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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
