Optical field analysis by means of reduced Karhunen-Loeve representation with full element accounting

Yurij S. Musatenko; Vitalij N. Kurashov

doi:10.1117/12.295718

1 December 1997 Optical field analysis by means of reduced Karhunen-Loeve representation with full element accounting

Yurij S. Musatenko, Vitalij N. Kurashov

Proceedings Volume 3317, International Conference on Correlation Optics; (1997) https://doi.org/10.1117/12.295718
Event: International Conference on Correlation Optics, 1997, Chernivsti, Ukraine

Abstract

In this paper we suggest an algorithm of approximate Karhunen-Loeve (KL) transform which reduces the dimensionality of the problem. The new idea is to take into account every subsequent signal, which is not included in training set, with small counting cost. This signal is projected on somehow extended basis obtained on the previous step, then the correlation matrix int his representation is calculated, and the result is diagonalized, taking into account new signal. As far as KL basis obtained on the previous step should be quite optimal for every new analyzed signal, the correlation matrix will have small number of nondiagonal elements comparable with the average eigenvalue of the matrix. The main advantage is that we have quite good estimation of the KL basis at every moment of the calculation process. Hence, the suggested algorithm is well suited for real-time calculation.

Citation Download Citation

Yurij S. Musatenko and Vitalij N. Kurashov "Optical field analysis by means of reduced Karhunen-Loeve representation with full element accounting", Proc. SPIE 3317, International Conference on Correlation Optics, (1 December 1997); https://doi.org/10.1117/12.295718

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