images by using this algorthm combined with sub-second CT. The HTRR algorithm was developed on the basis of a special weighting function. The results of phantom and clinical studies demonstrated that the HTRR algorithm can provide high temporal resolution, substantially reduce moting artifacts and noise, and markedly improve the quality of cardiac images and HRCT lung images at the cost of a slight degradation in spatial resolution. Further, the HTRR algorithm can obtain phase information by combining subsecond CT with the overlapping cine reconstruction technique and ECG information. Using the HTRR algorithm, the effective temporal resolution(FWHM) is 0.4 sec for a 0.8 sec scan.

Image enhancement using a human visual system model

In this paper we report the result of a set of computer experiments carried out to enhance digital images. We use a special line weight function (LWF) which is a combination of zero- and second-order Hermite functions. We are motivated by the physiological evidence reported in R. A. Young, Spatial Vision 2(4), 273–293 (1987), that visual receptive fields are shaped like the sum of a Gaussian function and its Laplacian. This function can also be derived mathematically when the contrast sensitivity experiments in psychophysics are posed as an eigenvalue problem (A. L. Stewart and R. Pinkham, Biol. Cybernetics 64, 373–379 (1991). Analyses of the edge location error show that the proposed function has extremely good localization capability (i.e. the points marked by the operator is as close as possible to the center of the true edge). We also show that the LWF does not detect phantom edges which do not correspond to significant image intensity changes.

A Fast Non‐Parametric Density Estimation Algorithm

Non-parametric density estimation is the problem of approximating the values of a probability density function, given samples from the associated distribution. Non-parametric estimation finds applications in discriminant analysis, cluster analysis, and flow calculations based on Smoothed Particle Hydrodynamics. Usual estimators make use of kernel functions, and require on the order of $n^2$ arithmetic operations to evaluate the density at $n$ sample points. We describe a sequence of special weight functions which requires almost linear number of operations in $n$ for the same computation.

A Fast Non-Parametric Density Estimation Algorithm

Non-parametric density estimation is the problem of approximating the values of a probability density function, given samples from the associated distribution. Non-parametric estimation finds applications in discriminant analysis, cluster analysis, and flow calculations based on Smoothed Particle Hydrodynamics. Usual estimators make use of kernel functions, and require on the order of n2 arithmetic operations to evaluate the density at n sample points. We describe a sequence of special weight functions which requires almost linear number of operations in n for the same computation. © 1997 John Wiley & Sons, Ltd.

The remainder term for analytic functions of symmetric Gaussian quadratures

For analytic functions the remainder term of Gaussian quadrature rules can be expressed as a contour integral with kernel K n . In this paper the kernel is studied on elliptic contours for a great variety of symmetric weight functions including especially Gegenbauer weight functions. First a new series representation of the kernel is developed and analyzed. Then the location of the maximum modulus of the kernel on suitable ellipses is determined. Depending on the weight function the maximum modulus is attained at the intersection point of the ellipse with either the real or imaginary axis. Finally, a detailed discussion for some special weight functions is given.

Reduction of robust stabilization problems to standard H∞ problems for classes of systems with structured uncertainty

We consider the problem of robustly stabilizing a family of linear time-invariant systems with a linear time-invariant controller. For classes of robust stabilization problems with unmodelled dynamics, recent breakthroughs in H ∞ theory lead to solution via two Riccati equations. For systems with structured real uncertainty, however, a similar comprehensive theory does not exist. The objective of this paper is to delineate classes of linear time-invariant systems with structured uncertainty (either real or complex) for which a similar solution to the robust stabilization problem is possible. The theory has the following salient features. First, for classes of uncertainty structures, no conservatism is introduced. For structured real parametric uncertainty, we make a connection with H ∞ theory that does not amount to any crude overbounding via complex discs; the stabilizability conditions we obtain are not only sufficient but also necessary. The second salient feature in the theory is a special weighting function which we construct. For example, for the case when the structured uncertainty enters only in the denominator, the robust stabilization problem is replaced by a standard H ∞ sensitivity minimization problem with our special weighting function. A similar H ∞ complementary sensitivity problem is associated with numerator uncertainty.

