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ing median filter with some signal dependent thresh-
olds and their optimal designing method based on
the noise probability distribution. In this paper, the
switching median filter, which has two kinds of the
thresholds, is introduced. One is switching thresholds
to detect the noise, and the other is selecting thresh-
olds to choose the suitable switching threshold. In the
proposed method, we employ a variance of signals for
the selecting threshold. Thus, the suitable switching
threshold is decided depending on the signal of con-
cern by using the selecting thresholds.
All of the switching and selecting thresholds of
the proposed switching median filter are automati-
cally designed by using GA, which is a search al-
gorithm based on the mechanism of natural selection
and natural genetics (Goldberg, 1989), (Davis, 1990).
GA solves optimization problems by using individu-
als which are represented by bit-strings or real valued-
genes. In the proposed method, GA tunes all thresh-
olds so as to minimize a distribution distance between
the assumed and the detected noises.
Through the experiments, the effectiveness and
validity of the proposed method are illustrated.
2 NOISE MODEL AND
SWITCHING MEDIAN FILTER
2.1 Random-valued Impulse Noise
In this paper, we consider a monochrome image cor-
rupted with the random-valued impulse noise in a
transmission of the digitalized signal. Impulse noises
are caused by malfunctioning pixels in camera sen-
sors, faulty memory locations in hardware or trans-
mission in a noisy channel.
A signal x(i, j) corrupted with the random-valued
impulse noise is represented by:
x(i, j) =
{
s(i, j), probability 1 − p,
h, probability p,
(1)
where, s(i, j) is the source signal, and takes 256 level
(8 bit) values. p represents a noise occurrence proba-
bility. The noise-corrupted pixel value h takes from 0
to 255, because each bit in s(i, j) inverts randomly.
This model is the most popular and focuses on a
bit error in the digitalized signal transmission. There-
fore, the signals corrupted with the random-valued
impulse noises can be assumed as a uniform distri-
bution.
2.2 Detailed-preserving Median Based
Filter
A detailed-preserving median based filter is the most
popular switching median filter (Sun and Neuvo,
1994). In this method, the impulse noises are detected
by considering difference between a pixel value of
concern and a median of its neighboring pixel values.
This method uses a noise position image f
(ε)
(i, j)
defined by:
f
(ε)
(i, j) =
{
1, |x(i, j) − x
MED
(i, j)| ≥ ε,
0, otherwise,
(2)
where x
MED
(i, j) stands for the output signal at the
pixel (i, j) by the ordinary median filter. The noise
position image contains coordinate information of the
detected noises. In the noise position image, “1” rep-
resents that the pixel is corrupted by the noise. The
switching median filter carries out the median filter-
ing only for the detected pixels by using the noise po-
sition image. Here ε is a threshold.
In the past, various types of the switching median
filter have been proposed for the effective detection
of the salt-pepper impulse noise. Furthermore, some
of them have been also applied to the detection of the
random-valued impulse noise. However, in the con-
ventional methods, the suitable threshold ε has been
adjusted manually and empirically depending on the
situations, because effective indicators for the filter
design have not been discussed so far. Additionally,
the switching median filter with only a fixed thresh-
old has an inherent limitation on the noise detection
performance.
In order to raise the noise detection performance,
it is preferable to change the threshold depending on
the target and its neighboring signals automatically.
3 PROPOSED METHOD
3.1 Counstruction of Proposed
Switching Median Filter
The proposed switching median filter has two sets of
thresholds. One is the switching thresholds {ε
m
| m =
1,··· ,N}, and the other is the selecting thresholds
{v
n
| n = 1, ··· , N − 1}. Each switching threshold is a
value, and it is used in order to judge the target signal
as the source or the noise. The selecting thresholds
work to choose the suitable switching threshold from
the set of the switching thresholds. Thus, the pro-
SwitchingMedianFilterwithSignalDependentThresholdsDesignedbyusingGeneticAlgorithm
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