The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part BI. Beijing 2008 
Where Y=ln(y), X=ln(s) and N-ln(n). Log-transformed SAR 
image makes multiplicative speckle noise additive. Thus, 
multiplicative correlations between pixels in original images are 
non-existent among that of log-transformed images, in other 
words, pixels of log-transformed images are mutually 
independent. It makes less difficult to separate and extract SAR 
speckle noise from images. 
On the basis of this mutually independent characteristic of log- 
transformed SAR images, we propose a new insitu single- 
pointed wavelet-based (ISPW) algorithm to reduce speckle 
noise locally, not affecting features of other useful signals. The 
fundamental principle of ISPW method is to discern speckle 
noises according to features of noise independent impulse 
response, then to specifically identify speckle noise and to 
reduce speckle noise in located positions. It can preserve image 
edge information in maximal extent and avoid such 
disadvantages of conventional denoising algorithms as over- 
filtering resulting in a loss of a great deal of point-target 
electromagnetic scattering characteristics, so it is undoubtedly 
benefit for computation of stereo-imaging. 
Speckle noise belongs to single-point impulse and its response 
bands are broad which approximately don’t attenuate in 
frequency domain; this means speckle noise represent fairly 
similar characteristic in both high and low frequency. 
Conventional FIR filters are almost ineffective in suppressing 
speckle noise because of inability to separate different 
frequency bands; while wavelet decomposition can achieve 
such separation. The discrete wavelet transform (DWT) of a 
two-dimensional image to a level J obtains an approximation 
subband cAf, containing the low-frequency components of 
images, and three detailed subbands cHj,cVj,cDj , high- 
frequency portions of images including horizontal, vertical and 
diagonal features in the images (Mallat, 1989). Distribution of 
cAj is used as source of discerning and locating speckle noise, 
then cAj,cHj,cVj,cDj of these located positions should be 
operated to appropriate values instantaneously in each wavelet 
scale in that separated impulse responses are one-to-one 
correspondences in each frequency band. 
Furthermore, an effective wavelet base plays an indispensable 
role in detecting and locating speckle noise. Different wavelet 
bases fit for monitoring and detecting different types of signals, 
thus a wavelet base that is more sensitive to single-point 
impulse than that of others is obviously more helpful in 
reducing speckle noise. 
Figure 1. Fundamental flow of proposed method 
2.2 Method specifications 
Fundamental flow of proposed method for denoising speckle 
noise in a SAR image is shown in Figure 1. Detailed processing 
steps are described as follows: 1 2 3 
1) Carry out the logarithmic transform of the original SAR 
image f(x, y). 
2) Apply discrete wavelet transform on the log-transformed 
image g(x, y), obtaining wavelet coefficient of first scale: 
approximate information cA and detailed information in 
horizontal, vertical and diagonal directions cH, cV and cD. 
3) Employ discrete wavelet transform on cA, acquiring 
wavelet coefficient of the second scale: approximate 
information cAl and detailed information in horizontal, 
vertical and diagonal directions cHl, cVl and cDl. 
4) Perform insitu operation 1. According to wavelet 
coefficient distribution of cAl, choose appropriate 
parameters p, q, m, and n to apply insitu operation on cAl, 
cHl, cVl and cDl. 
IfcAl(i, j)<-p*var(cAl), 
then cAl(i, j)=-p*var(cAl), cHl(i, j)=m, cVl(i, j)=m, 
cDl(i, j)=m; 
If cAl(i, j)>q*var(cAl), 
then cAl(i, j)=q*var(cAl), cHl(i, j)=n, cVl(i, j)=n, cDl(i, 
j)=n- 
5) Reconstruct the wavelet coefficient experienced insitu 
operation 1 in step 4 to the first scale, obtaining new 
wavelet coefficient of approximate component in the first 
scale, namely, cA'. 
6) Perform insitu operation 2. According to wavelet 
coefficient distribution of cA / , choose appropriate