HYPERBOLIC SIGMA-PI NEURAL NETWORK OPERATORS APPLIED TO IMAGE PROCESSING AND RECONSTRUCTION

TitleHYPERBOLIC SIGMA-PI NEURAL NETWORK OPERATORS APPLIED TO IMAGE PROCESSING AND RECONSTRUCTION
Publication TypeJournal Article
Year of Publication2002
AuthorsLenze, B
Volume6
Issue1
Start Page17
Pagination9
Date Published2002
ISSN1083-2564
AMS26E40, 41A05, 41A63, 92B20
Abstract

In this paper, we recall how to design three-layer feedforward neural network operators based on hyperbolic sigma-pi units in order to act as approximation and interpolation devices for regular gridded data. The basic part of the paper consists of an application of this strategy in connection with image processing and reconstruction.

URLhttp://www.acadsol.eu/en/articles/6/1/2.pdf
Refereed DesignationRefereed
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REFERENCES
[1] C. K. Chui and X. Li, Approximation by ridge functions and neural networks with one hidden
layer, J. Appr. Theory, 70 (1992), 131–141.
[2] K. Hornik, M. Stinchcombe and H. White, Multilayer feedforward networks are universal
approximators, Neural Networks, 2 (1989), 359–366.
[3] B. Lenze, On multidimensional Lebesgue-Stieltjes convolution operators, in: Multivariate Approximation
Theory IV, C.K. Chui, W. Schempp, and K. Zeller (Eds.), ISNM 90, Birkh¨auser
Verlag, Basel, 1989, 225–232.
[4] B. Lenze, Constructive multivariate approximation with sigmoidal functions and applications
to neural networks, in: Numerical Methods of Approximation Theory, D. Braess and L.L.
Schumaker (Eds.), ISNM 105, Birkh¨auser Verlag, Basel, 1992, 155–175.
[5] B. Lenze, Quantitative approximation results for sigma-pi-type neural network operators, in:
Multivariate Approximations: From CAGD to Wavelets, K. Jetter and F. Utreras (Eds.), World
Scientific, Singapore, 1993, 193–209.
[6] B. Lenze, Local behaviour of neural network operators –Approximation and Interpolation–,
Analysis, 13 (1993), 377–387.
[7] B. Lenze, How to make sigma-pi neural networks perform perfectly on regular training sets,
Neural Networks, 7 (1994), 1285–1293.
[8] B. Lenze, One-sided approximation and interpolation operators generating hyperbolic sigma-pi
neural networks, in: Multivariate Approximation and Splines, G. N¨urnberger, J.W. Schmidt,
and G. Walz (Eds.), ISNM 125, Birkh¨auser Verlag, Basel, 1997, 99–112.
[9] H. N. Mhaskar and C. A. Micchelli, Degree of approximation by neural and translation networks
with a single hidden layer, Adv. in Appl. Math., 16 (1995), 151–183.
[10] A. Pinkus, TDI-subspaces of C(IRd
) and some density problems from neural networks, J. Appr.
Theory, 85 (1996), 269–287.
[11] L. L. Schumaker, Spline Functions: Basic Theory, John Wiley & Sons, New York, 1981.