Image enhancement and speckle reduction of full polarimetric SAR data by Gaussian Markov random field

Abstract

In recent years, the use of Polarimetric Synthetic Aperture Radar (PolSAR) data in different applications dramatically has been increased. In SAR imagery an interference phenomenon with random behavior exists which is called speckle noise. The interpretation of data encounters some troubles due to the presence of speckle which can be considered as a multiplicative noise affecting all coherent imaging systems. Indeed, speckle degrade radiometric resolution of PolSAR images, therefore it is needful to perform speckle filtering on the SAR data type. Markov Random Field (MRF) has proven to be a powerful method for drawing out eliciting contextual information from remotely sensed images. In the present paper, a probability density function (PDF), which is fitted well with the PolSAR data based on the goodness-of-fit test, is first obtained for the pixel-wise analysis. Then the contextual smoothing is achieved with the MRF method. This novel speckle reduction method combines an advanced statistical distribution with spatial contextual information for PolSAR data. These two parts of information are combined based on weighted summation of pixel-wise and contextual models. This approach not only preserves edge information in the images, but also improves signal-tonoise ratio of the results. The method maintains the mean value of original signal in the homogenous areas and preserves the edges of features in the heterogeneous regions. Experiments on real medium resolution ALOS data from Tehran, and also high resolution full polarimetric SAR data over the Oberpfaffenhofen test-site in Germany, demonstrate the effectiveness of the algorithm compared with well-known despeckling methods.

Full text

IMAGE ENHANCEMENT AND SPECKLE REDUCTION OF FULL POLARIMETRIC
SAR DATA BY GAUSSIAN MARKOV RANDOM FIELD
M. Mahdian a, *, M. Motagh b, V. Akbari c
a Dept. of Geomatics Engineering, College of Engineering, University of Tehran, Tehran, Iran - m.mahdian@ut.ac.ir
b GeoForschungsZentrum (GFZ) Potsdam, Telegrafenberg, D-14473 Potsdam, Germany - motagh@gfz-potsdam.de
c Dept. of Physics and Technology, University of Tromsø, Tromsø, Norway - vahid.akbari@uit.no
KEY WORDS: Speckle reduction, Polarimetric SAR, Markov random field, Contextual analysis, Pixel-wise analysis.
ABSTRACT:
In recent years, the use of Polarimetric Synthetic Aperture Radar (PolSAR) data in different applications dramatically has been
increased. In SAR imagery an interference phenomenon with random behavior exists which is called speckle noise. The
interpretation of data encounters some troubles due to the presence of speckle which can be considered as a multiplicative noise
affecting all coherent imaging systems. Indeed, speckle degrade radiometric resolution of PolSAR images, therefore it is needful to
perform speckle filtering on the SAR data type. Markov Random Field (MRF) has proven to be a powerful method for drawing out
eliciting contextual information from remotely sensed images. In the present paper, a probability density function (PDF), which is
fitted well with the PolSAR data based on the goodness-of-fit test, is first obtained for the pixel-wise analysis. Then the contextual
smoothing is achieved with the MRF method. This novel speckle reduction method combines an advanced statistical distribution
with spatial contextual information for PolSAR data. These two parts of information are combined based on weighted summation of
pixel-wise and contextual models. This approach not only preserves edge information in the images, but also improves signal-to-
noise ratio of the results. The method maintains the mean value of original signal in the homogenous areas and preserves the edges of
features in the heterogeneous regions. Experiments on real medium resolution ALOS data from Tehran, and also high resolution full
polarimetric SAR data over the Oberpfaffenhofen test-site in Germany, demonstrate the effectiveness of the algorithm compared with
well-known despeckling methods.
* Corresponding author.
1. INTRODUCTION
Polarimetric analysis enhances the discrimination capability of
SAR sensors and this makes the PolSAR data very useful for
various land use applications. However, polarimetric SAR data
suffer from some limitations related to unavoidable presence of
speckle noise caused by coherent interface of waves reflected
from many elementary scatterers (J.-S. Lee 1981). The presence
of speckle in PolSAR data complicates the image processing
and interpretation and also reduces the accuracy of image
segmentation and classification. Consequently, reduction of
such noises is a principal step in preprocessing procedure and
should be realized before other analysis applied to data. Speckle
degrades radiometric resolution of SAR images (Espinoza
Molina, Gleich, and Datcu 2012) and understanding PolSAR
speckle statistics can be beneficial for different applications
such as change detection (Moser and Serpico 2006), ice
monitoring (Dierking and Busche 2006), and land cover
classification (Tison et al. 2004).
Various techniques are presented in literature for speckle
reduction. These techniques include the very simple idea of
moving average and multi-look processing to more
sophisticated statistical modelling (J. S. Lee and Pottier 2009).
Generally, speckle reduction methods are divided into
parametric and nonparametric approaches. Nonparametric
methods are used according to local statistics of the image while
parametric methods use a proper statistical model for data and
estimate its parameters using either pixel-wise or contextual
analysis (Tello Alonso et al. 2011).
Markov Random Field (MRF) has proven to be a powerful
parametric model for drawing out eliciting contextual
information from remote sensing imagery (Moser and Serpico
2006). One of the most important benefits of MRF method is its
extraordinary ability to model the spatial correlation between
neighbouring pixels. MRF models have been used in different
kinds of image analysis applications such as image
segmentation, texture extraction, image denoising and data
fusion (Li 2009). The potential of MRF models to retrieve
spatial contextual information makes it desired to reduce the
speckle noise of the PolSAR data. This research presents a
novel approach for speckle reduction of PolSAR images by
combining advanced statistical modeling and spatial context
within an MRF framework. MRF models have been used in
different image analysis problems such as segmentation (Deng
and Clausi 2004) and classification (Tison et al. 2004).
In this paper, a combination of pixel-wise and contextual
analysis is introduced for the representation of restored PolSAR
data. First a probability density function (PDF) which is fitted
well with the used data based on goodness-of-fit test, is
obtained for pixel-wise analysis. Then the contextual smoothing
is achieved with MRF model. A new idea which is proposed for
speckle reduction of SAR data based upon weighted summation
of these two sections (i.e. pixel-wise and contextual analysis).
The weights are determined according to the spatial correlation
between pixels over pre-defined neighbourhood system. For
each window, if the correlation between the central pixel and
neighbouring pixels is high, more weight is assigned to pixel-
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-1/W3, 2013
SMPR 2013, 5 – 8 October 2013, Tehran, Iran
This contribution has been peer-reviewed. The peer-review was conducted on the basis of the abstract.
263

