Biomedical Engineering Reference
In-Depth Information
S
n
s(nT) Signal samples
nth sample of kth sifted version of a 2
j
j,k W
n
scaled discrete wavelet
N
number of signal samples.
There are four thresholds frequently used, i.e., hard threshold, soft threshold,
semi-soft threshold, and semi-hard threshold. The hard-thresholding function
keeps the input if it is larger than the threshold, otherwise, it is set to zero. It is
described as in Eq. (
8
)
f
h
ðÞ¼
x
if x
k
ð
8
Þ
¼
0
otherwise
The hard-thresholding function chooses all wavelet coefficients that are greater
than the given threshold kwand sets the others to zero. The threshold k is chosen
according to the signal energy and the noise variance 2r. If a wavelet coefficient is
greater than k, we assume that as significant and attribute it to the original signal.
Otherwise, we consider it to be due to the additive noise and discard the value. The
soft-thresholding function has a somewhat different rule from the hard-thresholding
function. It shrinks the wavelet coefficients by kwtoward zero, which is the reason
why it is also called the wavelet shrinkage function. It is explained in Eq. (
9
) as:
f
s
ð
x
Þ¼
x
k ifx [ k
¼
0 x\k
¼
x
þ
k
ð
9
Þ
ifx
k
The soft-thresholding rule is chosen over hard-thresholding, as the soft-
thresholding method yields more visually pleasant images over hard-thresholding.
Then finally IDWT is calculated by Eq. (
10
)
int
ð
N
=
2
j
þ
1
Þ
log
2
N
X
X
s
n
¼
1
N
S
j
;
k
j
;
kw
n
ð
10
Þ
j
¼
0
k
¼
0
where
j, kw
n
nth sample of kth sifted version of a 2
j
scaled discrete wavelet
J,k
row index
n
column index [
8
].
In our work we have used OTSU'S thresholding to denoise the image which
chooses the threshold in such a way that all variances available in black and white
pixels in the same signal are minimized.
level = graythresh (I) computes a global threshold (level) that can be used to
convert an intensity image into a binary image with im2bw. level is a normalized
intensity value that lies in the range [0, 1].
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