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COMPARATIVE ANALYSIS OF VISU SHRINK AND
PMD MODEL ON SAR IMAGES FOR SPECKLE NOISE
REDUCTION
Kalaiyarasi Alagumani
Department of Electronics and Communication Engineering,
V.S.B. Engineering College, Karur District, Tamil Nadu, (India).
E-mail: mukalaiyarasi@gmail.com
ORCID: https://orcid.org/0000-0001-9306-2654
Perumal Balasubramani
Department of Electronics and Communication Engineering, Kalasalingam Academy of
Research and Education,Virudhunagar District, Tamil Nadu, (India).
E-mail: palanimet@gmail.com
ORCID: https://orcid.org/0000-0003-4408-9396
Pallikonda Rajasekaran Murugan
Department of Electronics and Communication Engineering, Kalasalingam Academy of
Research and Education, Virudhunagar District, Tamil Nadu, (India).
E-mail: m.p.raja@klu.ac.in
ORCID: https://orcid.org/0000-0003-4408-9396
Recepción:
11/11/2019
Aceptación:
09/02/2021
Publicación:
30/11/2021
Citación sugerida:
Alagumani, K., Balasubramani, P., y Murugan, P. R. (2021). Comparative analysis of VISU shrink
and PMD model on SAR images for speckle noise reduction. 3C Tecnología. Glosas de innovación aplicadas
a la pyme, Edición Especial, (noviembre, 2021), 261-277. https://doi.org/10.17993/3ctecno.2021.
specialissue8.261-277
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ABSTRACT
Removing noise from original image is often the initial step in image analysis. The best
de-noising technique should not be only reducing the noise, but do so without blurring
or changing the location of the edges. Many approaches have been proposed for noise
reduction. Speckle noise can be easily removed by simple method such as partial Dierential
Equations method (PDEs). In this paper, Perona-Malik Diusion (PMD) models have been
proposed and compared with VISU Shrinkage (VS) method. Although both the methods
are seemed to be comparable with removing speckle noise, speckles are more visible to
mages processed by VS method. The experimental results show that the PMD model
obtains superior performance with the PSNR value of 61.90%, SSI of 0.40, EPI of 0.51
and SSIM of 69.05%. The PSNR value has been increased by 20.2% when compared with
VS de-speckling method.
KEYWORDS
De-speckling, PDE, Synthetic Aperture Radar, VISU shrink, DWT.
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1. INTRODUCTION
Remote sensing images are captured by various sensors. The captured images are often
degraded by speckle noise called multiplicative noise. Speckle is predominantly due to the
meddling of the requiting wave of the transducer aperture. It is one of the most perilous
commotions that amend the quality of Synthetic Aperture Radar (SAR) coherent images
(Choi & Jeong, 2019) and decreases the potentiality of the images. Speckle noise in SAR
image is broadly severe, precipitating diculties for image interpretation. It is generated
because of the coherent processing of backscattered signals from multiple distributed
targets of the earth surface.
The speckle noise reduction is usually the initial step in the analysis of SAR images. There
are a several de-noising lters such as average lter, mean lter, median lter, Lee lter,
sigma lter, Lee-sigma lter, and wiener lter etc., which are used in the noise removal of
SAR images. These lters reduce speckle noise by smoothing and sharpening the original
image. Due to which some unavoidable blur has been introduced in the de-noised image,
and also the main problem in using adaptive procedure techniques is the empirical choice
of thresholds to determine the size of windows. To overcome the above cited drawbacks,
PDEs based methods are used for de-speckling SAR images. The PDE algorithm is more
ecient for de-speckling the SAR images eectively without blurring the edges of original
SAR images.
2. RELATED WORKS
Various Second-Order PDE methods including the anisotropic model (Kriti, Virmani, &
Agarwal, 2019; Shen Liu et al., 2012) and the total variational model (Rudin & Osher,
1994; Morteza et al., 2019) were developed for suppressing noise. In Kriti et al. (2019),
Fuzzy Morphological Anisotropic Diusion method was utilized for SAR image speckle
noise reduction. In Shen Liu et al. (2012), the anisotropic diusion lter was used to reduce
the speckle noise in ultrasound images. This method produced blur at the edges of the de-
speckled image. In Rudin & Osher (1994), total variation with free local constraints method
was used for noise reduction. In Morteza et al. (2019), Nonlinear total variation-based model
was developed for noise removal of the image. This method produced sharp edges at the
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de-noised images. In Ehsan et al. (2014), Complex diusion method for image enhancement
was proposed and compared with the second, fourth-order PDE and showed that the
complex diusion method oers better result when the noise is low. The performance of
this method is declined when the noise level is high.
