Function approximation of Seidel aberrations by a neural network

Rossella Cancelliere; Mario Gai

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 3, page 687-696
  • ISSN: 0392-4041

Abstract

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This paper deals with the possibility of using a feedforward neural network to test the discrepancies between a real astronomical image and a predefined template. This task can be accomplished thanks to the capability of neural networks to solve a nonlinear approximation problem, i.e. to construct an hypersurface that approximates a given set of scattered data couples. Images are encoded associating each of them with some conveniently chosen statistical moments, evaluated along the x , y axes; in this way a parsimonious method is obtained that allows a really effective approach to Seidel aberration diagnostics.

How to cite

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Cancelliere, Rossella, and Gai, Mario. "Function approximation of Seidel aberrations by a neural network." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 687-696. <http://eudml.org/doc/194600>.

@article{Cancelliere2004,
abstract = {This paper deals with the possibility of using a feedforward neural network to test the discrepancies between a real astronomical image and a predefined template. This task can be accomplished thanks to the capability of neural networks to solve a nonlinear approximation problem, i.e. to construct an hypersurface that approximates a given set of scattered data couples. Images are encoded associating each of them with some conveniently chosen statistical moments, evaluated along the $\\{x, y\\}$ axes; in this way a parsimonious method is obtained that allows a really effective approach to Seidel aberration diagnostics.},
author = {Cancelliere, Rossella, Gai, Mario},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {687-696},
publisher = {Unione Matematica Italiana},
title = {Function approximation of Seidel aberrations by a neural network},
url = {http://eudml.org/doc/194600},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Cancelliere, Rossella
AU - Gai, Mario
TI - Function approximation of Seidel aberrations by a neural network
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/10//
PB - Unione Matematica Italiana
VL - 7-B
IS - 3
SP - 687
EP - 696
AB - This paper deals with the possibility of using a feedforward neural network to test the discrepancies between a real astronomical image and a predefined template. This task can be accomplished thanks to the capability of neural networks to solve a nonlinear approximation problem, i.e. to construct an hypersurface that approximates a given set of scattered data couples. Images are encoded associating each of them with some conveniently chosen statistical moments, evaluated along the $\{x, y\}$ axes; in this way a parsimonious method is obtained that allows a really effective approach to Seidel aberration diagnostics.
LA - eng
UR - http://eudml.org/doc/194600
ER -

References

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  11. MINSKY, M.- PAPERT, S., Perceptrons, Cambridge, MA:MIT Press, 1969. Zbl0197.43702
  12. RUMELHART, D.- HINTON, G. E.- WILLIAMS, R. J., Learning internal representation by error propagation. Parallel Distribuited Processing (PDP): Exploration in the Microstructure of Cognition, MIT Press, Cambridge, Massachussetts, 1 (1986), 318-362. 
  13. WIZINOWICH, P.- LOYD-HART, M.- ANGEL, R., Adaptive Optics for Array Telescopes Using Neural Networks Techniques on Transputers, Transputing '91, IOS Press, Washington D.C., 1 (1991), 170-183. 

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