P. Refregier et F. Goudail, DECISION-THEORY APPROACH TO NONLINEAR JOINT-TRANSFORM CORRELATION, Journal of the Optical Society of America. A, Optics, image science,and vision., 15(1), 1998, pp. 61-67
We propose a new decision theory approach adapted to practical target
detection and location tasks in which the spectral density of Gaussian
additive noise is unknown. We determine the maximum likelihood and th
e maximum a posteriori solutions for that problem. We demonstrate that
the nonlinear joint-transform correlation, which is frequently used i
n optical correlators, can be considered an approximation of these opt
imal processors. This new result constitutes a theoretical support in
the context of detection theory for the use of nonlinearities in optic
al correlators. (C) 1998 Optical Society of America.