In Liu et al. (2012a), PDE with Auxiliary images were used to de-speckle the SAR image.
Here, the auxiliary images were used as priors. Multispectral and hyperspectral images were
used in this experiment. The major drawback of using second-order Partial Dierential
Equation is the procreation of blocking eect in the de-noised image (Liu, Lai, & Pericleous,
2014, Van Rie et al., 2019). To reduce the block eect, the fourth-order PDE method was
developed by replacing the gradient operator by the Laplacian operator and this method
gives better results by reducing the block eect (You & Kaveh, 2000). In Didas (2004),
and Didas, Weickert and Burgeth (2005), Higher-order PDE based noise removal were
performed. The higher-order PDEs are not widely used in de-speckling of SAR images
because of its complex numerical implementation and enormous computations.
This paper is further organized as follows. Section III explains the materials and methods
used in this paper. Section IV gives the various performance metrics used for comparing the
performance of both de-speckling method. Section V provides the results and discussion.
Conclusion of this paper is given in Section VI.
3. MATERIALS AND METHODS
Speckle noise diminishes the look and quality of SAR images which in turn decreases
the performances of SAR image processing and Analysis. Therefore, the noise must be
suppressed before processing the SAR images using various image processing techniques
like multiple-look processing, adaptive and non-adaptive lters, etc.
3.1. VISU SHRINKAGE
De-speckling using wavelet shrinkage method, reduce the speckle noise existing in the noisy
image with conserving the textual and edge attributes of the image. VISU Shrinkage (VS) is
one the wavelet shrinkage method. In VS, thresholding is performed by applying universal
threshold (UT) and it is proposed by Donoho (1994). The block diagram of VS de-speckling
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method is shown in g 1. In this method, no need to calculate the threshold value at every
subband level. Initially, 2D-DWT is applied on the speckled SAR image where the image
is separated into four subband regions namely LL LH, HL and HH (Chang, Yu, & Vetterli,
2000). Then UT soft thresholding is performed on the wavelet coecients. There are two
types of thresholding viz. Hard thresholding produce unwanted artifacts in the de-speckled
images while soft thresholding yields visually pleasing images. In soft thresholding, the
coecients below UT are set to zero while important coecients are replaced by UT value.
The shrinkage of the wavelet co-ecient is given by (Donoho, 1994):
(1)
where,
, is the standard deviation of the noise and 'n' is the number of pixel elements
in the image. While UT selection, it is most necessary to evaluate the standard deviation
of the noise (
) from the wavelet coecients. It is obtained by using the below formula:
(2)
where, MAD is the median of the absolute values of the wavelet coecients (HH band
of speckled image). In this experiment, 0.4349 is used as the universal threshold. At last,
compute the 2D-IDWT to get the de-speckled SAR image. This technique is simple and
eective, it removes speckle noise co-ecient that is insignicant relative to UT. The UT
tends to be high for large values of MAD, it over smoothens the speckled SAR image and
aects many original images co-ecient along with speckle noise. Also, it has been observed
that threshold value should be smaller value for soft thresholding (Bruce & Gao, 1996). For
de-speckling of SAR images, VISU shrink does not adapt well to suppress:
DWT
IDWTThresholding
Speckled
SAR Image
De-speckled
SAR image
Figure 1. VISU Shrinkage (VS) De-speckling method.
Source: own elaboration.
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3.2. PMD MODEL
SAR images are aected by various noises which include both non-additive and additive
noise. The non-additive ie, multiplicative noise in SAR image is otherwise called as speckle
noise and it is dened as (Rafati et al., 2016):
(3)
Where, I (x,y), is the observed SAR image, u (x,y) is the multiplicative component of a
speckled image, n (x,y) is the additive component of the speckled image. Since, the speckle
noise is multiplicative, removing the speckle noise present in the remote sensing images is
important. Only the multiplicative component is considered and the additional component
is not to be considered. Therefore equation (3) can be rewritten as:
(4)
The process used to de-speckle the SAR image using the PMD model is given in Figure 2.
To convert the multiplicative component into the additive component, the log transform
has been applied on both the sides of the above equation. Therefore, the above equation
becomes,
(5)
PMD model depends on heat diusion equation which is dened as (Perona & Malik, 1990):
(6)
Here, S(x,y,t) is the log transformed noisy SAR image, c(x,y,t) is the diusivity,
is the gradient
operator,
is the divergence operator. This equation was developed by Perona and Malik
(1990). It can be expanded as:
(7)
This equation is more eective for suppressing the speckle noise while preserving the edge
characteristics of the image. In this case, initially the gradient of the SAR image grad x, grad
y is calculated in both x and y directions respectively. Then diusivity is computed by using
the below equation which is stated in (Khristenko et al., 2019).
