The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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1 3(m, n) e B k s s \\, (/', j) - (m, k)| < a 
or \A O',» - (m, «)| > 360° - or 
0 else 
The relationship between B k '5,5+1 and B k s ,s+1 is: 
B 5,5+1 — B\ 5,5+1 'U 52 5,5+1 
(3) 
(4) 
Where, 
51*5,5+1 = jo»./) e | D k ~ l (i,j) = l} 
52*5,5+1 = \m,n) g 5*;1, I VO J) e M s ,D k s ~^' m ' n) = o} 
/* a j) = J^+i a* e B2 k s J+1 
i,?+1 ’ 1 I s (i,j),else 
A k j0 y) = G B2 k s J + 1 
In the equation, D k represents the correlation 
between the point (/,7) in A/ 5 and the 
point (m, n) of 5* — ’5,5+1 . Z)f _1 0,7, rn, n) = 1 that means the 
two points are correlated with each other and vice versa. 
If 0,7) is th e point of 5”5,5+1, through above iteration, it can 
be extended to the whole edge. With the step of edge fusion, it 
can be assumed that we have gotten the robust and accurate 
edge information in current level, which is then used as 
auxiliary information for the speckle filtering. 
3.3 Improved Local Wavelet Soft-threshold with Edge 
Preservation 
With consideration that for different levels and different 
wavelet sub-bands, the coefficients of them differ a lot. So it is 
inappropriate to use a universal threshold to filter the high 
frequency. The threshold Thr used in this paper for each 
wavelet sub-bands is derived by itself information, that is: 
ti t = sgn(ry)(|ry| - T) = 
\co\-T 
a»Thr 
0 
|ry|< Thr 
\co\ + T 
co < -Thr 
(6) 
Here CO is the wavelet coefficient of the point not marked as edge 
and Tjj is the filtered wavelet coefficient. 
4. PERFORMANCE EVALUATION 
In this paper, the performance of our filter was evaluated and 
compared with several the most widely used self-adaptive filter 
based on the spatial domain, including the Median, Lee, Frost 
and Gamma filter. 
To quantitative evaluate of a filter, several criteria such as 
equivalent number of looks, relative standard deviation, edge 
preservation, texture preservation, are used. 
4.1 Image Variance (IV) 
/K= ^ZZ<^- £ < X » 2 (7) 
i j 
Where N is the total number of pixel, X is the matrix of pixel 
intensity, E(X) is mean value. 
4.2 Mean Square Error (MSE) 
MSE indicates the average difference of the pixels throughout 
the image. A higher MSE indicates a greater difference 
between the original and denoising image. This means that 
there is a significant speckle reduction. Nevertheless, it is 
necessary to be very careful with the edges. The formula for the 
MSE calculation is given as: 
(8) 
Where N is the size of the image, X is the denoising image, and v is the 
original image. 
4.3 Relative Standard Deviation (RSD) 
The reduction of the RSD is a good measure of the efficiency 
for a filter when the image mean varies little. The relative 
standard deviation is given as: 
RSD^Jlv / E(X) 
Where E(X) is image mean value. 
(9) 
Thr = <y. 
-log («) 
n 
(5) 
Here cr = <J = MAD/ 0.6745 is given by Donoho (Donoho, 
1995) and MAD is media absolute deviation of wavelet coefficients. 
And to preserve the detail in the images, filtering is only 
applied to the pixels that are not marked by the edge points, 
that is: 
4.4 Equivalent Number of Looks (ENL) 
The ENL is used to measure the speckle level in a SAR image 
over a uniform image region. A large value of ENL reflects 
better quantitative performance of the filter. The value of ENL 
depends on the size of the tested region. The equivalent number 
of looks is given as: 
ENL = 
(10)