06-11-2012, 04:05 PM
Image processing optimization by genetic algorithm with a new coding scheme
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Abstract
An original coding scheme is introduced to take advantage of the two-dimensional structural information of images within
the genetic algorithm framework. Results are presented showing that this new technique outperforms classical optimization
methods for the optimization of 32 × 32 and 128 x 128 holograms
Introduction
In the last ten years, iterative optimization techniques
have been applied in a wide range of domains,
from electronic circuit design to image processing.
These techniques are particularly adapted to nonlinear
multi-dimensional problems where no analytical solutions
can be found and where the search space is too
large for combinatorial search.
This paper compares some of these techniques in
the particular application of computer generated holograms
which have arisen as a very promising domain
in the field of reconfigurable optical devices with applications
in telecommunication and network design.
The main problem in this case is that a fully complex
transfer function, which is the optimal solution cannot
be displayed on the currently available fast ferroelec-
tric liquid crystal (FLC) electro-optical devices for
which the coding domain is limited to binary images
only. Iterative techniques therefore have to be applied
to find the optimal binary image whose Fourier transform
(called reconstruction of the hologram) gives a
determined image (called target).
Inverse Fourier transform algorithm
This technique is derived from the classical Projection
Onto Convex Set ( POCS) algorithm which was
first introduced by Levi and Stark (1983). This algorithm
relies on imposing constraints and finding the
optimal solution under these constraints. It is an iterative
procedure where, during each iteration, the solution
is projected onto each set of constraints at every
iteration until a stop condition is met. Convergence is
only ensured when the constraints define convex sets
in the search space with a non-empty intersection.
Kotzer et al. (1993; 1994a; 1994b) extended the
algorithm to non-convex sets with possibly empty intersection
and proved the convergence. However, in
the last case, the optimal solution does not lie in any
of the constraint sets. In our example, a projection is
therefore required to transform such an optimal (but
useless) solution into a binary image X. This operation
often leads to sub-optimal solutions when compared
with solutions where the input binary nature of
the image is taken into account during the iterative
process itself.
Genetic algorithm
The genetic algorithm is a population-based iterative
optimization method. Instead of just pushing iteratively
a single candidate toward the optimal solution,
it acts on a set of such solution candidates by
simultaneously exploring several zones of the search
space and by combining promising solution candidates,
hopefully for the better.
We use a standard steady-state genetic algorithm
(Davis, 1990) with an elitist selection strategy (the
best candidate from one iteration is always kept to the
next one notwithstanding that it might have been modified
by mutation or crossover). The mutation operator
is applied as usual on randomly chosen candidates
and a single pixel of the candidate image is change.
Conclusion
We have presented a new genetic algorithm coding
scheme which takes into account the particular twodimensional
structure of an image. This new scheme
has been tested for computer generated hologram design
on a classical target example. The results have
also been compared with those obtained with other
techniques such as Hill Climbing, Simulated Annealing
and Projection Onto Convex Set.