78 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 46, NO. 1, JANUARY 1999
Progressive Switching Median Filter for the Removal
of Impulse Noise from Highly Corrupted Images
Zhou Wang and David Zhang
Abstract— A new median-based filter, progressive switching median
(PSM) filter, is proposed to restore images corrupted by salt–pepper
impulse noise. The algorithm is developed by the following two main
points: 1) switching scheme—an impulse detection algorithm is used
before filtering, thus only a proportion of all the pixels will be filtered
and 2) progressive methods—both the impulse detection and the noise
filtering procedures are progressively applied through several iterations.
Simulation results demonstrate that the proposed algorithm is better than
traditional median-based filters and is particularly effective for the cases
where the images are very highly corrupted.
Index Terms— Image enhancement, impulse detection, median filter,
nonlinear filter.
I. INTRODUCTION
Images are often corrupted by impulse noise due to errors generated
in noisy sensors or communication channels. It is important to
eliminate noise in the images before some subsequent processing,
such as edge detection, image segmentation and object recognition.
For this purpose, many approaches have been proposed [1]. In the
past two decades, median-based filters have attracted much attention
because of their simplicity and their capability of preserving image
edges [1]–[4]. Nevertheless, because the typical median filters are
implemented uniformly across the image, they tend to modify both
noise pixels and undisturbed good pixels. To avoid the damage of
good pixels, the switching scheme is introduced by some recently
published works [3]–[7], where impulse detection algorithms are
employed before filtering and the detection results are used to control
whether a pixel should be modified. Fig. 1 shows a general framework
for such kinds of algorithms which proved to be more effective
than uniformly applied methods when the noise pixels are sparsely
distributed in the image. However, when the images are very highly
corrupted, a large number of impulse pixels may connect into noise
blotches. In such cases, many impulses are difficult to detect, thus
impossible to be eliminated. In addition, the error will propagate
around their neighborhood regions.
In this paper, we present a new median-based switching filter,
called progressive switching median (PSM) filter, where both the im-
pulse detector and the noise filter are applied progressively in iterative
manners. The noise pixels processed in the current iteration are used
to help the process of the other pixels in the subsequent iterations. A
main advantage of such a method is that some impulse pixels located
in the middle of large noise blotches can also be properly detected and
filtered. Therefore, better restoration results are expected, especially
for the cases where the images are highly corrupted.
II. PSM F
ILTER
A. Impulse Detection
Similar to other impulse detection algorithms, our impulse detector
is developed by a prior information on natural images, i.e., a noise-
Manuscript received April 30, 1997; revised June 12, 1998. This work was
supported in part by the UGC Fund, Hong Kong. This paper was recommended
by Associate Editor A. Nishihara.
The authors were with the Department of Computer Science, City Univer-
sity of Hong Kong, Kowloon, Hong Kong. They are now with the Department
of Computing, Hong Kong Polytechnic University, Kowloon, Hong Kong.
Publisher Item Identifier S 1057-7130(99)01479-2.
Fig. 1. A general framework of switching scheme-based image filters.
free image should be locally smoothly varying, and is separated by
edges [4]. The noise considered by our algorithm is only salt–pepper
impulsive noise which means: 1) only a proportion of all the image
pixels are corrupted while other pixels are noise-free and 2) a noise
pixel takes either a very large value as a positive impulse or a very
small value as a negative impulse. In this paper, we use noise ratio
R
(0
R
1)
to represent how much an image is corrupted. For
example, if an image is corrupted by
R
=30
% impulse noise, then
15% of the pixels in the image are corrupted by positive impulses
and 15% of the pixels by negative impulses.
