The correlation performance of the nonlinear joint transform correlator for input images containing a target embedded in input noise is investigated. We focus on a class of images for the target, the input image, and the input noise for which nonlinear joint transform correlators perform well. The target and the input noise have low-pass characteristics; that is, they are not band limited but have most of their energies in the low spatial frequency domain. The analytical results show that for this class of low-pass (but not band-limited) images, the binary joint transform correlator outperforms other types of kth-law nonlinear joint transform correlators with k ≠ 0 when the input-noise bandwidth is less than the target bandwidth. We show that binary nonlinear joint transform correlators perform well when the input noise is signallike; that is, the input noise or the objects to be rejected have energy spectra that are similar to the target energy spectrum. Correlation tests with computer simulations are presented. The nonlinear joint transform correlator performance is determined for various degrees of nonlinear transformations and for different input-noise parameters. For the nonlinear joint transform correlator the correlation-signal term and the output-noise term arising from the input noise are determined for various degrees of nonlinearity for the target embedded in input noise.
© 1994 Optical Society of America
Original Manuscript: October 19, 1992
Revised Manuscript: July 16, 1993
Published: February 10, 1994
Bahram Javidi, Jun Wang, and Amir H. Faziollahi, "Performance of the nonlinear joint transform correlator for images with low-pass characteristics," Appl. Opt. 33, 834-848 (1994)