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(8)
Here, k is a small constant used to control the diusivity. It must be chosen between 5 to
100. The value of diusivity:
Figure 2. Work ow of PMD Model.
Source: own elaboration.
'c' changes at dierent regions of the image. The gradient of the image is high during the
edges of the images, this leads to diusivity has a small value. This consequently preserves
the edges from smoothing. After that, the diusivity is multiplied with the gradient image
grad x and grad y images respectively. Thereafter, the divergence of grad x and grad y images
are computed and both the images are fused to get the resultant divergence image. At last,
take the exponential transform to get the de-speckled SAR image.
4. PERFORMANCE METRICS
To evaluate the performance improvement four dierent performance measures such as
PSNR, SSI, EPI, and SSIM are enumerated based on the speckled SAR image and the
de-speckled SAR image.
4.1 PEAK SIGNAL TO NOISE RATIO (PSNR)
PSNR is most widely used as a performance analyzing parameter. The higher value of
PSNR gives a better quality of the de-speckled image. PSNR is dened as (Kalaiyarasi,
Saravanan, & Perumal, 2016):
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(9)
Where,
is the maximum possible value of the original image. MSE is the mean square
error, which must be lower value.
4.2 SPECKLE SUPPRESSION INDEX (SSI)
SSI is used to nd the eciency of the de-speckling algorithm, which is dened as
(Dellepiane & Angiati, 2014):
(10)
SSI should be the lowest value and the range lies between [0,1].
4.3 EDGE PRESERVATION INDEX (EPI)
Another parameter EPI can be computed by comparing the edges of the de-speckled image
and the noisy SAR image. An ecient de-speckling method must have higher in Edge
Preservation Index EPI (Ji & Zhang, 2017).
(11)
4.4 STRUCTURAL SIMILARITY INDEX MEASURE (SSIM)
When suppressing the speckle noise in SAR image processing, preserving edges is the
most challenging one. Therefore, the additional parameters like EPI and SSIM have been
evaluated here. SSIM is utilized to quantify the closeness amid the original SAR and the
de-speckled SAR image. SSIM is dene as (Nadernejad, Koohi, & Hassanpour, 2008):
(12)
Where,
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5. RESULTS AND DISCUSSION
Dierent SAR images have been used for this experiment which is shown in Figure 3.
(a) (b) (c) (d)
Figure 3. SAR images in different location. (a) Eastem Kariba, (b) Colombia Deforestation, (c) Airport SAR
Image, (d) Ellis Island.
Source: own elaboration.
The de-speckled image using VS method is shown in Figure 4. In this method, noise
reduction mainly depends on the UT value. The range of UT lies between 0 to 1. Here
0.4349 has been used as UT for thresholding the SAR image.
(a) (b) (c) (d)
Figure 4. De-speckled SAR images using VS method. (a) Eastem Kariba, (b) Colombia Deforestation, (c)
Airport SAR Image, (d) Ellis Island.
Source: own elaboration.
The de-speckled image using PMD model is shown in Figure 5. The VS method provides
poor edge preservation. To overcome that, in PMD model the diusivity plays an important
role in preserving the edges of the images. The value of diusivity co-ecient must be low
for preserving the edges of the images. The obtained minimum and maximum value of
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diusivity for dierent SAR images have been listed in Table 1. The gradient value will be
high during the edges of the image. From equation (8), it can be noticed that diusivity will
be low when the gradient has a larger value. This technique is used to preserve the edges
of the SAR images in the PMD model. The de-speckled image after the PMD model looks
more cheerful, by eliminating the noise without aecting the edges and at the same time, it
also reduces the block eect.
(a) (b) (c) (d)
Figure 5. De-speckled SAR images using PMD model. (a) Eastem Kariba, (b) Colombia Deforestation, (c)
Airport SAR Image, (d) Ellis Island.
Source: own elaboration.
From the above ocular results shown in Figures 4-5, it can be deduced that almost all speckle
noise is removed, and the de-speckled image looks more comfortable without blocky eect.
It is concluded that the PMD model has produced better visual images than the VS method.
Table 1. The minimum and maximum value of Diffusivity for SAR images.
Images Minimum Maximum
Eastem Kariba 0.0201 0.9997
Colombia Deforestation 0.0202 0.9952
Airport SAR Image 0.0108 0.9981
Ellis Island 0.0131 0.9972
Source: own elaboration.
