3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference

Nikolai I. Chernov; Genadij A. Ososkov; Luc Pronzato

Applications of Mathematics (1992)

  • Volume: 37, Issue: 6, page 437-452
  • ISSN: 0862-7940

Abstract

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Let v 1 , v 2 , . . . , v k be vertices in the X Y Z -space, each vertex producing several tracks (straight lines) emanating from it within a narrow cone with a small angle about a fixed direction ( Z -axis). Each track is detected (by drift chambers or other detectors) by its projections on X Y and Y Z views independently with small errors. An automated method is suggested for the reconstruction of vertices from noisy observations of the tracks projections. The procedure is based on the likelihood inference for mixtures. An illustrative example is considered.

How to cite

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Chernov, Nikolai I., Ososkov, Genadij A., and Pronzato, Luc. "3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference." Applications of Mathematics 37.6 (1992): 437-452. <http://eudml.org/doc/15726>.

@article{Chernov1992,
abstract = {Let $v_1, v_2,..., v_k$ be vertices in the $XYZ$-space, each vertex producing several tracks (straight lines) emanating from it within a narrow cone with a small angle about a fixed direction ($Z$-axis). Each track is detected (by drift chambers or other detectors) by its projections on $XY$ and $YZ$ views independently with small errors. An automated method is suggested for the reconstruction of vertices from noisy observations of the tracks projections. The procedure is based on the likelihood inference for mixtures. An illustrative example is considered.},
author = {Chernov, Nikolai I., Ososkov, Genadij A., Pronzato, Luc},
journal = {Applications of Mathematics},
keywords = {3-dimensional multivertex reconstruction; 2-dimensional tracks observations; projections; reconstruction of vertices; noisy observations; likelihood inference for mixtures; 3-dimensional multivertex reconstruction; 2-dimensional tracks observations; projections; reconstruction of vertices; noisy observations; likelihood inference for mixtures},
language = {eng},
number = {6},
pages = {437-452},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference},
url = {http://eudml.org/doc/15726},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Chernov, Nikolai I.
AU - Ososkov, Genadij A.
AU - Pronzato, Luc
TI - 3-dimensional multivertex reconstruction from 2-dimensional tracks observations using likelihood inference
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 6
SP - 437
EP - 452
AB - Let $v_1, v_2,..., v_k$ be vertices in the $XYZ$-space, each vertex producing several tracks (straight lines) emanating from it within a narrow cone with a small angle about a fixed direction ($Z$-axis). Each track is detected (by drift chambers or other detectors) by its projections on $XY$ and $YZ$ views independently with small errors. An automated method is suggested for the reconstruction of vertices from noisy observations of the tracks projections. The procedure is based on the likelihood inference for mixtures. An illustrative example is considered.
LA - eng
KW - 3-dimensional multivertex reconstruction; 2-dimensional tracks observations; projections; reconstruction of vertices; noisy observations; likelihood inference for mixtures; 3-dimensional multivertex reconstruction; 2-dimensional tracks observations; projections; reconstruction of vertices; noisy observations; likelihood inference for mixtures
UR - http://eudml.org/doc/15726
ER -

References

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  6. Silvey S. D., Optimal Design, Chapman & Hall, London, 1980. (1980) Zbl0468.62070MR0606742
  7. Torsney B., A moment inequality and monotonicity of an algorithm, Semi-Infinite Programming and Applications (A. V. Fiacco and K. O. Kortanek, eds.), Springer-Verlag, Berlin, 1983, pp. 249-260. (1983) Zbl0512.90082MR0709281
  8. Torsney B., Computing optimizing distributions with applications in design, estimation and image processing, Optimal Design and Analysis of Experiments (Y. Dodge, V. V. Fedorov and H. P. Wynn, eds.), North-Holland, Amsterdam, 1988, pp. 361-370. (1988) 
  9. Wynn H. P., 10.1214/aoms/1177696809, Annals of Math. Stat. 41 (1970), 1655-1664. (1970) Zbl0224.62038MR0267704DOI10.1214/aoms/1177696809

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