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CHAPTER 5
FILTERING ALGORITHMS FOR REMOVAL OF MULTIPLICATIVE SPECKLE NOISE IN
IMAGES WITH EDGE PRESERVATION
5.1 INTRODUCTION
Synthetic Aperture Radar (SAR) is an active sensor that uses
microwave signals for transmission and it detects the wave that is reflected
back by the objects. SAR is widely used for obtaining high resolution images
of the earth. It is used in the fields of remote sensing, oceanography, geology,
ecology and interferometry. Pixels in the image represent the back scattered
radiation from an area in the imaged scene. Brighter areas are produced by
stronger radar responses and darker areas are from weaker radar responses.
Speckle noise is an undesirable effect caused by coherent
reconstruction of the image and gives the image a grainy appearance. Speckle
may be modelled as a correlated signal and it is modelled as a multiplicative
noise in contrast to additive Gaussian and impulse noise as explained by
Zaman and Moloney (1993). Speckle noise is the primary source of
corruption in coherently illuminated images. Typical noise smoothing
methods are not well suited for the removal of speckle noise as explained by
Mark and Qing (1995). Various researchers, namely, Lee, Kuan, Frost have
proposed speckle removing algorithms useful for the radar community. The
filter algorithm proposed by Lee (1981) is based on the variance over an area
and smoothing will be performed only if the variance is low or constant over
an area. Another disadvantage is that the speckle noise in the edges is not
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removed by the filter. A simple speckle smoothing algorithm proposed by Lee
(1983) is based on the sigma probability of a Gamma distribution and is
effective in removing speckle but does not perform well in preserving edges.
This is because of the fact that if edges do not lie in the two sigma range, they
are not considered for averaging. The two sigma filter removes noise and the
smoothed image suffers some contrast loss as stated by Lee (1983). The kuan
et al (1987) filter is considered to be superior to the Lee filter. It simply
models the multiplicative noise of speckle into an additive linear form, but it
relies on the ENL from a SAR image. The only limitation with kuan filter is
that the ENL parameter is needed for computation. The Enhanced Frost filter
proposed by Lopes et al (1990) is an extension of the Frost filter that further
divides the image into homogeneous, heterogeneous and isolated point target
areas. By using this filter, the speckle noise in the heterogenous regions is
reduced but not removed so as to preserve the quality of image. De noising
using wavelet based algorithm is also known to be more efficient than
standard speckle filters. But they have a disadvantage of more computational
complexity than the speckle removing filters based on local order statistics
and also they require a compact support of wavelet basis functions that allows
wavelet transformation to efficiently represent the signals which have
localised features.
The adaptive filters that have been proposed in the earlier chapters
are tested with the images contaminated by speckle noise. Even though
adaptive filters perform well for any kind of image and any kind of noise, it is
found that the filters proposed in the chapters 2, 3, 4 do not completely
remove speckle noise. In order to remove speckle noise completely with edge
preservation properties, a computationally efficient and simple algorithm is
proposed in this chapter. The subjective and objective analyses of the filters
are done and the filter is compared with the standard sigma filter, mean,
median and adaptive bidirectional max/median filters.
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5.2 SPECKLE SMOOTHING ALGORITHM WITH EDGE
PRESERVATION
5.2.1 Noisy corrupted image model
The original signal is corrupted by a multiplicative noise of mean 1
and variance σn. It is given as below
),(),(),( jinjixjis (5.1)
where x(i,j) is the original signal , n(i,j) is the multiplicative noise whose
statistics depend on the signal and s(i,j) is the noise corrupted signal.
5.2.2 Proposed filter Algorithm
A new filtering structure is proposed to remove speckle noise with
edge preservation and removal of noise in the edges also.
The proposed algorithm is based on local order statistics to remove
speckle noise with edge preservation capabilities and the filtering algorithm is
given the name ‘New Filter III’.
The block diagram of the proposed filter is depicted as below
Figure 5.1 Block diagram of New Filter III
3 sigma filter
Edge detector
Reconstructed image y(i,j)
Corrupted image,s(i,j)
f(i,j)
e(i,j)
Filtering of Edges (If they are corrupted)
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The algorithm is explained as below.
