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3-dimensional multivertex reconstruction; 2-dimensional tracks observations; projections; reconstruction of vertices; noisy observations; likelihood inference for mixtures
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.
[1] Böhning D: Likelihood inference for mixtures: geometrical and other constructions of monotone step-length algorithms. Biometrika 76 no. 2 (1989), 375-383. DOI 10.1093/biomet/76.2.375 | MR 1016029
[2] Fedorov V. V.: Theory of Optimal Experiments. Academic Press, New York, 1972. MR 0403103
[3] Lindsay B. G.: The geometry of mixture likelihoods: a general theory. Annals of Stat. 11 no. 1 (1983), 86-94. MR 0684866 | Zbl 0512.62005
[4] Mallet A.: A maximum likelihood estimation method for random coefficient regression models. Biometrika 73 no. 3 (1986), 645-656. DOI 10.1093/biomet/73.3.645 | MR 0897856 | Zbl 0615.62083
[5] Pázman A.: Foundations of Optimum Experimental Design. co-editor VEDA, Bratislava, Reidel, Dordrecht, 1986. MR 0838958
[6] Silvey S. D.: Optimal Design. Chapman & Hall, London, 1980. MR 0606742 | Zbl 0468.62070
[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. MR 0709281 | Zbl 0512.90082
[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.
[9] Wynn H. P.: The sequential generation of D-optimum experimental designs. Annals of Math. Stat. 41 (1970), 1655-1664. DOI 10.1214/aoms/1177696809 | MR 0267704 | Zbl 0224.62038
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