Cryptography Reference
In-Depth Information
Thus, with Eq. (12.11), the reconstructed vector is the conditional expec-
tation X
(1)
=
1
3
(j
17
+ j
18
+ j
19
) .
(4) If both channels break down, no description is received. We randomly
choose 0 or 1 to represent the embedded watermark bit W
2,k
. Also,
because no description is received, nothing can be reconstructed, hence
we set the luminance of that block to 128 for the 8-bit per pixel grey level
images.
12.7 Optimization with Tabu Search
12.7.1 Tabu Search Fundamentals
Tabu search is the meta-heuristic approach, or a kind of iterative search, and
is characterized by the use of a flexible memory. It is able to eliminate local
minima and to search areas beyond a local minimum [12, 13].
The process with which tabu search overcomes the local optima problem is
based on an evaluation function that chooses the highest evaluation solution
at each iteration. The building blocks of tabu search are stated as follows.
Forbidding strategy:
This strategy is employed to avoid cycling problems
by forbidding certain moves or classifying them as forbidden, or
tabu
.To
prevent the cycling problem, it is su
cient to check whether a previously
visited solution is revisited or not. An alternative way might be by not
visiting the solutions already visited during the last T
S
iterations. T
S
is
normally named the
tabu list length
or
tabu list size
. With the help of an
appropriate value of T
S
, the likelihood of cycling effectively vanishes.
Aspiration criteria and tabu restrictions:
An aspiration criterion is
applied to make a tabu solution which is not a forbidden state. That is
if this solution is of su
cient quality and is is able to prevent cycling. A
solution is acceptable if the tabu restrictions are satisfied. However, a tabu
solution is also assumed acceptable if an aspiration criterion applies re-
gardless of the tabu status. We also make use of tabu restrictions to avoid
repetitions but not reversals. A tabu restriction is typically activated only
when its attributes occur within a limited number of iterations prior to
the present iteration. Or they have occurred with a certain frequency over
a larger number of iterations. Finally, the appropriate use of aspiration
criteria can be very significant for enabling a tabu search to achieve its
best performance.
Freeing strategy:
The freeing strategy is taken into account in order to de-
cide what can exit the tabu list. This strategy removes tabu restrictions
of the solutions so that they can be reconsidered in further steps of the
search. The attributes of a tabu solution remain on the tabu list for a
