DECISION-THEORY APPROACH TO NONLINEAR JOINT-TRANSFORM CORRELATION

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.