The corrupted signal pixels are designated as s(i,j). The mean of s(i,j) is
),(),(),(),( jixjinjixjis (5.2)
This is because of the established fact in theory that speckle obeys a negative
exponential distribution and, therefore, is multiplicative in nature in the sense
that its standard deviation is equal to its mean.
5.2.2.1. 3 Sigma filter
The corrupted image is processed by a 3 sigma filter as below
i) Let the corrupted signal considered within m x n window be
s(m,n)and its variance is calculated as
Var(s(m,n)) = [standard deviation of s(m,n)/mean of s(m,n)]2; (5.3)
ii) Let the average value of the pixels of ‘s’ be mean(s(m,n)) and
the lower and upper intensity values are calculated as
)),(var()),((3),(( nmsnmsmeannmsmeancl (5.4)
)),(var()),((3),(( nmsnmsmeannmsmeancu (5.5)
iii) The intensity value of each pixel inside the window is compared
with the values of cl and cu. If it lies between the limits of cl
and cu, then the pixel is considered to be the pixel within the
lower and upper variance limits. The centre pixel in the window
is then replaced by the mean of the pixels whose intensity
values lie between cl and cu.
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Since the intensity values lying within the limited variance are
involved in the averaging, the speckle noise is removed with better reduction
in blur.
Since the noise is multiplicative, the intensity value of the corrupted
pixels is high if the value of the original brightness of the pixel is very high.
In 3 sigma filter, the pixels within the prescribed standard deviation are
averaged. Since the edges are of high intensity values, they are not involved
in the averaging process. In order to preserve these discarded edges, a high
pass filter is used to detect edges and the edges are preserved. The edges are
preserved if they are not corrupted and they are replaced by the non corrupted
neighbourhood pixel in case of corruption.
5.2.2.2 Edge detection and preservation
The edges in an image are detected using a computationally simple
technique ie., using a high pass filter. Edges are of high intensity values and if
they are corrupted by multiplicative noise, their intensity values are further
increased. The edges can be identified by comparing the absolute value of the
difference in the amplitude of the two samples with a threshold. For an image
of s(i,j) with a window 3×3, the edges in all the four directions such as the
horizontal, vertical, diagonal and sub diagonal directions are detected as
eh(i,j), ev(i,j),ed(i,j) and esd(i,j) .e(i,j) is considered as eh(i,j), the horizontal
edge if
| e(i-1,j) –e(i,j) | > ‘t’ (or) | e(i+1,j) –e(i,j) | > ‘t’
e(i,j) is considered as ev(i,j) , the vertical edge if
| e(i,j-1) –e(i,j) | > ‘t’ (or) | e(i,j+1) –e(i,j) | > ‘t’
e(i,j) is considered as ed(i,j) , the diagonal edge if
| e(i-1,j-1) –e(i,j) | > ‘t’ (or) | e(i+1,j+1) –e(i,j) | > ‘t’
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e(i,j) is considered as esd(i,j) , the sub diagonal edge if
| e(i-1,j+1) –e(i,j) | > ‘t’ (or) | e(i+1,j-1) –e(i,j) | > ‘t’
The optimum value of ‘t’ is found by using many images and different
amounts of noise.
In theory, the objective quality of the image is not degraded if a
pixel is replaced by the neighbourhood pixel. This is because of the fact that
the pixel along with its neighbourhood pixels influences the visual
interception. Hence if the edges are found to be corrupted by speckle noise,
they are replaced by the minimum neighbourhood uncorrupted pixel. The
signal is identified as corrupted by multiplicative noise by the fact that the
‘coefficient of variation’, (ratio of the standard deviation to the signal value)
remains constant. Hence the output of the edge filtering block is free from
noise and thus the edges are preserved and are free from noise.
The reconstruction block does the work of combining the output of
the 3 sigma filter and the output of the edge filter. If e(i,j) = 0, then the
output= f(i,j) and if f(i,j)=0, then output=e(i,j). Thus the simple technique
efficiently provides the output image which is free from speckle noise. The
edges are preserved and noises in edges are also removed.
