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IEEE International Conference on Computer-Aided Design

作者： Arun Chandrasekharan Mathias Soeken Daniel Große Rolf Drechsler Group of Computer Architecture University of Bremen Germany EPFL Inteorated Systems Laboratory Switzerland Universitat Bremen Bremen Bremen DE Cyber Physical Systems DFKI GmbH Bremen Germany

approximation circuits offer superior performance (speed and area) compared to traditional circuits at the cost of computational accuracy. The accuracy of the results in approximation circuits is evaluated based on several error metrics such as worst-case error, bit-flip error, or error-rate. Several applications have varied requirements in error metrics, i.e., all the error criteria have to be met together at a time, or in combinations. Nevertheless, all applications benefit from improved delay and area. An automated synthesis approach with formal guarantees on error metrics is very helpful in generating circuits that meet these criteria. Furthermore, each of these metrics are independent quantities (value of one metric does not correlate with the other), and automated synthesis can discover opportunities to trade off one or more of the relaxed metrics with a strict requirement on the other, resulting in better performance. In this paper, we present an automatic synthesis approach using And-Inverter Graphs (AIGs) based rewriting that not only improves the performance but also guarantees the bounds of approximation errors introduced. Our synthesis approach is evaluated on a wide range of designs and standard benchmark circuits to show the usefulness and applicability. In particular, we show that our synthesis results are even comparable with the optimization achieved with hand crafted adhoc approximation circuits such as approximation adders in a case study on image compression.

关键词： approximation algorithms Delays Adders Logic gates approximation error Boolean functions

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Comparing 2-D recursive and nonrecursive least-square-error approximation filters

Comparing 2-D recursive and nonrecursive least-square-error ...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： G. Shaw R. Mersereau School of Electrical Engineering Georgia Institute of Technology Atlanta GA USA

Seventy-two 2-D recursive and nonrecursive filters of varying order are designed to approximate, in the least-squares sense, four circularly-symmetric unit-pulse responses, corresponding to four lowpass filters. The approximation error obtained for a given number of filter coefficients is then used as the basis for comparing the efficiency of the designed 2-D recursive and nonrecursive filters.

关键词： Nonlinear filters approximation error Nonlinear equations Stability Algorithm design and analysis Difference equations Convolution Cutoff frequency

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Estimation error bounds for denoising by sparse approximation

Estimation error bounds for denoising by sparse approximatio...

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IEEE International Conference on Image Processing

作者： A.K. Fletcher Kannan Ramchandran University of California Berkeley USA

If a signal is known to have a sparse representation with respect to a given frame, the signal can be estimated from a noise-corrupted observation of the signal by finding the best sparse approximation to the observation. The ability to remove noise in this manner depends on the frame being designed to efficiently represent the signal while it inefficiently represents the noise. This paper gives bounds to show how inefficiently white Gaussian noise is represented by sparse linear combinations of frame vectors. Combined with knowledge of the approximation efficiency of a given family of frames for a given signal class, this work leads to a better understanding of the merits of frame denoising.

关键词： Estimation error Noise reduction Maximum likelihood estimation approximation error Signal design Dictionaries Redundancy Yield estimation Matching pursuit algorithms Video compression

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The best approximation to C/sup 2/ functions and its error bounds using Gaussian hidden units

The best approximation to C/sup 2/ functions and its error b...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： B. Liu J. Si Department of Electrical Engineering Arizona State University Tempe AZ USA

ISBN: (纸本)0780312813

It is proved that any C/sup 2/ function of m real variables with support in the unit hypercube can be approximated by a Gaussian radial basis network. This network uses a single layer of N Gaussian radial basis functions. The centers of the Gaussian functions are uniformly distributed on the unit hypercube. From the viewpoint of the best approximation theory, an upper bound of this approximation O(/spl sigma//sup 2/ + N/sup -2/) is obtained, where /spl sigma/ is the deviation Gaussians. The authors' results provide an explicit expression of the relationship between the number of hidden nodes and the approximation error.< >

关键词： Hypercubes Nonhomogeneous media approximation methods Upper bound approximation error Integral equations Multilayer perceptrons Measurement standards Vectors Neural networks

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Quantitative Fourier analysis of approximation techniques: Part I - Interpolators and projectors

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1999年第10期47卷 2783-2795页

作者： Blu, T Unser, M Swiss Fed Inst Technol EPFL Biomed Imaging Grp CH-1015 Lausanne Switzerland

We present a general Fourier-based method that pro, ides an accurate prediction of the approximation error as a function-of the sampling step T, Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory, We claim that are can predict the L-2-approximation error by integrating the spectrum of the function to approximate-not necessarily bandlimited-against a frequency kernel E(omega) that characterizes the approximation operator. This prediction is easier yet more precise than was previously available, Our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function. Our error prediction is exact for stationary processes, as well as for bandlimited signals. We apply this method to the comparison of standard interpolation and approximation techniques. Our method has interesting implications for approximation theory. In particular, we use our results to obtain some new asymptotic expansions of the error as T --> 0, as well as to derive improved upper bounds of the kind found in the Strang-Fix theory. We finally show how we can design quasi-interpolators that are near optimal in the least-squares sense.

关键词： Interpolation Sampling methods Signal sampling approximation error Convolution Kernel Signal processing approximation methods Image sampling Spline

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AN IMPROVEMENT TO THE RYTOV approximation IN DIFFRACTION TOMOGRAPHY

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 1986年第4期33卷 394-401页

作者： SOUMEKH, M Department of Electrical Engineering Worcester Polytechnic Institute Worcester MA USA

A method for reducing the approximation errors introduced in the Rytov inversion of the inhomogeneous wave equation is presented. The approach is based on the filtering of the Rytov function components at the receiver line that correspond to the Rytov distortion term. Signal processing issues associated with the implementation of the scheme are discussed. Reconstruction results for simulated soft-scattering cylinders are presented. Copyright © 1986 by The Institute of Electrical and Electronics Engineers, Inc.

