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BAYESIAN-BASED DESPECKLING IN WAVELET DOMAIN USING “A TROUS” 
ALGORITHM 
of Rajski H. Abrishami Moghaddam *, M. J. Valadan Zouj "^, M. Dehghani 
| of dual 
ce of The “Dept. of Electrical Engineering, K. N. Toosi Univ. of Technology, Tehran, Iran, moghadam(@saba.kntu.ac.ir 
® Dept. of Geodesy and Geomatics Engineering., K. N. Toosi Univ. of Technology, Tehran, Iran, dehghani_rsgsi@@yahoo.com 
KEY WORDS: Transformation, Estimation, SAR, Radar, Statistics, Multiresolution. 
ABSTRACT: 
In this paper an improved speckle noise reduction method is presented based on wavelet transform. A 2D Gaussian function is found 
to be the best model fitted to the speckle noise pattern cross-section in the logarithmically transformed noisy image. Therefore, a 
Gaussian low pass filter using a trous algorithm has been used to decompose the logarithmically transformed image. A Bayesian 
estimator is then applied to the decomposed data to estimate the best value for the noise-free wavelet coefficients. This estimation is 
based on alpha-stable and Gaussian distribution hypotheses for wavelet coefficients of the signal and noise, respectively. 
Quantitative and qualitative comparisons of the results obtained by the new method with the results achieved from the other speckle 
noise reduction techniques demonstrate its higher performance for speckle reduction in SAR images. 
1. INTRODUCTION 
Imaging techniques using coherent illumination, such as laser 
imaging, acoustic imagery and synthetic aperture radar (SAR), 
which generate coherent images [4], are subject to the 
phenomenon of speckle noise. Speckle noise is generated due to 
constructive and destructive interference of multiple echoes 
returned from each pixel. As a result, a granular pattern is 
produced in the radar image which corrupts significantly the 
appearance of the image objects. Speckle noise can be modeled 
as multiplicative random noise in spatial domain [16]. 
Many attempts were made to reduce the speckle noise. An 
appropriate method for speckle reduction is one which increases 
the signal to noise ratio while preserving the edges and lines in 
the image. Generally, there are two main approaches for speckle 
noise removal. The first is applied before image generation which 
is called multi-look processing [16]. In this method the synthetic 
aperture is divided into some pieces. Each of these apertures is 
processed separately to obtain a pixel with a special along-track 
dimension. The N images are summed to form an N-look SAR 
image. The N-look processing reduces the standard deviation of 
the speckle. The second approach is filtering the image using 
different filters [14,9]. Two types of filters are used for speckle 
reduction. Low pass filters such as mean or median generally 
smooth the image. The second type is adaptive filtering [13,10]. 
These filters adapt themselves to the local texture information 
within a box surrounding a central pixel in order to calculate a 
new pixel value. Adaptive filters demonstrated their superiority 
compared to lowpass filters, since they take into account the local 
statistical properties of the image. Adaptive filters perform much 
better than low-pass smoothing filters, in preservation of the 
image sharpness and details while suppressing the speckle noise. 
Both multi-look processing and spatial filtering reduce speckle at 
the expense of resolution and they both essentially smooth the 
image. Therefore, the amount of speckle reduction desired must 
be balanced with the particular application and the amount of 
details required. 
Generally, a successful speckle reduction method has to 
accomplish these requirements: 7) variance reduction in 
homogeneous areas, ii) texture, edge and line preservation, iii) 
point scatterer exclusion, and iv) artifact avoidance. 
07 
In all speckle noise reduction techniques, the statistical 
distribution of SAR data plays an important role. These 
statistical properties can be used to develop specialized filters 
for speckle noise reduction. However, in the above mentioned 
methods some information in the image such as edges and lines 
will be lost. Therefore, methods based on spatial filtering are 
not appropriate in applications in which preserving of spatial 
details is important. 
Recently, few attempts have been made to reduce the speckle ’ 
noise using wavelet transform as a multi-resolution image 
processing tool [6]. Speckle noise is a high-frequency 
component of the image and appears in wavelet coefficients. 
One common method used for speckle reduction is wavelet 
shrinkage [15]. According to this method, large wavelet 
coefficients of the image correspond to the signal and the 
smaller ones represent the noise. The threshold is computed 
based on statistical properties of the noisy data using different 
shrinkage rules. A shrinkage function such as Garrote- 
thresholding, hard-thresholding or soft-thresholding uses this 
threshold to modify the wavelet coefficients [5]. The main 
difficulty with this method is to optimally determine the 
threshold value. 
Achim ef al. [2] presented a Bayesian-based method for speckle 
noise reduction in medical ultrasonic images. They used a least 
square method for estimation of the wavelet coefficient 
distributions corresponding to the signal and noise. Then a 
Bayesian estimator has been used for estimating the noise free 
wavelet coefficients. 
This paper presents an efficient algorithm for Bayesian-based 
speckle noise reduction using optimally implemented a frous 
algorithm for image decomposition [1, 11, 12]. It is shown that 
the Lapalacian of Gaussian (LOG) is the best wavelet function 
to be used for image decomposition in speckle reduction 
problem. Since complete reconstruction of the image using this 
wavelet function is not possible, another wavelet function called 
Coiflet which is similar to LOG function is used. Further 
improvement is achieved by using a trous algorithm for image 
decomposition applying a lowpass Gaussian filter. This 
algorithm uses an undecimated wavelet transform to avoid the 
artifacts produced by subsampling. 
In the next section, the improved Bayesian-based algorithm for 
~ 
speckle noise reduction is presented. Section 3, is devoted to