wise part and vice versa. Therefore, we can optimize the role of
contextual smoothing in the speckle reduction by giving
appropriate weight to it. Our proposed methodology is applied
to full polarimetric L medium resolution ALOS data from
Tehran, Iran and also to high resolution L-band PolSAR data
over the Oberpfaffenhofen test-site in Germany. These images
cover both urban and non-urban areas. The results of this
adaptive speckle reduction method are compared to other well-
known de-speckling methods. The efficiency of the approach
has evaluated by quantitative metrics (i.e. Signal to noise ratio,
Equivalent number of look and Root mean square error).
Section 2 of this paper describes the methodology and
introduces our proposed filtering technique. In the next section
experimental results presented and discussion and conclusion
offered in continuation.
2. METHODOLOGY
The main purpose of despeckling is the estimation of the noise-
free image from the observed image. The noise-free image is
achieved in this study by performing of both pixel-wise and
contextual analysis simultaneously but their effective
combination remains a major challenge. Figure 1 illustrates the
detailed flowchart of methodology we used for this challenging
combination.
Figure 1. Flowchart of proposed approach.
We base our theory upon the doubly stochastic product model
(Espinoza Molina, Gleich, and Datcu 2012), which decompose
single look complex (SLC) value as:

k
(1)
Where the strictly positive scalar random variable τ models
texture, and represents the backscatter variability due to
heterogeneity of the radar cross section (Oliver and Quegan
2004). The second component, the speckle noise term ω,
follows complex Gaussian distribution. With a logarithm
transformation, the multiplicative nature of the above equation
gets additive as follows:


ln
2
1
,ln,ln
ln
2
1
lnln


YXkZ
k
(2)
We will use the homogeneous Gauss-MRF to model the spatial
correlation between pixels for both texture and speckle
components.
)(
ˆ
)(
ˆˆ
)(
ˆ
)(
ˆˆ
21
21
contextuaYpixelwiseYY
contextulXpixelwiseXX


