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