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Table 2. Comparison of performance parameters of VS and PMD model.
S.No Images
PSNR SSI EPI SSIM
PMD VS PMD VS PMD VS PMD VS
1 Eastem Kariba 62.17 42.36 0.39 0.23 0.56 0.37 66.84 53.29
2
Colombia
Deforestation
61.88 39.96 0.36 0.28 0.68 0.60 61.44 55.18
3 Airport Image 59.93 40.63 0.36 0.26 0.46 0.36 62.21 50.28
4 Ellis Island 62.99 43.15 0.44 0.16 0.42 0.31 75.13 67.20
5 Wetland 64.64 42.80 0.43 0.10 0.50 0.34 74.70 67.73
6
Airborne SAR
Image
63.16 40.81 0.41 0.16 0.50 0.53 70.22 50.54
7 Sea Ice 63.20 40.79 0.41 0.16 0.49 0.44 70.11 57.77
8
Barents Sea Ice
Image
59.53 41.53 0.38 0.12 0.40 0.45 65.54 60.40
9 Arctic Sea Ice 60.91 39.51 0.44 0.11 0.47 0.42 75.58 63.34
10
Sea Ice
MEASURES
62.62 42.13 0.37 0.15 0.38 0.39 63.28 57.59
11 Amazon_2010 56.92 42.54 0.40 0.28 0.50 0.36 68.67 59.29
12 Amazon_2020 64.03 44.57 0.45 0.27 0.67 0.22 77.11 53.22
13 Amazon_2030 63.95 42.63 0.43 0.25 0.55 0.35 74.09 62.17
14 Amazon_2040 61.62 42.27 0.41 0.19 0.67 0.38 69.74 55.54
15 Amazon_2050 60.96 39.84 0.35 0.24 0.50 0.47 61.16 52.45
Average 61.90 41.70 0.40 0.19 0.51 0.39 69.05 57.73
Source: own elaboration
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Figure 6. Graphical representation of PSNR, SSI, EPI and SSIM for VS method and PMD model.
Source: own elaboration.
Table 2 gives the comparison of performance parameters of VISU shrinkage and NSO-
PDEs method on dierent SAR images respectively. From both the methods, VISU Shrink
has the least performance as theoretically it uses a universal threshold for all sub-bands
which is not optimal (Dixit et al., 204). Figure 6 shows the comparison of PSNR, SSI, EPI,
and SSIM for the two methods. From the four charts, it is inferred that the PMD model
provides better PSNR, EPI, SSI and SSIM than VS method.
Table 3. Average Values of Performance Metrics.
Parameters
Methods
PMD VS
PSNR 61.90 41.70
SSI 0.40 0.19
EPI 0.51 0.39
SSIM 69.05 57.73
Source: own elaboration.
The average values of performance metrics are given in Table 3. The average values have
been calculated by taking the mean average values of total images used for this experiment.
The graphical illustration of comparative analysis has been presented in Figure 7. From
the graphical illustration analysis, it is noticed that the PMD de-speckling method produces
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better outcomes in terms of various performance metrics which includes PSNR of 61.90%,
SSI of 0.40, EPI of 0.51 and SSIM of 69.05%.
61,9
69,05
41,7
57,73
PSNR SSIM
PMD VS
0,4
0,51
0,19
0,39
SSI EPI
PMD VS
Figure 7. Comparative analysis of Performance metrics of PMD and VS de-speckling methods. a) PSNR and
SSIM, b) SSI and EPI.
Source: own elaboration.
6. CONCLUSIONS
PDE method has been most broadly used in SAR image processing particularly in suppressing
speckle noise. In this paper, the PMD model has been proposed for speckle noise reduction.
The performance of the PMD model is compared with the VISU shrinkage method. VS
method follows the universal threshold scheme. This method does not minimize the mean
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squared error and it does not remove the speckle noise eectively. The experimental results
show that the PMD model of speckle noise reduction yields a better result when compared
to the VISU Shrinkage method. Additionally, the quality of the de-speckled image is better
enhanced using the PMD model in terms of PSNR of 61.90%, SSI of 0.40, EPI of 0.51
and SSIM of 69.05%. The PSNR value has been increased by 20.2% when compared with
the VS de-speckling method
ACKNOWLEDGMENT
We thank the Department of ECE of Kalasalingam Academy of Research and Education
(Deemed to be University), Tamil Nadu, India for the computational facilities made
available in Centre for Signal Processing Laboratory (Supported by Department of Science
and Technology (DST), New Delhi under FIST Programme). (Reference No: SR/FST/
ETI-336/2013 dated November 2013).
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