RAT EEE 
ee MEL MEM RE 
OM nw nr A" 
Enhanced Lee Filter[10]: Based on the Lee filter, 
A.Lopes modified it to improve the ability of 
preserving the edges in the image. 
Enhanced Frost Filter[10]: The similar modification 
as Enhanced Lee Filter was introduced to the Frost 
Filter. 
Gamma MAP Filter[9]: It is derived under the 
assumption of the image scene having a Gamma 
Distribution, which is believed more suitable to the 
realistic case. 
The formula for these filters mentioned above is given 
in table 1. 
Table 1. The formula for several filters 
  
  
  
  
  
  
  
  
  
  
  
  
Filter Weighting Function Filtering Formula 
Box W(x,y) = 1 ld s x, bs», 1 = 1*W 
3 0 otherwise 
Median i- 7 Median (x, y)) 
x| Sxoo |y] yo 
; Y » 
Lee W(x.y)=1- Cu I=1-W+I(1-W) 
...... C; (x, y) 
Frost W(x, y) 2 K,e eX» | -I«W 
s Te Sm = 
Kuan Wo» Ci TC I=I-W+I(0-W) 
I+C, 
Enh. Lee i-i CC, 
Sant bk. pese Î=I-W+Id-W) 
x -— e max i» 
C, < C < Ca 
i=l, CC; 
Enh. iL. C RC, 
Frost -K, Cm C fa ni] 7j. 
W(x, y) -— Ke Cms 7 Cr ON I "m I W Cu s C di Cras 
CC 
GMAP j=l CC 
k=oa-N-1 mn [FET 3 
where OK XD +40NI 
1+C, Lai" TES TT 
CE: C;<C<C_, 
PIC» 
  
  
  
  
Where C,, is standard speckle index, C, is varied 
standard speckle index, N is the number of looks, 
C is the upper threshold and K, is called 
max 
damping factor. 
3. Testing Statistical Model for ERS-1 and 
ERS-2 Images. 
Several ERS-1 and ERS-2 single-look images and 
ERS-1 3-look images are chosen to test the statistical 
results for SAR images. 
The testing is obtained from three aspects: 
Speckle index: it is defined as follows, 
= (5) 
H 
It is used as a measure of speckle reduction. The 
smaller that the speckle index is, the less speckle noise 
is left in the images. The standard speckle index for 
  
  
  
  
  
  
  
  
  
  
  
  
  
amplitude SAR images is related with the number of ill 
looks and is expressed as, TI 
C,20.523/4N (6) H 
There are three results shown in Fig.1 (a),(b),(c). of 
1 ERS-1 single—-look image Sp 
1,2x10 [ T T T lir 
- Pi 
1.0x10* = 
- se 
sr Pr 
3 8.0x10 T pr 
3 I El 
6.0x10* F TI 
o 
s L sh 
* x Fi 
P TI 
2.0x10? I S4. 0.523000 M.V.=0.547930 S.D. 0.0731530 c4 sli 
0 EL eet oar dere ; oie | 0.C 
5.0x10? 1.0x10* 1.5x10* 2.0x10* 2.5x10* 
Mean Value 
ERS-2 single-look image 0.C 
1.2x10* CES SUONI 1 OS TE TA ITA 
1.0x10* - oc 
^4 
e 80x10? q $ 0c 
9 4 
© 
o 4 
B 6.0x10° - ae 
o 
$ 4 
9 40x10? y 0.0 
] 0.0 
2.0x105 f= S.L.= 0.523000 M.V.=0.495972 S.D.= 0.0544654 
ol i " 1 1 A J 1 1 1 L 1 
5.0x10? 1.0x10* 1.5x10* 2.0x10* 2.5x10* 00 
Mean Value 
ERS-1 three-look image 
300r T EET Tree TOM RTT IST Y Tamer” l 
E i 0.0 
L 0.0 
p^ 2007 2 
> La 
9 L 0.0 
c 
? L 
S E. 
n 
= r 0.0 
- 7 0.0 
p S.L= 0.301954  MV.=0.307424 ^ S.D.-0.0331673 j 
VU S EE AE rre Er enorme meta reed ds lr eie 32] Fig 
200 300 400 500 600 700 
Mean Value 3 
Fig.1(a). Speckle index for ERS-1 single-look image 
(b). Speckle index for ERS-2 single-look image pd 
(c). Speckle index for ERS-1 3-look image. Spe 
: ; 3 the 
Fig.1(a) and (b) present the relationship between the she 
mean value and standard deviation value for single- Se 
look ERS-1 and ERS-2 images. The linear fit is done tha 
and tested speckle index is presented in the figure. S.I the 
represents the standard speckle index, M.V. represents d 
X PI 
the mean value of speckle index with raw data and S.D. hoi 
is the standard deviation of speckle index. Fig.1(c) 
166 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996