Spike noise removal in the scanning laser microscopic image
of diamond abrasive grain using a wavelet transform
Kazuhiro Koshino, Noriyuki Saito, Shigehito Suzuki*, Jun?ichi Tamaki
Department of Computer Science, Kitami Institute of Technology, 165, Koen-cho, Kitami 090-8507, Japan
Received 17 January 2002; received in revised form 5 May 2002; accepted 6 August 2002
To remove spike noise in the scanning laser microscopic image of diamond abrasive grain without blurring the sharp
edges, a new smoothing technique that combines a conventional averaging technique with wavelet transforms is pro-
posed. The diamond abrasive grain image is decomposed into high- and low-frequency subimages using wavelet filters,
and all subimages except the lowest frequency one are synthesized to obtain a high-frequency image, from whose pixel
values spike noise points are extracted. A conventional averaging technique is then applied to the same points in the
original image as the spike noise points in the high-frequency image. The smoothing technique successfully removes
both clustered and unclustered spike noise while preserving the sharp edges. Spike noise is removed without a loss in the
original grain shape. This smoothing technique will surely be effective for other applications.
? 2002 Elsevier Science B.V. All rights reserved.
Keywords: Spike noise removal; Scanning laser microscopic image; Diamond abrasive grain; A conventional averaging; Wavelet
transform; Edge-preserving smoothing
Scanning laser microscopic (SLM) images of
diamond abrasive grains are degraded by spike
noise due to the weak detection of laser reflection
intensity caused by slanting surfaces, hollows, and
so on. Spike noise thus makes it difficult to obtain
accurate information about diamond grains. To
improve the quality of such degraded images, the
noise interference must be removed. In this study,
we propose a smoothing technique that combines
a conventional averaging technique with a 2-D
discrete wavelet transform in order to remove
spike noise in the SLM diamond abrasive image
without the blurring of sharp edges generally
caused by smoothing.
This new smoothing technique decomposes the
original image corrupted by noise into high- and
low-spatial frequency subimages using high- and
low-pass wavelet filters. All subimages except the
lowest frequency one are synthesized to obtain the
high-frequency image, from whose pixel values
spike noise points are extracted. A conventional
averaging technique is then applied to the same
1 October 2002
Optics Communications 211 (2002) 73–83
*Corresponding author. Fax: +81-157-26-9344.
E-mail address: email@example.com (S. Suzuki).
0030-4018/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved.
points in the original image as the spike noise
points in the high-frequency image. Although our
proposed smoothing technique employs a con-
ventional averaging technique which has a draw-
back of causing spatial blurring, it produces
excellent smoothing results with sharp edges pre-
served because it takes advantage of the spike
noise point information for smoothing. To dem-
onstrate its effectiveness, we compare our tech-
nique with representative smoothing methods.
In our technique, the wavelet transform is only
used to extract noise information from the high-
frequency image, which is a difference from
wavelet-based de-noising techniques. Since many
wavelet de-noising techniques have been reported,
we briefly introduce the most recent ones [1–10].
Most of them [1–6] were threshold-based tech-
niques using hard or soft thresholding [11,12]
although they took various approaches to the
problem of noise removal. In principle, the tech-
niques either set to zero all wavelet coefficients
which have an absolute value lower than a
threshold (hard thresholding), or shrink coeffi-
cients larger than the threshold towards zero with
an amount equal to the threshold value (soft
thresholding). The de-noising image is recon-
structed from the modified wavelet coefficients.
Soft thresholding is applied to wavelet coefficients
obtained by wavelet decomposition , and to
those that are iteratively obtained using a regu-
larization method , and is included in the op-
thresholding and soft thresholding are applied to
wavelet packet . The two are used in the
technique  using both wavelet and Karhunen–
Loeve transforms for calculating the weighting
coefficients for wavelet coefficients and obtaining
the correlation matrix from the weighted wavelet
coefficients. Thresholding rules are obtained using
a Bayesian wavelet de-noising technique .
Several of the wavelet-based techniques [7,8]
modify coefficients according to statistical prop-
erties of wavelet coefficients such as kurtosis. The
wavelet coefficients that are definitely corrupted
by noise are set to zero  or are replaced by
interpolated values .
In the present work, wavelet coefficients of
spike noise had much larger absolute values than
the signal components. This noise-interference
situation is greatly different from general situa-
tions where wavelet-coefficient levels of spike are
smaller than those of the signal components and
hence thresholding is effective for eliminating
noise. For this reason, we use the wavelet trans-
forms to extract spike noise information from their
wavelet reconstructed images by discriminating
spike noise from the signal component. For the
same points in the original image as the noise
points in the reconstructed image an averaging
technique is iteratively applied. The smoothing
method is therefore fundamentally different from
the above wavelet-based de-noising techniques.
The SLM image of diamond abrasive grain to
be smoothed is decomposed into subbands using
wavelet filters. Then, all subbands except the
lowest spatial frequency subband are synthesized
to obtain the high-frequency image. The high-fre-
quency image is used to distinguish between noise
and edge components and to extract information
about the magnitude and position of noise. On the
basis of the noise information, pixel points to be
processed are selected and smoothing filters for the
points are determined. In this way, the present
smoothing technique attempts to remove spike
noise from the original SLM diamond grain image
without a loss in edge sharpness.
A 2-D discrete wavelet transform can be im-
plemented using 1-D low- and high-pass wavelet
filters on the rows in the 2-D image array and then
on the columns. The 1-D discrete wavelet filtering
 is implemented as follows:
hðk ? 2mÞsðlÞ
gðk ? 2mÞsðlÞ
where fhg and fgg are the low- and high-pass fil-
ters, respectively, and sðlÞ
and high-frequency components in the level l,
respectively. Taking sð0Þ
components are decomposed into subbands using
mare the mth low-
mas the original value, the
K. Koshino et al. / Optics Communications 211 (2002) 73–83
necessary to discern the edge and spike noise using
geometrical structures of the edges such as edge
lines. These are subjects for a further study.
To remove spike noise in the SLM image of
diamond abrasive grain without blurring sharp
edges, a new smoothing technique that combines a
conventional averaging technique with a 2-D dis-
crete wavelet transform was proposed. This tech-
nique proved effective for removing both clustered
and unclustered spike noise while preserving sharp
edges. Because the spike noise was eliminated
without loss of the original shape, good restora-
tion of the original diamond shape could be
achieved. This smoothing technique will surely be
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