关键词： Tomography Testing Acoustic scattering Partial differential equations Signal processing approximation error Filtering Image reconstruction Acoustic diffraction Acoustic refraction

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approximation of Wide-Sense Stationary Stochastic Processes by Shannon Sampling Series

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IEEE TRANSACTIONS ON INFORMATION THEORY 2010年第12期56卷 6459-6469页

作者： Boche, Holger Moenich, Ullrich J. Tech Univ Berlin Heinrich Hertz Chair Mobile Commun D-10578 Berlin Germany

In this paper, the convergence behavior of the symmetric and the nonsymmetric Shannon sampling series is analyzed for bandlimited continuous-time wide-sense stationary stochastic processes that have absolutely continuous spectral measure. It is shown that the nonsymmetric sampling series converges in the mean-square sense uniformly on compact subsets of the real axis if and only if the power spectral density of the process fulfills a certain integrability condition. Moreover, if this condition is not fulfilled, then the pointwise mean-square approximation error of the nonsymmetric sampling series and the supremum of the mean-square approximation error over the real axis of the symmetric sampling series both diverge. This shows that there is a significant difference between the convergence behavior of the symmetric and the nonsymmetric sampling series.

关键词： approximation error mean-square convergence nonsymmetric sampling series power spectral density Shannon sampling series stochastic process uniformly bounded weak-sense stationary

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Algorithm for building a neural network for function approximation

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IEE PROCEEDINGS-CIRCUITS DEVICES AND SYSTEMS 2002年第5-6期149卷 301-307页

作者： Jayadeva Deb, AK Chandra, S Indian Inst Technol Dept Elect Engn New Delhi 110016 India Indian Inst Technol Dept Math New Delhi 110016 India

A technique for constructing a multilayer tree-structured neural network, which provides a continuous, piece-wise linear function approximation, is presented. The method uses a growth network with linear threshold neurons. Neurons are added to a binary tree until the approximation error at all sampling points is brought down to within a specified +/-Delta. The number of neurons in the constructed network depends on the samples provided as well as the specified tolerance Delta, thus enabling a trade-off between accuracy and network size. In comparison to approaches such as backpropagation, the proposed technique requires no assumptions regarding the number of neurons, learning rate, momentum term, or initial weight values. It also does not suffer from problems of local minima. Examples are presented to illustrate the effectiveness of the technique.

关键词： multilayer tree-structured neural network trees (mathematics) tolerance piecewise linear techniques growth network linear threshold neurons binary tree accuracy approximation error piece-wise linear function approximation function approximation network size initial weight values multilayer perceptrons linear programming

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STOCHASTIC CHOICE OF BASIS FUNCTIONS IN ADAPTIVE FUNCTION approximation AND THE FUNCTIONAL-LINK NET

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1995年第6期6卷 1320-1329页

作者： IGELNIK, B PAO, YH Electrical Engineering and Applied Physics Department Case Western Reserve University Cleveland OH USA

A theoretical justification for the random vector version of the functional-link (RVFL) net is presented in this paper, based on a general approach to adaptive function approximation, The approach consists of formulating a Limit-integral representation of the function to be approximated and subsequently evaluating that integral with the Monte-Carlo method, Two main results are: 1) the RVFL is a universal approximator for continuous functions on bounded finite dimensional sets, and 2) the RVFL is an efficient universal approximator with the rate of approximation error convergence to zero of order O(C/root n), where n is number of basis functions and with C independent of n, Similar results are also obtained for neural nets with hidden nodes implemented as products of univariate functions or radial basis functions, Some possible ways of enhancing the accuracy of multivariate function approximations are discussed.

关键词： Stochastic processes Function approximation Integral equations Random variables approximation error Convergence Neural networks Writing Hypercubes

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On the continuum approximation of the on-and-off signal control on dynamic traffic networks

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2014年 61卷 73-97页

作者： Han, Ke Gayah, Vikash V. Piccoli, Benedetto Friesz, Terry L. Yao, Tao Univ London Imperial Coll Sci Technol & Med Dept Civil & Environm Engn London SW7 2AZ England Penn State Univ Dept Civil & Environm Engn University Pk PA 16802 USA Rutgers State Univ Dept Math Sci Camden NJ 08102 USA Rutgers State Univ CCIB Camden NJ 08102 USA Penn State Univ Dept Ind & Mfg Engn University Pk PA 16802 USA

In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. While accurate, the use of binary variables can cause problems when studying large networks with many intersections. Instead, the signal control can be approximated through a continuum approach where the on-and-off control variable is replaced by a continuous priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment. Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach;i.e., to what extent is this a valid approximation for the on-and-off case. The goal of this paper is to answer these basic research questions and provide further guidance for the application of such continuum signal model. In particular, by employing the Lighthill-Whitham-Richards model (Lighthill and Whitham, 1955;Richards, 1956) on a traffic network, we investigate the convergence of the on-and-off signal model to the continuum model in regimes of diminishing signal cycles. We also provide numerical analyses on the continuum approximation error when the signal cycles are not infinitesimal. As we explain, such convergence results and error estimates depend on the type of fundamental diagram assumed and whether or not vehicle spillback occurs to the signalized intersection in question. Finally, a traffic signal optimization problem is presented and solved which illustrates the unique advantages of applying the continuum signal model instead of the on-and-off model. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Traffic signal Continuum approximation LWR model Convergence approximation error Vehicle spillback

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