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Estimation of interpolation errors in scalp topographic mapping

ELECTROENCEPHALOGRAPHY AND CLINICAL NEUROPHYSIOLOGY 1996年第5期98卷 422-434页

作者： Fletcher, EM Kussmaul, CL Mangun, GR UNIV CALIF DAVIS CTR NEUROSCIDAVISCA 95616 UNIV CALIF DAVIS DEPT COMP SCIDAVISCA 95616 UNIV CALIF DAVIS DEPT PSYCHOLDAVISCA 95616

Topographic maps are commonly constructed from electrical scalp recordings (such as EEGs and ERPs) using several different interpolation methods. It is important to determine the accuracy of such maps. Previous assessments of interpolation methods have been based on global error measures and the visual appearance of the topographic maps. However, the relationship of interpolation error to local contributing factors requires a more detailed analysis. In this paper, we use simulations to explore and quantify the relationship of error to global and local factors for different interpolation methods. We find that among the best interpolation methods, adequate electrode density is more important than the method used. For shallow sources, we show that local interpolation error is most correlated with potential gradient, and has a lesser correlation with distance to nearest electrode. The greatest correlation, however, is with the product of gradient and distance. Thus, interpolation error can be controlled locally by making the interelectrode distance inversely proportional to the expected potential gradient. With shallow sources, areas far from any electrode and having high apparent gradient are likely to have high interpolation error. Moreover, all areas far from any electrode may contain high interpolation errors, and should be interpreted with caution.

关键词： interpolation errors scalp topographic mapping

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Study of the maximal interpolation errors of the local polynomial method for frequency response function measurements

Study of the maximal interpolation errors of the local polyn...

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29th Annual IEEE International Instrumentation and Measurement Technology Conference (I2MTC)

作者： Schoukens, J. Vandersteen, G. Pintelon, R. Emedji, Z. Rolain, Y. Vrije Univ Brussel Dept ELEC Pl Laan 2 B-1050 Brussels Belgium Ecole Polytech Fed Lausane Lausanne Switzerland

ISBN: (纸本)9781457717710

Frequency response function measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterisation of a linear dynamic behaviour. The major problems to be faced are leakage- and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. At the resonance frequencies, where often most information about the system is to be retrieved, the dominating error is the interpolation error. In this paper it is shown that the interpolation error for sufficiently low damping is bounded by (B-LPM/B-3dB)(R+2) with B-LPM the local bandwidth of the LPM, R the degree of the local polynomial that is selected to be even (user choices), and B-3dB the 3dB bandwidth of the resonance, which is a system property.

关键词： frequency response function nonparametric error analysis interpolation errors

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Investigations of interpolation errors of angle encoders for high precision angle metrology

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MEASUREMENT SCIENCE AND TECHNOLOGY 2018年第6期29卷 064007-064007页

作者： Yandayan, Tanfer Geckeler, Ralf D. Just, Andreas Krause, Michael Akgoz, S. Asli Aksulu, Murat Grubert, Bernd Watanabe, Tsukasa TUBITAK UME Baris Mah Dr Zeki Acar Cad Pk54 TR-41470 Gebze Turkey Phys Tech Bundesanstalt Bundesallee 100 D-38116 Braunschweig Germany MOLLER WEDEL OPT GmbH Rosengarten 10 D-22880 Wedel Germany AIST NMIJ Tsukuba Cent 31-1-1 Umezono Tsukuba Ibaraki 3058563 Japan

interpolation errors at small angular scales are caused by the subdivision of the angular interval between adjacent grating lines into smaller intervals when radial gratings are used in angle encoders. They are often a major error source in precision angle metrology and better approaches for determining them at low levels of uncertainty are needed. Extensive investigations of interpolation errors of different angle encoders with various interpolators and interpolation schemes were carried out by adapting the shearing method to the calibration of autocollimators with angle encoders. The results of the laboratories with advanced angle metrology capabilities are presented which were acquired by the use of four different high precision angle encoders/interpolators/rotary tables. State of the art uncertainties down to 1 milliarcsec (5 nrad) were achieved for the determination of the interpolation errors using the shearing method which provides simultaneous access to the angle deviations of the autocollimator and of the angle encoder. Compared to the calibration and measurement capabilities (CMC) of the participants for autocollimators, the use of the shearing technique represents a substantial improvement in the uncertainty by a factor of up to 5 in addition to the precise determination of interpolation errors or their residuals (when compensated). A discussion of the results is carried out in conjunction with the equipment used.