5.3 RESULTS AND DISCUSSION
The proposed algorithm is tested using a remotely sensed image of
256 × 255 pixels with 8 bits /pixel and a natural image ‘Lena’ image of
256 × 256 pixels with 8 bits /pixel. The original image is corrupted with a
speckle noise at different densities.
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The performance of the filter is evaluated both quantitatively and
qualitatively. The evaluation measures used to evaluate the performance of
the filter are Mean Square error/pixel, Image Enhancement Factor, Peak
Signal to Noise Ratio, Noise Variance and Equivalent Number of looks
(ENL).
The definitions of MSE/pixel, IEF, PSNR are presented in
chapter 2. Guo et al (1994) proposed two approaches of estimating the
speckle noise level. They are
i) Measuring ENL over a uniform image region
ii) Noise variance.
A lower MSE indicates a less difference between the original image and
filtered image. This means that there is a significant noise reduction. A higher
value of IEF denotes not only the higher noise reduction and also the greater
enhanced image. Higher the value of PSNR refers to the better performance
of filter in eliminating the noise.
5.3.1 Equivalent Number of Looks (ENL)
A larger value of ENL corresponds to a better quantitative
performance. The value of ENL also depends on the size of the tested image.
In this work ENL is calculated for 4 noise looks. The formula for ENL
calculation is given by
2
ENL (5.6)
where µ is the mean of the uniform region and σ is the standard deviation of
the uniform region.
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5.3.2 Noise variance (NV)
NV determines the contents of the speckle in the image. A lower
variance gives a smoother image as more amount of speckle is reduced. The
formula for calculating the noise variance is given as
1
0
1
0
22 ),(1 N
i
N
jjiu
N (5.7)
where u(i,j) is the de noised image at (i,j)th spatial coordinate.
The noisy image is formed by multiplying speckle of various
densities. This noisy image is processed by the proposed filter with a window
size of 3×3 and 5×5.
The performance of the filter is compared with the median, simple
speckle smoothing algorithm by Lee, Frost filter, Kuan filter, MATMF in
terms of MSE, IEF, PSNR, NV, ENL and is shown in Table 5.1. A remotely
sensed image is corrupted by a speckle of density 0.05 and processed by a
window of size 5×5. The higher value of PSNR, IEF and ENL for the
proposed filter shows the better performance comparatively. Lower value of
MSE/ pixel and NV is also a factor of its improved performance. The value of
MSE/pixel increases with the increase in the amount of noise.
The qualitative analysis of the performance of the filter is shown in
Figure 5.2. In this analysis, the original remotely sensed image is corrupted by
a speckle noise of variance 0.02, 0.05 and 0.1 and the results of the algorithm
for these corrupted images are depicted in Figure 5.2(a) through
Figure 5.2(g). The edge preservation and noise elimination is more if the
corrupted amount of noise is less.
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A comparative analysis of the PSNR of various filters with that of
the proposed filter for various amounts of speckle noise is shown in
Figure 5.3. A higher value of PSNR shows an excellent performance of the
proposed filter in terms of its noise elimination. The PSNR comparison has
been depicted using a remotely sensed image as the test image.
As depicted in Figure 5.4 the IEF shows the superior performance of
the new filter in terms of its noise elimination with the edge preservation
properties. The test image ‘Lena’ is corrupted by various amounts of speckle
noise. The performance is compared with the results of MATMF, median,
Lee, Frost and Kuan filters.
All the evaluation measures are calculated for a ‘lena’ image
corrupted by a speckle noise density of 0.1 and the comparative analysis is
shown in Table 5.2.
A graph in Figure 5.5 relating various noise densities and
MSE/pixel for the ‘lena’ image shows that the new filter offers lower
MSE/pixel than the MSE/pixel of other filters. It shows that more amount of
speckle noise is removed by the proposed filter.
If the ‘lena’ image is corrupted by a speckle noise intensity of 0.1
and they are processed by various filters. The qualitative performance of the
proposed filter is compared with the performance of the various adaptive
filters using Figure 5.6(a) to Figure 5.6(g). The proposed filter is found to
provide better edge preservation than the other filters.
