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 the maximum a posteriori solutions for that problem. We demonstrate that the nonlinear joint-transform correlation, which is frequently used in optical correlators, can be considered an approximation of these optimal processors. This new result constitutes a theoretical support in the context of detection theory for the use of nonlinearities in optical correlators.
© 1998 Optical Society of America
Original Manuscript: March 10, 1997
Revised Manuscript: July 28, 1997
Manuscript Accepted: August 18, 1997
Published: January 1, 1998
Philippe Réfrégier and François Goudail, "Decision theory approach to nonlinear joint-transform correlation," J. Opt. Soc. Am. A 15, 61-67 (1998)