Two image sequences are generated during the impulse detec-
tion procedure. The first is a sequence of gray scale images,
ff
x
(0)
i
g
;
f
x
(1)
i
g
;
111
;
f
x
(
n
)
i
g
;
111g
, where the initial image
f
x
(0)
i
g
is
the noisy image to be detected,
x
(0)
i
denotes the pixel value at position
iii
=(
i
1
;i
2
)
in the initial noisy image and
x
(
n
)
i
represents the pixel
value at position
iii
in the image after the
n
th iteration. The second
is a binary flag image sequence,
ff
f
(0)
i
g
;
f
f
(1)
i
g
;
111
;
f
f
(
n
)
i
g
;
111g
,
where the binary value
f
(
n
)
i
is used to indicate whether the pixel
iii
has been detected as an impulse, i.e.,
f
(
n
)
i
=0
means the pixel
iii
is good and
f
(
n
)
i
=1
means it has been found to be an impulse.
Before the first iteration, we assume that all the image pixels are
good, i.e.,
f
(0)
i
0
.
In the
n
th iteration
(
n
=1
;
2
;
111
)
, for each pixel
x
(
n
0
1)
i
we first
find the median value of the samples in a
W
D
2
W
D
(
W
D
is an odd
integer not smaller than 3) window centered about it. If we use
W
i
to represent the set of the pixels within a
W
2
W
window centered
about
iii
W
i
=
f
jjj
=(
j
1
;j
2
)
j
i
1
0
(
W
0
1)
=
2
j
1
i
1
+(
W
0
1)
=
2
;
i
2
0
(
W
0
1)
=
2
j
2
i
2
+(
W
0
1)
=
2
g
(1)
then we have
m
(
n
0
1)
i
=Med
f
x
(
n
0
1)
j
j
jjj
2
W
i
g
:
(2)
The difference between
m
(
n
0
1)
i
and
x
(
n
0
1)
i
provides us with a simple
measurement to detect impulses
f
(
n
)
i
=
f
(
n
0
1)
i
;
if
j
x
(
n
0
1)
i
0
m
(
n
0
1)
i
j
<T
D
1
;
else
(3)
where
T
D
is a predefined threshold value. Once a pixel
iii
is detected
as an impulse, the value of
x
(
n
)
i
is subsequently modified
x
(
n
)
i
=
m
(
n
0
1)
i
;
if
f
(
n
)
i
6
=
f
(
n
0
1)
i
x
(
n
0
1)
i
;
if
f
(
n
)
i
=
f
(
n
0
1)
i
:
(4)
Suppose the impulse detection procedure is stopped after the
N
D
th iteration, then two output images—
f
x
(
N
)
i
g
and
f
f
(
N
)
i
g
are
obtained, but only
f
f
(
N
)
i
g
is useful for our noise filtering algorithm.
It should be mentioned that the impulse detection measurement
used here is first introduced by Sun and Neuvo in their switch I
scheme [4]. The difference between our method and Sun and Neuvo’s
algorithm is that our method is iteratively applied, so that the impulses
are detected progressively through several iterations. Later simulation
results show that our algorithm performs better when the noise ratio
is high.
1057–7130/99$10.00 1999 IEEE
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 46, NO. 1, JANUARY 1999 79
B. Noise Filtering
Like the impulse detection procedure, the noise filtering
procedure also generates a gray scale image sequence,
ff
y
(0)
i
g
;
f
y
(1)
i
g
;
111
;
f
y
(
n
)
i
g
;
111g
, and a binary flag image
sequence
ff
g
(0)
i
g
;
f
g
(1)
i
g
;
111
;
f
g
(
n
)
i
g
;
111g
. In the gray scale
image sequence, we still use
y
(0)
i
to denote the pixel value at
position
iii
in the noisy image to be filtered and use
y
(
n
)
i
to represent
the pixel value at position
iii
in the image after the
n
th iteration. In
a binary flag image
f
g
(
n
)
i
g
, the value
g
(
n
)
i
=0
means the pixel
iii
is
good and
g
(
n
)
i
=1
means it is an impulse that should be filtered.
