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according to the theory of these filtering algorithms. 
Currently, the common software packages, such as 
MICRO BRIAN, ILWIS, ERDAS,PCI,and ER Mapper 
are widely used in remote sensing and they include the 
different filters in them so as to meet the needs of 
different application purposes. 
What we want to do now is to obtain more information 
from SAR speckle image data and to compare several 
speckle filtering algorithms in order to provide some 
results concerning ERS-1&2 image application. This 
paper is organized as follows, 
(1) General review of speckle reduction techniques. 
It will present the mathematics model of SAR speckle 
and the theoretical expression of several speckle filters. 
It includes a discussion on these filters. 
(2) Analyzing the speckle properties for ERS-1&2 
data. 
Statistical results are obtained by testing ERS-1&2 
images. The statistical results are show in this section 
and the detailed analyses concerning these test results 
are presented. 
(3) Testing result analysis. 
Trying the different speckle filters for ERS-1&2 
imagery to evaluate the performance of speckle 
reduction by quantitative evaluation and qualitative 
evaluation. The comparison results are shown in tables 
and filtered images. The test results are discussed in 
detail. 
2. Basic Principle of Speckle Theory and 
Filtering Techniques 
2.1 Statistical Model for SAR speckled image 
Much literature has been published concerning speckle 
characteristics and SAR image  models[1][2][3]. 
Among them, the multiplicative model has proved to 
be one of the most accurate and suitable for SAR 
imagery. 
A more realistic model for explaining a SAR image to 
simply measuring a patch of homogeneous area in a 
SAR image, can be expressed as 
I(x,y)=R(x,y)-S,(x,y) (1) 
where (x,y) are the spatial range and azimuth 
coordinates of the resolution cell center, J(x,y) is the 
intensity of SAR image, R(x,y) is a random process 
of radar reflectivity (unspeckled radiance) , § (x,y) is 
model as speckle noise having a stationary random 
process with unit mean and variance proportional to 
the effective number of looks N and is statistically 
independent of. R(x, y). 
Usually, SAR images are classified into two classes. 
One is ‘homogeneous’ and the other is 
‘heterogeneous’. In order to filter speckle in 
heterogeneous areas, some primary mathematical 
165 
models have been established[9]. The most common 
one defined an N-look SAR image as having a Gamma 
distribution with mean value R(x,y) and variance 
value R? (x, y)/ N is expressed as follows, 
NI In 
R= 6 1 (2) 
BUR N DIR * 
For the homogeneous area, the pdf of SAR image is, 
NY! In 3) 
p(I) - pa! R)- f 
——— € 
(N —Di" 
However, for heterogeneous areas, the radar 
reflectivity R(x, y) itself is a random process, so that 
the pdf of the intensity of SAR image have, 
p) — [p 1! R): p(R)- dR (4) 
Equation (3) demonstrates the general distribution for 
the homogeneous area, which is well accepted by 
scientists. However, to what kind of distribution the 
radar reflectivity R(x, y) belongs, is still a dilemma. In 
fact, the main point of speckle filtering techniques is to 
recover R(x,y) by means of the priori information 
about speckle pdf and image pdf. 
2.2 Filtering techniques for speckle reduction 
The speckle filtering techniques can be classified into 
two categories[6].The techniques in the first category 
are equivalent to applying a low-pass filter to the 
image, such as multi-look processing and the box filter. 
This step is taken as a part of preprocessing. The 
second category is to reduce speckle noise after the 
SAR image has been formed. It is considered as a part 
of the post-processing of SAR images. Here only the 
filters for the second category are discussed as follows, 
Box Filter[4]: It is a typical low-pass filter, which can 
remove the noise with a high frequency spectrum as 
well as smoothing the details, such as the edges and 
points etc. 
Median Filter[5]: It is a nonlinear filter and is derived 
from the maximum-likelihood (ML) estimation 
principle by assuming the signal to be contaminated by 
additive noise with a Laplace distribution. In some 
cases, it is much more efficient than most other filters. 
Lee Filter[6][7]: It was derived from the minimum 
square error(MMSE) criteria by introducing the local 
statistics method in it. It was believed that it can reduce 
speckle noise while preserving the edges in the image. 
Frost Filter[8]: It was also derived from the principle 
of MMSE. The filter kernel can vary with the local 
statistical value of the images so as to reduce the noise 
while at the same keeping the edges. 
Kuan Filter[12]: It is derived from MMSE criteria 
under the assumption of a nonstationary mean and 
nonstationary variance(NMNV). It is quite similar to 
the Lee Filter in form. However, it is considered to be a 
a little more accurate than Lee Filter due to the fact that 
no approximation is required in the total derivation. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996