APPROXIMATE PERFORMANCE OF THE NONLINEAR JOINT TRANSFORM CORRELATOR IN SIGNALLIKE NOISE

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.