A higher value of ENL is offered by the new filter in removing the
speckle noise in a remotely sensed image than the value of ENL while
removing the speckle noise in a lena image. This is depicted in Figure 5.7
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and it shows that the new filter performs well for the remote sensing image
than for a general image.
Even though many evaluation measures quantify the performance of
the New Filter III, as in the theory, the qualitative analysis is of more
importance for the human vision. The qualitative analysis of the filter is
compared with the results of other filters if the original remote sensing image
is corrupted with a speckle density of 0.1in Figure 5.8(a) through 5.8(g).
The mean of the remote sensing image is more than that of the lena
image. The performance of the filter using a remotely sensed corrupted image
is depicted in Table 5.3. The comparative performance of the New Filter III
on to the Lena image processed at different window size 3×3 and 5×5 is
shown in Table 5.4. As the window size increases, the values of PSNR
increases and the values of MSE/Pixel decrease for the proposed filter. This
shows that the noise reduction is more as the window size increases but the
quality of the images gets blurred.
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Table 5.1 Comparative analysis of the New Filter III in terms of various evaluation measures
(with remotely sensed image as test image)
Type of filter Speckle noise density
Evaluation Measures
MSE/pixel IEF PSNR ENL NV
General median filter 0.05 840 2.9 6.9 3.3 3.90E+04
MATMF 0.05 590 3.5 8.9 4.2 3.80E+04
Lee filter 0.05 342 3.3 11.7 3.8 3.80E+04
Enhanced Frost Filter 0.05 613 2.4 8.6 3.9 3.90E+04
Proposed filter 0.05 105 7.2 27.2 4.1 2.80E+04
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(a) (b) (c)
(d) (e) (f)
(g)
Figure 5.2 Qualitative illustration of the New Filter III (a) Original test
image. (b) ,(d) and (f) Original image corrupted with a
speckle noise of variance 0.1, 0.05 and 0.02 respectively (c),
(e) and(g) Results of the proposed filter for the noise
variance of 0.1, 0.05 and 0.02 respectively
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Figure 5.3 Comparison of quantitative performance of the
New Filter III in terms of PSNR with that of other filters
with the remotely sensed image as test image.
Figure 5.4 Comparison of quantitative performance of the New Filter
III in terms of IEF with that of other filters with the lena
image as test image
0
5
10
15
20
25
30
35
40
0.02 0.04 0.06 0.08 0.1Speckle Noise density
PSNR
Proposed f ilter
Enhanced Frost Filter
Median Filter
Lee Filter
MATMF
0
1
2
3
4
5
6
7
0.02 0.04 0.06 0.08 0.1
Speckle Noise variance
Imag
e En
hanc
emen
t Fac
tor
Proposed f ilter
Lee filter
Enhance Frost f ilter
Genealised median f ilter
M ATM F
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Table 5.2 Comparative analysis of the New Filter III in terms of various evaluation measures
(with lena image as test image)
Type of filter Speckle noise density Evaluation Measures
MSE/pixel IEF PSNR ENL NV
General median filter 0.05 203 3.7 11.4 2.4 3.20E+04
MATMF 0.05 193 4.4 16.6 2.9 3.15E+04
Lee filter 0.05 155 5.4 18.6 2.8 3.10E+04
Enhanced Frost Filter 0.05 356 3.3 12.3 2.6 3.16E+04
Proposed filter 0.05 130 6.7 21.1 3 3.00E+04
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Figure 5.5 Comparative analysis of the performance of the New Filter
III in terms of MSE/Pixel
0
50
100
150
200
250
300
350
400
450
500
550
0.02 0.04 0.06 0.08 0.1Speckle Noise density
MSE
/Pix
el
Proposed f ilter
Enhanced Frost Filter
Median Filter
Lee Filter
MATMF
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(a) (b) (c)
(d) (e) (f)
(g) Figure 5.6 Qualitative illustration of the New Filter III (using Lena
image as test image) (a) Original test image. (b) Original
image corrupted with a speckle noise density of 0.1(c) Result
of Enhanced Frost Filter (d) Image filtered by Generalised
