14-05-2013, 01:08 PM
An Improved Hybrid Model for Molecular Image Denoising
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Abstract
In this paper an improved hybrid method for removing
noise from low SNR molecular images is introduced.
The method provides an improvement over the one
suggested by Jian Ling and Alan C. Bovik (IEEE Trans.
Med. Imaging, 21(4), 2002). The proposed model consists
of two stages. The first stage consists of a fourth order
PDE and the second stage is a relaxed median filter, which
processes the output of fourth order PDE. The model enjoys
the benefit of both nonlinear fourth order PDE and relaxed
median filter. Apart from the method suggested by Ling and
Bovik, the proposed method will not introduce any staircase
effect and preserves fine details, sharp corners, curved structures
and thin lines. Experiments were done on molecular
images (fluorescence microscopic images) and standard test
images and the results shows that the proposed model performs
better even at higher levels of noise.
Introduction
Image denoising is an active area of interest for image
processing researchers for a long period. The use of par-
tial differential equations (PDEs) in image processing has
grown significantly over the past years and a large number
of PDE based methods have particularly been proposed to
tackle the problem of image denoising with a good preservation
of edges, and also to explicitly account for intrinsic
geometry [1–5]. Before the development of non-linear
PDE based methods, the problem of noise reduction in images
was treated through linear filtering, in which the image
intensity function is convolved with a Gaussian [6]. The
main problem with this method is the blurring of image
edges. Since the pioneering work of Perona and Malik [7]
on anisotropic diffusion there has been a flurry of activity in
PDE based denoising techniques. Although the method proposed
by Perona and Malik and its variants are much better
in denoising images, these methods tend to cause blocky
effects in images. This blocky effect is visually unpleasant
and the possibility of detecting them as false edges by edge
detection algorithms is high. In [8] it is noted that even without
noise, staircasing effect can arise around smooth edges.
Anisotropic diffusion is designed such that smooth areas are
diffused faster than less smooth ones and blocky effects will
appear in the early stage of diffusion, even though all the
blocks will finally merge to form a level image.
Fourth Order PDEs
Non-linear fourth order PDEs is a comparatively new approach
for effective image denoising. A number of fourth
order PDEs have been proposed in recent years for image
denoising [6, 14, 15] and [16]. Although discrete implementation
of these methods produces impressive results, very little
is known about the mathematical properties of the equations
themselves. Indeed there are good reasons to consider
fourth order equations. First, fourth order linear diffusion
dampens oscillations at high frequencies (i.e. noise) much
faster than second order diffusion. Second, there is the possibility
of having schemes that include effects of curvature
(i.e. the second derivatives of the image) in the dynamics,
thus creating a richer set of functional behaviors [6].
Conclusion
A method to improve the performance of Ling-Bovik
method is introduced in this paper. The artifacts generated
by the Ling-Bovik method can be can be considerably reduced
by this approach. The method preserves curve like
structures and edges much better than the existing method.
The filter is tested against molecular images and standard
test images (by adding different levels of noise). The analysis
shows that Ling-Bovik method can be improved by applying
the proposed approach.