Page 129 - Introduction to Information Optics

14 2. Signal Processing with Optics

1 Read the input data for the target and the antitarget train sets.
2. Determine the effective pixels of the BCF in the spatial domain. For
example, in an effective pixel there is at least one training target or
antitarget image the value of which is nonzero of this pixel. Notice that
the noneffective pixels are equiprobable to either — 1 or 1.
3. Assign different desired correlation distributions for the target training
set and the antitarget train set, respectively. In fact, a sharp correlation
profile can be assigned for the target training images and a null profile
for the antitarget training set, as illustrated in the chart.
4. Set the allowable error value. For example, a J % error rate is frequently
used.
5. Assign an initial bipolar composite filter function (IBCF), which is
assumed to have a random distribution of — 1 and 4-1 values.
6. Set the initial system temperature T. We select the initial kT in the order
of the desired correlation energy, as defined in step 3.
7. Calculate the energy function E for the initial system, which is the
mean-square error between the desired correlation function and the
correlation distribution obtained with the IBCF. We have

2
2
I ( f f{[OUx, y)~ W\x, y)] 4-[0? H(x, J')- W(x, y)] } dxdy) ,
•M= l \J J /

where O^x, y) and 0£,(x, y) are the target and antitarget correlation distribu-
tions for the mth training image obtained with IBCF, respectively. If we
let h(x, y) be the filter function of BCF, the correlation distribution with
respect to target function t m and antitarget a m can be expressed as

m(x, y) = h(x + x', y + y')t*(x, y') dx' dy'
j
f f (2.97)
£(x, y) = h(x + x',y + y')a*(x', y')dx'dy'.

8. By reversing the sign of a pixel (e.g., from — 1 to + 1) within the IBCF,
a new system energy E' is established. Calculate the change of system
energy AE of the system. If A£ < 0, the change sign of the pixel is
unconditionally accepted. Otherwise, it will be accepted based on the
Boltzmann probability distribution. Since h(x, y) is a bipolar function,
the iterative procedure for reversing the pixel processes is given by

w
fh (n + ' >(x, y) = ~ h (x, y), A£ < 0,
( + n
(n
\h " (x, y) = h \x, y) • sgn{ran[/KA£)] - p(A£)j, A£ ^ 0, c)