Sampled-data controller reduction procedure

The problem of controller order reduction aimed at preserving the closed-loop performance of a sampled-data closed-loop system is investigated. Past sampling of the system at a multiple of the sampling frequency followed by lifting allows capturing of the system's intersample behavior and yields a time-invariant single-rate system; this then permits standard order-reduction ideas to be applied. Special weighting functions aimed at preserving the closed-loop transfer function are obtained, and weighted balanced truncation is used to reduce the controller, An example shows that without the use of fast-sampling, an unstable closed loop can result from the reduction.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Unsteady conjugated heat transfer in laminar pipe flow

This study analyses the transient conjugated heat transfer in laminar pipe flow, where the flow is both hydrodynamically and thermally fully developed. Two cases are considered: a prescribed constant wall temperature and a constant heat flux at the wall. A non-standard method of separation of variables is applied, which treats the fluid and the solid as one region with certain discontinuities. The resulting eigenfunctions, which are not orthogonal to each other with respect to the usual weight function according to the Sturm-Liouville theorem, are made orthogonal to each other with respect to a special weight function. It is concluded that the degree of conjugation and viscous dissipation may have a great impact on the temperature distribution in the fluid.

A non‐Jacobian numerical quadrature for semi‐infinite integrals

AbstractA non‐Jacobian numerical quadrature is proposed for evaluating improper integrals over a semi‐infinite range. The quadrature first transforms the semi‐infinite integration limit into a finite limit between – 1 and 1. Standard numerical integration procedures such as Gauss–Chebyshev or Gauss–Legendre schemes can then be used to obtain the integral value. Unlike traditional methods using Laguerre or Hermite polynomials, numerical results show that no specific weight function is required for the proposed quadrature to converge as long as the integral exists. The transformation also includes a scale parameter which effectively expands the numerical‐integration sampling points along its original semi‐infinite integration path. Numerical examples shows that selection of the scale parameter is rather flexible and convergence can always be achieved within a wide range of parameter values. Several applied mechanics problems are also illustrated to validate the proposed numerical scheme. The quadrature can be easily incorporated into finite element or boundary element schemes for the evaluation of semi‐infinite integrals.

Application of special weight functions to input signal recovery in instrumental transducers of mechanical parameters

Application of special weight functions to input signal recovery in instrumental transducers of mechanical parameters

Extrapolation of near-field RCS measurements to the far zone

An algorithmic procedure for extrapolating near-field radar cross-section (RCS) measurements to the far zone has been derived, coded, and experimentally validated. The deviation of the extrapolation algorithm uses an optical model to estimate the surface currents induced on the scattering body by the incident field, and a specially weighted version of the Fourier transform to calculate the near-field scattering amplitudes associated with such surface currents. The extrapolation entails three steps. First, near-field measurements of the scattered electric and/or magnetic field are used to infer the monostatic vector potential. Next, the inverse Fourier transform of the inferred vector potential is multiplied by a special weighting function to estimate an equivalent obliquity factor. Finally, the far-field scattering pattern is estimated by taking the Fourier transform of the reweighted obliquity factor. This extrapolation procedure has been validated using anechoic-chamber data taken on a right-circular aluminium cylinder 25 lambda high and 2.5 lambda in radius at near-field range of 19% of 2D/sup 2// lambda where D is the nominal target diameter and lambda the radiation wavelength. The extrapolated RCS pattern for this target was compared with an analytical estimate of its far-zone pattern and good amplitude and phase agreement was observed over a 20 degrees cone of scattering angles.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimum prediction with a mean weighted square error criterion

The linear prediction theory is examined using a mean weighted square error criterion. A specific nondeterministic weighting function is used. The problem is reduced to that of solving integral equations which are written in terms of correlation functions which can be calculated by averaging over the ensemble. A complete solution is given for the problem using Gaussian statistics with no correlation between noise and true signal.