(3)
Therefore, we can separate pixel-wise and contextual parts as:
)
ˆ
(
ˆ
)
ˆˆ
()
ˆˆ
(
ˆ2211
CcontextualpixelwiseZ
YXYXZ


(4)
and their weighted summation is written as equation (5).
CRYXRZ
ContextualRPixelwiseRZ
ˆ
)1()
ˆˆ
(
ˆ
)1(
ˆ
11 

(5)
2.1 Pixel-wise statistical analysis
The texture term of the product model is given by the gamma
distribution with PDF given by:
)exp(
)(
),( 1











p
(6)
With shape parameter α > 0 and unit mean value E{τ}=1.
The flexibility of the gamma distribution by different shape
parameters is shown in Figure 2. The resulting distribution of
the product model follows K-distribution.
Figure 2. Flexibility of gamma distribution with different values
of shape parameter.
2.2 Contextual analysis by MRF
For extraction of contextual information and its integration with
pixel-wise term for improving of speckle reduction, we adopt an
MRF model which generally presents spatial correlation
between neighbouring pixels. As a consequence, an MRF can
be applied for contextual term and gamma distribution while
Gaussian model are used for pixel-wise term for the SAR image
statistics.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-1/W3, 2013
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264

2.2.1 Markov random field
MRF theory enables the modeling of contextual dependencies
between a set of sites S which are given by:
 
NjMijisS  1,1);,(
(7)
These sites might be pixels in an image or individuals in a
social network. Also a value random field defined in the S as
follows:
 
SsB
ss  ,,

(8)
Where B denotes the pixel lattice and set of all possible values
in the image. The values for a set of sites S will be denoted by:
 
n
xxxX ,...,,21

(9)
We introduce first and second-order neighbourhood systems as
illustrated graphically in Figs. 3 - 4(Levada, Mascarenhas, and
Tannús 2008).
Figure 3. First-order neighbourhood system and its division
into cliques. The black squares represent the site of interest and
the white squares represent the neighbouring sites.
Figure 4. Second-order neighbourhood system.
In this research Gauss-MRF will be presented that is more
suitable for modeling images with a large number of intensity
levels. This model is defined by the choice of continuous
potential functions. Pairwise cliques, having two sites, are the
smallest cliques to convey contextual information. Models with
higher order cliques can potentially model more complex
interactions between values than models using only pairwise
cliques. The models discussed in this paper use only single and
pairwise cliques. The Gaussian model is defined for continuous
values by its mean and covariance terms. The conditional
probability density function (pdf) for the label at a site given the
labels of the neighbouring sites is given by:
2
2)(
2
1
2
2
1
)|( 








 



i
Ni iiii
i
xx
Ni exxp



(10)
Also we can estimate this pdf with help of energy function
which is as follows:


cccX V
z
xU
z
xp ))(exp(
1
))(exp(
1
)(

(11)
The single site and pairwise clique potential functions for the
Gaussian model are:
2
2
2
2
))((
),(
2
)(
)(





iiii
ii
ii
i
xx
xxV
x
xV






(12)
2.2.2 Energy function for Gauss-MRF model
Assuming second-order neighbourhood system, the energy
function of the Gauss-MRF is given by:
 








































j
iji
j
iji
j
iji
ji ji
xxxx
xxxx
xU 22
22
)()(
)()(
)(

(13)
That
i
x
is central pixel and
j
x
is neighbouring pixel in each
clique. For the simplicity of computations, the current study
confines an isotropic second-order isotropic neighbourhood
system and the related set of pairwise cliques (Levada,
Mascarenhas, and Tannús 2008), as depicted in Figure 4.
2.3 Weight determination
In the previous section, we discussed about how to determine
pixel-wise and contextual terms separately. Now we modulate
these parts by giving appropriate weights to each of them. A
novel idea is proposed here for modulating these parts based
upon weighted summation of these two sections (i.e.,pixel-wise
and contextual analysis). The weights are determined based on
the spatial correlation between pixels over a given
neighbourhood system. For each window, if the correlation
between the central pixel with neighbouring pixels is high, more
weight is assigned to pixel-wise part and vice versa. Therefore,
we can optimize the role of contextual smoothing in the speckle
reduction by giving the appropriate weight to it. This approach
maintains the mean value of the original signal in the
homogenous areas and preserves the edges of features in the
heterogeneous regions.
Therefore, weight parameter in Equation (14) (R parameter) can
be estimated as follows:
2
2
)(
)(1
i
i
total
total
mean
mean
R