关键词： SI angle unit radian autocollimators angle encoders interpolation errors

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Error concealment for motion-compensated interpolation

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IET IMAGE PROCESSING 2010年第3期4卷 195-210页

作者： Wu, Y. Swamy, M. N. S. Ahmad, M. O. Concordia Univ Dept Elect & Comp Engn Ctr Commun & Signal Proc Montreal PQ H3G 1M8 Canada

Motion-compensated interpolation is usually employed at the receiver end in order to improve the quality of the video, when a low-bit-rate video is encoded in conjunction with frame dropping. The authors propose a scheme that can exploit the block-based motion vector field available at the decoder to avoid the complex motion estimation. The scheme is based on an iterative refinement technique that employs the finite-element method to efficiently conceal the interpolation errors caused by unfilled holes or overlapped pixels in the predicted frames. As a consequence, no pixel classification is needed in the proposed scheme, thus reducing substantially the computational complexity. The scheme is capable of concealing the errors in the homogeneous regions as well as in regions containing sharp edges. The proposed scheme is simulated with the original frames of a number of test sequences, as well as implemented with the H.264/AVC decoded frames. The results from these extensive simulations show that the proposed scheme results in reconstructed frames having a better visual quality and a lower computational complexity than the existing schemes.

关键词： pixel classification finite element method motion compensation complex motion estimation Computer vision and image processing techniques Image and video coding decoder frame dropping block-based motion vector field visual quality motion-compensated interpolation video coding error handling H.264/AVC decoded frames low bit rate video error concealment Video signal processing iterative refinement technique computational complexity video quality interpolation errors

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On spatial adaptivity and interpolation when using the method of lines

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APPLIED NUMERICAL MATHEMATICS 1998年第1-2期26卷 117-133页

作者： Berzins, M Capon, PJ Jimack, PK Univ Leeds Sch Comp Studies Leeds LS2 9JT W Yorkshire England Tessella Support Serv PLC Abingdon Oxon England

The solution of time-dependent partial differential equations with discrete time static remeshing is considered within a method of lines framework. Numerical examples in one and two space dimensions are used to show that spatial interpolation error may have an important impact on the efficiency of integration. Analysis of a simple problem and of the time integration method is used to confirm the experimental results and a computational test for monitoring the impact of this error is derived and tested. (C) 1998 Elsevier Science B.V.

关键词： adaptive remeshing method of lines interpolation errors

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New interpolation method for quadrature encoder signals

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2002年第5期51卷 1073-1079页

作者： Tan, KK Zhou, HXX Lee, TH Natl Univ Singapore Dept Elect & Comp Engn Singapore 117548 Singapore

This paper presents a new interpolation method suitable for increasing the measurement resolution obtainable from quadrature encoder signals. Based on the existing sinusoidal signals, high-order sinusoids can be derived, from which binary pulses can be generated, which can be decoded using only standard servo controllers for position information. A look-up table, constructed off-line, serves as the inferencing engine for the proposed method. Imperfections in the encoder signals can be directly compensated for in the look-up table, including mean and phase offsets, amplitude difference, and waveform distortion. Simulation and experimental results are provided in this paper.

