Thread: Amen Ra
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Old 12-30-2009, 08:14 PM   #198
Avalon Senior Member
Join Date: Oct 2008
Posts: 3,117
Default Re: Amen Ra

Now let's look at the "Sharp" Frequency

The Cycle Spinning-based Sharp Frequency Localized Contourlet Transform
for Image Denoising

Images acquired by sensors are often abrupt by
noise. Since the noise spreads over all the coefficients
while image information concentrates on a few largest
ones in the wavelet transform domain, wavelet
becomes the most successful transform for denoising.
However, traditional two dimension wavelet is hard to
represent sharp image transitions [1] and smoothness
along the contours [2]. Hence, bandelet [1] with
adaptation to the geometric structure and contourlet [2]
with anisotropy scaling law and directionality are
presented to sparsely represent natural images. They
both achieve better denoising performance than
wavelet and also outperform wavelet in image fusion
[3] [4]. However, the computation of geometry in
bandelet is in high complexity thus it is not commonly
used in other image processing tasks except image
denoising, compression [1] and fusion [3].
Contourlet [2] proposed by Minh N. Do and Martin
Vetterli is utilized to capture intrinsic geometrical
structure and offer flexible multiscale and directional
expansion form images. Because of the nearly critical
sampling and fast iterated filter bank algorithm,
contourlet is in lower complexity than bandelet.
However, non-ideal filter are used in the original
contourlet result in significant amount of aliasing
components showing up at location far away from the
desired support [5] and exhibit some fuzzy artifacts
along the main image ridges. Yue Lu [5] proposes a
new construction of the contourlet, called sharp
frequency localization contourlet transform (SFLCT)
and alleviates the non-localization problem even with
the same redundancy of the original contourlet.
Unfortunately, due to the downsamplers and
upsamplers presented in the directional filter banks of
SFLCT, SFLCT is not shift-invariant, which is
important in image denoising by thresholding and
easily causes pseudo-Gibbs phenomena around
singularities [6].In this paper, we apply cycle spinning
[6] to compensate for the lack of translation invariance
property of SFLCT and successfully employed in
image denoising. Experimental results demonstrate that
our proposed method outperforms the original
contourlet (CT), SFLCT and cycle spinning-based
contourlet (CS-CT) in terms of PSNR and visual effect
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