## Abstract

We propose a new technique to improve the performance of the joint
transform correlator (JTC). In this technique we have applied
the phase-iterative algorithm to a phase-shifting JTC
(PSJTC). By doing so, we restrain the noise that is contained
in the recovered phase of the joint transform power spectra for the
input images with background and additive noise. In the case in
which the input image is embedded in the input noise, we find that, by
using the phase-iterative techniques with the PSJTC, one can get a
higher cross-correlation peak and signal-to-noise ratio than with a
PSJTC alone. From the computer-simulation results, one can conclude
that the proposed algorithm successfully enhances PSJTC performance,
especially for an input image with large noise.

© 1998 Optical Society of America

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### Equations (7)

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(1)
$${J}_{i}\left(u,v\right)=|F\left(u,v\right){|}^{2}+|R\left(u,v\right){|}^{2}+2|F\left(u,v\right)\Vert R\left(u,v\right)|cos[2\mathit{bu}+{\mathrm{\varphi}}_{F}\left(u,v\right)-{\mathrm{\varphi}}_{R}\left(u,v\right)+{\mathrm{\delta}}_{i}].$$
(2)
$${\mathrm{\varphi}}_{\mathrm{JTPS}}=2\mathit{bu}+{\mathrm{\varphi}}_{F}\left(u,v\right)-{\mathrm{\varphi}}_{R}\left(u,v\right)=\mathrm{arctan}\left[\frac{{\displaystyle \sum _{n=0}^{N-1}}{J}_{i}\left(u,v\right)sin\left(2\mathrm{\pi}n/N\right)}{{\displaystyle \sum _{n=0}^{N-1}}{J}_{i}\left(u,v\right)cos\left(2\mathrm{\pi}n/N\right)}\right].$$
(3)
$${\mathrm{\varphi}}_{\mathrm{JTPS}}=2\mathit{bu}+{\mathrm{\varphi}}_{F}\left(u,v\right)-{\mathrm{\varphi}}_{R}\left(u,v\right)=\frac{\sqrt{3}\left({J}_{1}-{J}_{2}\right)}{2{J}_{0}-{J}_{1}-{J}_{2}}.$$
(4)
$$\mathit{PJ}=exp\left(j{\mathrm{\varphi}}_{\mathrm{JTPS}}\right)=exp\left\{j\left[2\mathit{bu}+{\mathrm{\varphi}}_{F}\left(u,v\right)-{\mathrm{\varphi}}_{R}\left(u,v\right)\right]\right\}$$
(5)
$${I}_{i}\left(u,v\right)=1+cos\left({\mathrm{\varphi}}_{\mathrm{JTPS}}+\frac{2\mathrm{\pi}}{N}i\right),$$
(6)
$$\mathrm{PCE}=\frac{I{\left(x,y\right)}_{\mathrm{Max}}}{{\displaystyle \sum _{x,y=1}^{N}}I\left(x,y\right)},$$
(7)
$$\mathrm{SNR}=\frac{{\left[I{\left(x,y\right)}_{\mathrm{Max}}\right]}^{1/2}}{{\left[\frac{1}{n}{\displaystyle \sum _{x,\mathit{y}\notin R}}I\left(x,y\right)\right]}^{1/2}},$$