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

in this paper we suggest an algorithm of approximate Karhumen-Loeve (KL) transform which reduces the dimensionality of the problem. The nevi idea is to take into account every subsequent signal, which is not included in training set, with small computing cost. This signal is projected on somehow extended basis obtained on the previous step, then the correlation matrix in this representation is calculated, and the result is diagonalized, taking into account new signal. As far as ML 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.