关键词： encoder resolution interpolation errors look-up tables measurement interpolation quadrature encoder signals

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PROJECTION-BASED FINITE ELEMENTS FOR NONLINEAR FUNCTION SPACES

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2019年第1期57卷 404-428页

作者： Grohs, Philipp Hardering, Hanne Sander, Oliver Sprecher, Markus Univ Wien Fak Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria Tech Univ Dresden Inst Numer Math Zellescher Weg 12-14 D-01069 Dresden Germany Swiss Fed Inst Technol Seminar Angew Math Ramistr 101 CH-8092 Zurich Switzerland

We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in a Euclidean embedding space, and then projected pointwise onto the manifold. We show optimal interpolation error bounds with respect to Lebesgue and Sobolev norms. Additionally, we show similar bounds for the test functions, i.e., variations of discrete functions. Combining these results with a nonlinear Cea lemma, we prove optimal L-2 and H-1 discretization error bounds for harmonic maps from a planar domain into a smooth manifold. All these error bounds are also verified numerically.

关键词： geometric finite elements projection nonlinear manifold interpolation errors discretization errors harmonic maps

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Effects of cross sections tables generation and optimization on rod ejection transient analyses

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ANNALS OF NUCLEAR ENERGY 2014年 73卷 387-391页

作者： Sanchez-Cervera, S. Garcia-Herranz, N. Herrero, Jose J. Cuervo, D. Univ Politecn Madrid Dept Nucl Engn E-28006 Madrid Spain

Best estimate analysis of rod ejection transients requires 3D kinetics core simulators. If they use cross sections libraries compiled in multidimensional tables, interpolation errors originated when the core simulator computes the cross sections from the table values are a source of uncertainty in k-effective calculations that should be accounted for. Those errors depend on the grid covering the domain of state variables and can be easily reduced, in contrast with other sources of uncertainties such as the ones due to nuclear data, by choosing an optimized grid distribution. The present paper assesses the impact of the grid structure on a PWR rod ejection transient analysis using the coupled neutron-kinetics/thermal-hydraulics COBAYA3/COBRA-TF system. For this purpose, the OECD/NEA PWR MOX/UO2 core transient benchmark has been chosen, as material compositions and geometries are available, allowing the use of lattice codes to generate libraries with different grid structures. Since a complete nodal cross-section library is also provided as part of the benchmark specifications, the effects of the library generation on transient behavior are also analyzed. Results showed large discrepancies when using the benchmark library and own-generated libraries when compared with benchmark participants' solutions. The origin of the discrepancies was found to lie in the nodal cross sections provided in the benchmark. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Neutronics-related uncertainties Tabulated cross sections libraries interpolation errors Optimized grid point distribution

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UNIFORM APPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS

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Acta Mathematica Scientia 2012年第6期32卷 2401-2410页

作者： G.S.Srivastava S.Kuma Department of Mathematics Indian Institute of Technology RoorkeeRoorkee-247667India Department of Mathematics Central University of Himachal PradeshDharamshala-176215India

In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obta... 详细信息

关键词： entire function generalized order generalized type approximation errors interpolation errors

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interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature

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JOURNAL OF APPROXIMATION THEORY 2009年第1期161卷 142-173页

作者： Wang, Li-Lian Guo, Ben-yu Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore 637616 Singapore Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Sci Comp Key Lab Shanghai Univ Shanghai E Inst Computat Sci Shanghai 200041 Peoples R China

We derive in this paper the asymptotic estimates of the nodes and weights of the Gauss-Lobalto-Legendre-Birkhoff (GLLB) quadrature formula, and obtain optimal error estimates for the associated GLLB interpolation in Jacobi weighted Sobolev spaces. We also present a user-oriented implementation of the pseudospectral methods based on the GLLB quadrature nodes for Neumann problems. This approach allows an exact imposition of Neumann boundary conditions, and is as efficient as the pseudospectral methods based on Gauss-Lobatto quadrature for PDEs with Dirichlet boundary conditions. (C) 2008 Elsevier Inc. All rights reserved.

关键词： GLLB quadrature rule Collocation method Neumann problems Asymptotic estimates interpolation errors

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