International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
  
Figure (4) illustrates the results of some currently used speckle 
reduction techniques on the same aerial image. As can be 
observed, the proposed method has performed better in 
reducing the speckle noise while preserving edge information. 
  
Figure 4. (a) Original noisy image, (b-d) Results of the 
proposed method, median filtering and Wiener filtering. 
Figure (5) shows the results of applying three different speckle 
noise reduction techniques including the proposed wavelet- 
based method, Wiener filtering and median filtering on a noisy 
SAR image. 
  
Figure 5. (a) Original noisy SAR image, (b-d) Results of the 
proposed wavelet-based method, Wiener filtering and median 
filtering. 
4. CONCLUDING REMARKS 
A speckle noise reduction method in wavelet domain using a 
trous algorithm was introduced. Major contributions of this 
work were the optimal selection of the wavelet function and the 
algorithm to be used for wavelet decomposition of the image. 
The best model fitted to speckle pattern was found to be a 
circularly symmetric Gaussian function. Therefore a two- 
dimensional Gaussian function was proposed as the best 
wavelet basis to be used. In order to achieve complete 
30 
reconstruction of the image using processed wavelet 
coefficients, and to obtain shift invariancy property of the 
wavelet transform, the a trous algorithm was selected as the 
most appropriate for wavelet decomposition. 
A Bayesian estimator was used for estimating the denoised 
wavelet coefficients. This estimator uses a priori knowledge on 
probability distribution of the signal and noise wavelet 
coefficients. This estimator performs like a feature detector, 
preserving the features that are clearly distinguishable in the 
speckled data such as lines and edges. 
The whole algorithm is computationally expensive. Particularly, 
parameter estimation of the signal and noise distributions is the 
most time consuming part of the algorithm. More efficient 
parameter estimation algorithms may reduce the computational 
cost of this part. Further improvements to this algorithm may be 
achieved using knowledge-based information such as image 
texture or PDF of radar cross section (RCS). Integrating these 
different kinds of information may be performed using Neural 
Networks. 
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