A difference between the impulse detection and noise-filtering
procedures is that the initial flag image
f
g
(0)
i
g
of the noise-filtering
procedure is not a blank image, but the impulse detection result
f
f
(
N
)
i
g
, i.e.,
g
(0)
i
f
(
N
)
i
:
In the
n
th iteration
(
n
=1
;
2
;
111
)
, for each pixel
y
(
n
0
1)
i
, we also
first find its median value
m
(
n
0
1)
i
of a
W
F
2
W
F
(
W
F
is an odd
integer and not smaller than 3) window centered about it. However,
unlike that in the impulse detection procedure, the median value here
is selected from only good pixels with
g
(
n
0
1)
j
=0
in the window.
Let
M
denote the number of all the pixels with
g
(
n
0
1)
j
=0
in the
W
F
2
W
F
window. If
M
is odd, then
m
(
n
0
1)
i
=Med
f
y
(
n
0
1)
j
j
g
(
n
0
1)
j
=0
;jjj
2
W
i
g
:
(5)
If
M
is even but not 0, then
m
(
n
0
1)
i
=(
Med
L
f
y
(
n
0
1)
j
j
g
(
n
0
1)
j
=0
;jjj
2
W
i
g
+Med
R
f
y
(
n
0
1)
j
j
g
(
n
0
1)
j
=0
;jjj
2
W
i
g
)
=
2
(6)
where
Med
L
and
Med
R
denote the left and the right median values,
respectively. That is,
Med
L
is the
(
M=
2)
th largest value and
Med
R
is the
(
M=
2+1)
th largest value of the sorted data. The value of
y
(
n
)
i
is modified only when the pixel
iii
is an impulse and
M
is greater
than 0:
y
(
n
)
i
=
m
(
n
0
1)
i
if
g
(
n
0
1)
i
=1
;
M>
0
:
y
(
n
0
1)
i
else.
(7)
Once an impulse pixel is modified, it is considered as a good pixel
in the subsequent iterations
g
(
n
)
i
=
g
(
n
0
1)
i
if
y
(
n
)
i
=
y
(
n
0
1)
i
0
if
y
(
n
)
i
=
m
(
n
0
1)
i
:
(8)
The procedure stops after the
N
F
th iteration when all of the impulse
pixels have been modified, i.e.,
i
g
(
N
)
i
=0
:
(9)
Then we obtain the image
f
y
(
N
)
i
g
which is our restored output
image.
III. I
MPLEMENTATION AND SIMULATION
In our experiments, the original test images are corrupted with
fixed valued salt–pepper impulses, where the corrupted pixels take
on the values of either 0 or 255 with equal probability. Mean square
error (MSE) is used to evaluate the restoration performance. MSE
is defined as
MSE
=
1
N
i
(
u
i
0
v
i
)
2
(10)
where
N
is the total number of pixels in the image,
u
i
and
v
i
are
the pixel values at position
iii
in the original and the test images,
respectively.
To implement the PSM algorithm, four parameters must be pre-
determined. They are the filtering window size
W
F
, the impulse
detection window size
W
D
, the impulse detection iteration number
N
D
and the impulse detection threshold
T
D
. Our experiments show
Fig. 2. The effects of
W
D
with respect to MSE, where
W
F
=3
,
N
D
=3
,
and
T
D
=50
.
Fig. 3. The effects of
T
D
with respect to MSE. For R = 10%,
W
F
=3
,
W
D
=3
, and
N
D
=3
; for R = 30%,
W
F
=3
,
W
D
=5
, and
N
D
=3
;
for R = 50%,
W
F
=3
,
W
D
=5
, and
N
D
=3
.
