International Journal of Computer Applications (0975 – 8887)
Volume 90 – No 7, March 2014
7
averages homogeneous areas and also preserves the edge and
textual information.
One more method had been proposed for speckle reduction
by correlating two measurements made at different spatial
positions [45]and by computing the optimum aperture
displacement. However, by using this method it is difficult to
retrieve small details.
The alternate solution for speckle reduction [45] which
makes use of the anisotropic diffusion which is commonly
employed to choose conduction coefficients for smoothing
edges and boundaries are also found.
The authors have suggested that it might be possible to
process the whole image in a single step [45] or by
partitioning using Zero Adjustment Procedure (ZAP).
Other standard filters like kalman, geometric, Oddy and
Adaptive Filter on Surfaces (AFS) filters have limitation of
algorithmic complexity. Kuan filter reconstruction estimate
is given by.
Where
. (3)
The oddy filter is a mean filter and its shape varies based on
local statistics.
Otherwise
where α filter parameter and wadaptive binary mask
The reconstructed estimate is given by
(4)
The above limitation can be overcome by adaptive filter
which suggests homomorphic technique (i.e.) multiplicative
noise log transformed into additive noise and estimate the
original image by performing exponential operation which in
turn results in poor reconstruction by losing important
information.
Later people started using Frequency domain techniques
using the wavelet & curvelet transforms based speckle
reduction since those techniques provide more information
and has been suggested by many researchers and has been
described below.
3.2 Frequency domain filtering techniques:
(Wavelet, Curvelet and Directionlet
Transform)
This domain uses manipulation of frequency and it is found
to be good for periodic noise reduction and for image
sharpening. The main drawback is that it is not suitable for
contrast enhancement and manipulates frequency only. The
following frequency domain filters exhibit their own merits
and demerits.
In order to obtain frequency, phase and amplitude
information, it has been preferred to use Complex wavelet
transform. Complex – valued extension to the real wavelets
and to the standard discrete wavelet transform is known as
complex wavelet transform. There are two types; redundant
and non-redundant complex wavelettransform. SAR image
despeckling using complex wavelet transform is
advantageous over discrete wavelettransform as they are
applicable for Multi-Resolution Analysis (MRA) and useful
for sparse representation [2], characterization of the structure
of an image and it also possesses high degree of shift
invariance in its magnitude, but it has a drawback, that it
exhibits 2d (d=dimension of the signal being transformed)
redundancy when compared to Discrete Wavelet Transform
(DWT).
Non redundant DWT for non stationary signal processing
application has also got many drawbacks such as, no
translation invariance i.e. loss of many important coefficients
during translation from original signal to sub bands[46].
Whether discrete or undecimated wavelet, the biggest
problem is the selection of optimal thresholding, small noise
distribution, mismatch at different scales, shift sensitivity,
poor directionality and absence of phase information.Here
the history behind the development in frequency domain
techniques right from Fourier transform to
curvelet[30]complex wavelets techniques including recent
developments have been presented.
Earlier, Fourier transform mathematical approach was used,
but the drawback in using Fourier transform is that it can
give only time localization or frequency localization at one
time. It is not possible to get both the information
simultaneously. Later on, Short time Fourier transform came
into practice and has the limitation of fixed window size,
inability to change window size, Hence it is not meant for
Multi Resolution Analysis. To overcome all these problems
wavelet transform has been used since it is a powerful tool
which supports MRA[2]. In wavelet sub bands, noise is
present in small co-efficient and feature details are present in
large coefficients. But it also has got the drawback of shift
variance and poor directional selectivity. It has three main
steps:
1. Calculate wavelet transform of noisy image
2. Manipulate the wavelet coefficients
3. Compute inverse transform [35]
Shape of the wavelet is chosen based on the different features
to extract. The wavelet transform allows the representation of
a signal onto the orthogonal basis. Each term of the basis
represents the signal at a given scale. It is decomposed into
basis which in turn gives details and approximation, and can
be stored as wavelet coefficient. This representation is called
as a wavelet representation. Among the infinite wavelet basis
choose the basis which is very close to the feature to be
extracted. By using the proportional relation between noise
coefficient and wavelet coefficient one can extract linear
features such as edges and thin stripes [33].
Since Noise contribution is more in high reflections,
normalization is performed which results in equal noise
contribution for all targets which does not produce smooth
edges and linear features. Asymmetric wavelet selection
works well for delineating edges and that of symmetric
wavelet selection to enhance thin features. Wavelet shrinking
technique has also been used but the drawback is setting zero
for the wavelet coefficient which are lower than the