P. Willett et B. Javidi, APPROXIMATE PERFORMANCE OF THE NONLINEAR JOINT TRANSFORM CORRELATOR IN SIGNALLIKE NOISE, Applied optics, 34(23), 1995, pp. 5218-5229
We present a statistical-analysis technique for a nonlinear joint tran
sform correlator (JTC) based on two the noise and the signal spectra a
re identical, and the signal energy is small relative to the The first
assumption, while admittedly convenient, is also defensible in that i
t is a worst case and in that image and scene noise can be similar in
texture. The second is also reasonable, given that even a clearly visi
ble signal may have small energy compared with the scene noise if it i
s of limited extent; in any case, the results appear moderately faithf
ul even for the case that signal and noise energies are equal. We disc
over that the optimal Fourier-plane transformation is spatially varian
t and tends to remove the Fourier amplitudes of the input image, and i
ndeed functions in a way very similar to the spatially variant binary
JTC. We also see that the classic (or spatially invariant linear) JTC
is a very inferior technique for signal-like noise, that the best spat
ially variant binary JTC uses a threshold proportional to the noise po
wer spectrum, and that, if a spatially invariant binary-thresholded JT
C is desired, then the median Fourier-plane value is an excellent choi
ce of threshold. The performance predictions are verified by simulatio
n and appear to be reasonable even for the highly nonlinear binary sch
emes.