The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
159 
Using this in (12) then 
u 
y\ 
y 2 - 
V3c 
w, = 
2(7 
i 
yf+y 2 2 
•J 3 * * * 7 . 
(13) 
3) Compute the noise variance estimation s * and 
un-noisy wavelet coefficient variance estimation 8 > at scale 
j • 
9 
4) Achieve Wj with (13); 
5) Restore original gray values of Wj ; 
6) Reconstruct and exponential transform the denoised 
image. 
The corresponding deadzone is 
deazone = 
+ y 2 2 ^ 
The wavelet coefficients in deadzone are considered noise and 
set zero, while the wavelet coefficients out of deadzone are 
considered noisy signal and processed with the threshold 
So] 
2(7 
Distribution of original noise joint pdf 
(a) 
Distribution of deduced noise joint pdf 
(b) 
Figure 1. (a). Distribution of equation (6), (b). 
Distribution of equation (10) 
Original 
SAR 
Image 
Logarithmic transform 
& DT-CWT 
Denoted 
SAR 
Image 
1DT-CWT &. 
Exponential transform 
(2.1) 
(3,1 ) 
(4,1) 
(5,1) 
(1.1) 
*3 
« 
(6.1) 
u>j 
<0 
(-2,1) 
(-3,1) 
(-4.1) 
(-5.1) 
(-1,1) 
-'4 U ' 
5-tl 
(-6.1) 
a; 
Denoiôing wirh 
<ji, l' • (i.r -, £ o';H2 a\ 
Restore gray valunss 
V _ J 
Figure 2. Flowchart of the speckle de-noising algorithm 
In step 3, noise variance estimation can be computed with the 
method proposed by Donoho. (David Donoho L., 1995) Lèvent 
S.endur and Ivan W. Selesnick (Lèvent S.endur et al., 2002b) 
have denoted the relationship among noise variance a " , 
noise-free wavelet coefficient variance G *• and wavelet 
coefficient variance > was y w *. Then the estimation 
of was a " ~ ~ a " . In (Lèvent S.endur et al., 2002b) Gy 
was computed by mean filter. Here we use the optimal wiener 
filter to achieve more accurate value. 
4. EXPERIMENT 
We choose eight real SAR images including airborne SAR, 
Radarsat-1, ERS-1 and ERS-2 satellite images. Speckle noise in 
these images is obvious. These images are shown in figure 3. 
Since bivariate shrinkage models have been proved superior to 
the soft thresholding in (Levent S.endur et al., 2002a; Levent 
S.endur et al., 2002b; Levent S.endur et al., 2002c), in this 
section, the proposed algorithm is only compared with the 
results in (Levent S.endur et al., 2002a). We use two criterions, 
PSNR and ENL, to compare the results quantitatively. 
Furthermore, canny edge detector has been used to compare the 
ability of different algorithms to conserve edges feature of 
denoised images. 
3. THE SPECKLE DENOISING ALGORITHM 
In Figure 2 the speckle denoising algorithm based on bsf and 
DT-CWT includes six steps: 
1) Logarithmic transform of the SAR image is 
decomposed with DT-CWT, the number of scales j 
usually is 5 or 6; 
2) Normalization of the wavelet coefficients; 
PSNR and ENL can represent how smooth is the de-noised 
image and how much noise are filtered. Higher are PSNR and 
ENL, smoother is the denoised image. The statistical results of 8 
images are shown in Table 1. Most of PSNR and ENL of images 
denoised by the proposed algorithm are higher than (Levent 
S.endur et al., 2002a). And the detailed results of Radarsat-1 
image are shown in figure 4. Obviously in sight much more 
speckle is removed in figure 4 (d) and (e), but edges feature in 
figure 4 (e) are smoother and continuous.