01-10-2012, 04:19 PM
An Image Noise Reduction Technique Based on the Fuzzy Rules
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Abstract
Aiming at that an image is typical non-stationary
signal, an image noise reduction technique based on
the fuzzy rules is proposed. This image processing
system(IPS) is realized as a time-variant system in
which the system parameters change continuously
depending on the local characteristics of the images.
Here Gaussian noise is considered in noise reduction.
The fuzzy rules are used to consider the unstableness
and uncertainty of signals. The nonlinear function
representing the fuzzy rule-based IPS depends on the
rules concerning the local characteristics of the input,
on the membership functions, and on the used
defuzzification method. In order to make the system
performance as high as possible, these factors must be
determined to be the most appropriate ones. In this
paper a method for designing the optimum nonlinear
function directly from the local characteristics of
training data is presented. Here the rules, the
membership functions, and the way of defuzzification
are not necessary to be known.
Introduction
An image is regarded as an unstable signal.
Unstableness must be considered in image processing.
One of efficient methods for image processing is to
control the system parameters relying on the local
characteristics of the image [1],[2]. Usual filtering
techniques are unable to be applied for removing noise
of an image corrupted by additive random noise,
because they smooth out the edges as well. Therefore,
the system must discriminate flat regional parts of the
image from steeply changing ones such as edges, and
then set the system parameters for each part separately.
But such control cannot be performed specifically, for
the definition of the signal characteristics and the rules
describing how to control the system parameters are
often represented in an uncertain form.
Design of image processing system based on
the fuzzy rules
The nonlinear function w(k,m) describing fuzzy
rule-based image processing system relies on the rules
correlating to the local characteristics of the input and
w(k ,m) , on the membership function, and on the
used diffuzification method. Correspondingly, the
performance of the image processing system depends
on these factors. These factors must be decided to be
the most appropriate ones. To make the system
performance as good as possible, Several methods are
suggested for optimization of the fuzzy systems, using
training methods such as genetic algorithms [4]. In
image processing system proposed here, as these
factors are reasoned in the nonlinear function w(k,m) ,
the total optimization of them can be more simply
implemented by optimizing the nonlinear function
w(k,m) . Here a method for designing the optimal
nonlinear function directly from the local
characteristics of training data is introduced.
Conclusion
A fuzzy rule-based image noise reduction technique
is presented in this paper which takes Gaussian noise as
an example for considering the application of this
image noise reduction system. Experiments show that
the proposed image noise reduction technique is better
than other filters such as the weighted averaging filter
and median filter. The methodology to represent fuzzy
rules as a nonlinear function for optimization can be
applied to other signal processing and control problems
as well. In optimizing the nonlinear function, any other
optimizing method can be used. However, in this paper
steplike approximation is chosen, because it is simple
and it can avoid disadvantages of other methods.