(14)
Normalized weighting coefficient is given by:
2
2
2
)(1
)(
)(1
total
total
i
i
total
total
mean
mean
mean
RNormalized






(15)
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-1/W3, 2013
SMPR 2013, 5 – 8 October 2013, Tehran, Iran
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265

3. QUANTITATIVE EVALUATION METRICS
The performance of the proposed algorithm for speckle
reduction is evaluated in term of quantitative metrics such as
signal to noise ratio (SNR), equivalent number of look (ENL),
root mean square error (RMSE). Also the results are compared
with other well-known speckle reduction methods. Larger SNR
values correspond to qualitative image. SNR can be calculated
from equation (16):
)(
)(
log10 2,
1 1
2,
2,
1 1
2,
nm
M
m
N
nnm
nm
M
m
N
nnm
BA
BA
SNR 

 
 



(16)
In this equation A, B are de-noised and original images
respectively and M×N is the size of image. The values of SNR
indicate the quality of image reconstruction.
Equivalent Number of Looks (ENL) is another metrics which
show the ability of speckle reduction and performance of
smoothing procedure. This quantitative index calculated using
the following equation:
2
)(


ENL
(17)
μ and σ are the mean and standard deviation of the images. The
higher values of ENL show the higher efficiency in smoothing
speckle on homogeneous areas.
Root Mean Square Error (RMSE) is other metrics which is root
of the square error averaged over m×n window. This parameter
is calculated as in (18) and lower values of that show higher
quality of de-speckled image.
 
2
1 1 ,,
1
 
 M
m
N
nnmnm BA
MN
RMSE
(18)
4. IMPLEMENTATION ON REAL POLSAR DATA
In this section we present restoration results applied to real
PolSAR data. The results of the proposed methodology are
shown using medium-resolution L-band ALOS data (image has
size 512 x 512) from the Tehran area in Iran (Fig. 5(a)) and a
sample data set of ESAR PolSAR data, from Oberpfaffenhofen
test site (Fig. 5(c)). Figures 5(b) and 5(d) show two filtered
images with the proposed method in this research. As seen in
Figures 5(b,d), preserving and sharpening of linear structures
such as roads and coastal line is visually evident.
(a) Original image (Tehran)
(b) Despeckled image
(Tehran)
(c) Original image
(Oberpfaffenhofen)
(d) Despeckled image
(Oberpfaffenhofen)
Figure 5. Despeckling Results of Amplitude Image.
Tables 1 and 2 list the comparison between quantitative indices
of some de-noising methods for our case study. Improvement in
the signal to noise ratio and amount of the RMSEs is also
evident in terms of these metrics.
Table 1. Quantitative Comparison for Despeckeling of ALOS
Image
Table 2. Quantitative Comparison for Despeckeling of ESAR
Image
Figures 6 and 7 present a visual comparison of proposed
method with other well-known methods.
Figure 6. Visual comparison for Despeckeling of ALOS Image.
Parameters
SNR
ENL
RSME
Methods
Lee
17.69
6.32
0.087
Kuan
17.41
6.49
0.086
Frost
19.89
5.97
0.079
Gauss
MRF
25.66
4.95
0.023
Parameters
SNR
ENL
RSME
Methods
Lee
16.11
6.05
0.072
Kuan
17.04
5.93
0.069
Frost
20.38
5.19
0.058
Gauss
MRF
27.41
4.08
0.019
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-1/W3, 2013
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266

Figure 7. Visual comparison for Despeckeling of ESAR Image.
5. CONCLUSION
In this paper a novel despeckling algorithm has been developed
for PolSAR imagery. This method works by integration of
advanced statistical analysis with spatial contextual information
with the help of Markov random field. We tested the proposed
algorithm for a real medium-resolution L-band ALOS PolSAR
data (image has size 512 x 512) from Tehran area in Iran and a
sample data set of ESAR PolSAR data, from Oberpfaffenhofen
test site. The obtained results confirm the effectiveness of
proposed algorithm by both visual inspection and quantitative
comparison. In particular, the proposed method has a good
performance in preserving edges of features and improving
signal to noise ratio in the final despeckled images.
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267