median filer (e) Result of MATMF (f)Result of Lee filter
(g)Image filtered by New Filter III
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Figure 5.7 Comparative analysis of the performance of the New Filter
III in terms of ENL for a remotely sensed image and for
Lena image as test image
0
1
2
3
4
5
0.02 0.04 0.06 0.08 0.1Speckle Noise density
ENL
Remote sensing image
Lena image
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(a) (b) (c)
(d) (e) (f)
(g)
Figure 5.8 Qualitative illustration of the New Filter III (using remotely
sensed image as test image) (a) Original test image. (b)
Original image corrupted with a speckle noise density of
0.1(c) Result of Generalised median Filter (d) Image filtered
by Enhanced Frost (e) Result of MATMF (f)Result of Lee
filter (g) Image filtered by the proposed filter
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Table 5.3 Performance of the New Filter III for various window sizes with remote sensing image as test image
Type of filter
Evaluation Measures (remote sensing image corrupted by a speckle noise variance of 0.08)
Size of the window=3×3 Size of the window=5×5
MSE IEF PSNR ENL NV MSE IEF PSNR ENL NV
General median filter 931 2.9 6.3 3.1 3.90E+04 885 4.3 7.1 3.4 3.80E+04
MATMF 485 3.6 9.8 4 3.83E+04 373 0.5 3.6 3.66 2.68E+04
Lee filter 520 5.1 9.1 3.5 3.72E+04 490 3 8.9 4.5 3.70E+04
Enhanced Frost Filter 708 2.2 8.1 4 3.84E+04 928 0.7 7 3.65 3.86E+04
New Filter III 430 7.1 20 2.9 3.70E+04 362 5.1 14 3 3.60E+04
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Table 5.4 Performance of the New Filter III for various window sizes with lena as test image
Type of filter
Evaluation Measures ( Lena image corrupted by a speckle noise variance of 0.08)
Size of the window = 3×3 Size of the window = 5×5
MSE IEF PSNR ENL NV MSE IEF PSNR ENL NV
General median filter 516 3.2 8.2 2.5 3.14e+04 444 5.2 10 2.7 3.1e+04
MATMF 246 5.4 14.8 2.9 3.13e+04 230 5.7 4.9 2.8 2.15e+04
Lee filter 256 5.2 14.5 2.8 3e+04 270 4.9 14 2.8 3.05e+04
Enhanced Frost Filter 424 2.6 11.2 2.8 3.16e+04 587 2.6 9.6 3.05 3.1e+04
New Filter III 157 6.4 20 3.1 2.94e+04 143 5.1 23.2 3.2 2.87e+04
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5.4. CONCLUSION
The adaptive filtering algorithms proposed in chapters 2,3 and 4
work well for the simultaneous removal of additive mixture of Gaussian
noise and impulse noise. Though they are adaptive in nature, it has been
found that they do not perform well in removal of speckle noise. In order to
remove speckle noise which is multiplicative in nature and which
contaminates a remotely sensed image, a non linear adaptive filtering
algorithm has been proposed in this chapter.
The New Filter III is based on the local order statistics and the
qualitative results show that it removes speckle noise in a remote sensing
image with an excellent preservation of edges better than speckle noise
removal in general image. The test images are corrupted by various
intensities of speckle noise. The speckle noise is removed by a 3 sigma filter
which uses the local statistics such as mean and standard deviation of the
noise corrupted signal. The adaptive filter provides edge preservation by
using an edge detector which is a high pass filter and the replacement of the
corrupted edge by the neighbourhood uncorrupted signal. The reconstructed
filter algorithm combines the filtered signal from the 3 sigma filter and the
edges from the edge filtered signal to provide a noise free and edges
preserved image.
Various quantitative evaluation measures have been calculated to
prove the performance of the filter. The higher values of PSNR and lower
values of MSE/pixel show its superior performance in filtering the noise as
compared to other speckle removing adaptive filters. The qualitative analysis
of the filter shows the efficiency of the proposed filter in preserving the edges.
SAR images are corrupted by speckle noise and it has been proved that the
proposed algorithm works excellent for the remote sensing image than the
general images.