International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
proportional to the effective number of looks L .The mean 
; 5 ; : uo 0 
intensity is proportional to the backscattering coefficient O 
of the pixel. 
  
Now we use the ERS-1/2 SLC data to produce the real image 
imaginary image phase image |! amplitude image(1-look) (g) intensity image(4-look) 
intensity image(1-look) amplitude image(4-looks) intensity Figl the histograms of different images 
image(4-look). The followings are their histograms. Form the above histograms, we can draw the conclusion that the 
real and imaginary image are both normal distributed; the phase 
image is uniformly distributed; the amplitude and intensity with 
single-look are respectively Rayleigh and negative exponential 
distributed; the amplitude and intensity with 4-look are 
  
respectively Gauss and Gamma distributed. This is accordant 
(a) real image with the hypothesis or the deduction. 
We can use the these statistical characters of SAR images to 
generate filters. 
3. Adaptive speckle filters 
Adaptive filter takes a moving filter window and calculates the 
statistical information of all piexels’ grey value, such as the 
  
(b) imaginary image local mean and the local variance. The central pixel's output 
value is dependent on the statistical information. 
Adaptive filters mainly include the Kuan filter’ Lee filter Frost 
filter Gamma MAP filter. 
3.1 Kuan filter 
First of all, a filter for additive noise is developed. Then the 
(c) phase image multiplicative noise model for radar images is considered. It is 
based on that the mean square error is minimum(MMSE). The 
linear MMSE filter estimate is given: 
tJ 
HORESIGB/4OESIOBUS/A0) NEC 
  
where the weighting function W is given by 
(d) amplitude image(1-look) 
Wins CC] 
22 
— 
and where C LO, /T is the noise variation coefficient. 
3.2 Lee filter 
  
It regards the multiplicative noise model as a linear 
  
(e) intensity image(|-look) approximation. And based on the MMSE to estimate. The Lec 
filter can be describe by (2) with 
7 ~ 2 12 
W(r)z1-C2/C; (4) 
3.3 Frost filter 
  
It is estimated by MMSE and based multiplicative noise model. 
(f) amplitude image(4-looks) It gives every pixel within the filter window a weighting value. 
130 
Internatio! 
e eter 
the weight 
A=1 
and centra 
filter wind 
Frost filter 
R = 
where Pi i 
3.4 Gamn 
Gamma N 
that the pr 
Gauss dist 
Then Lop 
noise fre 
distributec 
can be des 
R=4(1 
where 
where, N 
respective 
central pi; 
If the © 
correcte 
To form a