Fig. 4. A comparison of different median-based filters for the restoration of
corrupted image “bridge” under a large range of impulse noise ratio.
that almost all the best restoration results are obtained when
W
F
=3
and
N
D
=3
. In addition, these two parameters are not sensitive to
noise rate and image type. Therefore, we simply set both
W
F
and
N
D
to be 3. The other two parameters,
W
D
and
T
D
, are sensitive
to how much the image is corrupted. From Fig. 2, we can observe
that, for image “Bridge,”
W
D
=3
is more suitable for low noise
ratio and
W
D
=5
is better for high noise ratio, with a cross point at
about
R
=30
%. The experiments on some other images give similar
conclusion except that the cross point may be a little bit lower or
higher such as
R
=25
%or
R
=35
%. The influence of
T
D
is
investigated in Fig. 3. It appears that the best
T
D
is decreasing with
80 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 46, NO. 1, JANUARY 1999
(a) (b) (c) (d)
(e) (f) (g) (h)
Fig. 5. Restoration results of different median-based filters. (a) Corrupted image “peppers” with 50% salt–pepper noise. (b) Median filter with 3
2
3 window
size. (c) Iterative median filter with 3
2
3 window size and 8 iterations. (d) CWM filter with
5
2
5
window size and a center weight of 3. (e) Switch
I median filter with 3
2
3 window size. (f) Iterative switch I median filter with 3
2
3 window size and 8 iterations, where the noise detection threshold
is 40. (g) The PSM filter. (h) Original image of “peppers.”
the increase of
R
. To determine
W
D
and
T
D
, we first make a rough
estimation on the noise ratio, which again uses the impulse detection
measurement of Sun and Neuvo’s switch I scheme [4]. Initially, we
set
N
I
=0
(11)
where
N
I
is the number of impulses that have been detected. For
each pixel
x
i
, we find the median value of the samples in the 3
2
3
window centered about it
m
i
=Med
f
x
j
j
jjj
2
3
i
g
:
(12)
The difference between
m
i
and
x
i
is used to make a decision on
whether it is an impulse
if
j
m
i
0
x
i
j
T
I
;
then
N
I
+1
!
N
I
(13)
where the threshold
T
I
is predefined as 40 in our experiments. After
all the pixels in the image have been scanned once, we give an
estimation of the noise ratio as
^
R
=
N
I
=N
(14)
where
N
is the total number of pixels in the image. Then
W
D
and
T
D
are defined according to
^
R
W
D
=
3
;
if
^
R
T
R
5
;
if
^
R>T
R
(15)
T
D
=
a
+
b
1
^
R:
(16)
According to our experimental results, we choose
T
R
,
a
, and
b
as
25%, 65, and
0
50, respectively.
Although our parameter preselection scheme brings about several
new parameters, the restoration results are experimentally less sensi-
tive to them, thus only rough estimations are needed. This is important
for the usage of the PSM filter in real applications, where statistical
information about the given corrupted images may be unavailable.
While our parameter selection is based on the experiments on a small
set of images such as “bridge” and “Lena,” the results on other images
are also good.
We test our PSM algorithm and compare it with other well known
median-based filters, which are the simple median filters, the iterative
median filter (iteratively apply the simple median filter), the center
weighted median (CWM) filter, the switch I median filter, and
the iterative switch I median filter (iteratively apply the switch I
median filter). The experiments are carried out on several 512
2
512,
8 bits/pixel gray scale images. We provide the MSE performance
in Fig. 4 where the original test image “bridge” is corrupted with
different impulse noise ratios ranging from 5% to 70%. The MSE
curves demonstrate that our PSM algorithm is better than other
median-based methods, especially when noise ratios are high. In Fig.
5, we show the restoration results of different filtering methods for test
image “peppers” highly corrupted with 50% impulse noise. Both the
simple 3
2
3 median filter and the switch I median filter can preserve
image details but many noise pixels are remained in the image. The
CWM filter performs better than simple median filter, but it still
influences good pixels and misses many impulse pixels. The iterative
median filter removes most of the impulses, but many good pixels are
also modified, resulting in blurring of the image. Since the iterative
switch I filter does not modify good pixels in the image, it maintains
image details better than the iterative median filter, but many noise
blotches still remained in the image. Dramatic restoration results are
obtained by our PSM filter. It can remove almost all of the noise
pixels while preserve image details very well.
R
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