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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5837_Библиотеки_им_академика_М_И_Перельмана.pdf
4.3 Experimental Studies of the Wavelet and Guided Filter … 99
(a) Original image (b) SRBF (c) DPAD
(d) Andria (e) OBNLM (f) SAR-BM3-D
(g) Wavelet-Soft Shrinkage (h) Wavelet+bilateral (i) Wavelet+guided
Fig. 4.14 The removed noise images of the breast ultrasound image
careful observation of the image, we can see that the Andria filter (Fig. 4.13d) do
not obtain an obvious speckle reduction effect which is consistent with the simula-
tion results. The denoised image of Wavelet-Soft Shrinkage is shown in Fig. 4.13g.
It can filter most of small noise existing in high-pass component, but do not have
satisfactory performance for noise in low-pass component, and thus some speckle
noise still exists in the low-pass component after wavelet transformation. And other
filters obtain very fine speckle suppression performances by intuition.
However, only using the human eye perception to observe the de-noised images
cannot obtain the impartial evaluation, especially for the tiny details which the human
100 4 Despeckle Filtering of Medical Ultrasonic Images …
Table 4.6 NIQE of images
in Fig. 4.13
De-noising methods NIQE
Noisy image 5.7915
SRBF 7.3026
DPAD 4.5330
Andria 7.3836
OBNLM 6.6960
SAR-BM3-D 8.2565
Wavelet-Soft Shrinkage 7.3725
Wav e l et + bilateral 9.5018
Wav e l et + guided 9.7185
eye cannot perceive. Considering the fact that the medical ultrasound images with-
out noise do not exist, PSNR, SSIM and other quantitative performance measures
which need noise-free images as reference images will not work for evaluating med-
ical ultrasound images. Therefore, NIQE (no-reference image quality assessment)
is introduced to evaluate the quality of de-noised images. Just as its name suggests,
NIQE do not need noise-free image as reference image and is consistent with human
eye perception. The average NIQE values of filtered images are listed in Table 4.6.
It is shown that the proposed and Wavelet + bilateral methods have the fine NIQE
values which means they have the best speckle reduction effects in comparison with
other filters. The SRBF, Andria and Wavelet-Soft Shrinkage filters obtain similar
lower values than that of the SAR-BM3-D filter. This is because they blur image or
do not perform well on speckle suppression. Additionally, the DPAD filter perform
poorly in NIQE metric due to the reason that some obvious artifacts (as in massive
mosaics) appear in the filtered image (Fig. 4.13c).
In order to observe the changes of the details, the idea of removed noise images is
introduced. Figure 4.14 demonstrates the removed noise images of the experiments.
The removed noise image means the difference between clinical ultrasound image
and the corresponding filtered image. Removed noise images can present the visible
traces of man-made structures and the smoothing of sharp boundaries of the filters.
A removed noise image contains only speckle if the filter performs perfectly and has
an ideal de-speckling performance. On the contrary, if visible geometric structures
exist, it indicates an unwanted smoothing of sharp boundaries. The removed noise
image of the SRBF filter presents the trace of man-made structures marked by linear
structures at a high amplitude region in the images, which means the image exhibits
over-smooth phenomenon at the high amplitude region. Both Andria and Wavelet-
Soft Shrinkage have a little trace of man-made structures, but they do not filter
enough noise because the removed noise images have a little noise. The removed
noise image of the DPAD filter exhibits over-smooth and “artifact” phenomena at the
low amplitude region. It can also be seen that the removed noise image of OBNLM
filter presents obvious artifact relate to the structures of the filtered images. On the
4.3 Experimental Studies of the Wavelet and Guided Filter … 101
contrary, the removed noise image of SAR-BM3-D filter has a little trace of man-
made structures, which means that no over-smoothing of sharp boundaries exist in the
filtered image. With careful observation of the images, for the proposed method and
the Wavelet + bilateral de-specking method, it can be seen that the removed noise
images have uniform noise, and the proposed method can suppress more speckle
noise than the Wavelet + bilateral de-specking method.
From above, although the SRBF filter has low complexity, it tends to blur images
and cannot obtain satisfactory de-noised results. The DPAD filter has strong speckle
noise suppression ability, but the de-noised results may appear over-smooth phe-
nomenon and introduce some man-made artifacts. Additionally, the filter is an itera-
tive de-noising method, which will spend too much time. Since the speckle noise in
medical ultrasound images appears as a larger “granular”, the Andria and Wavelet-
Soft Shrinkage filters perform worse on speckle noise suppression. The wavelet de-
noising method can filter most of the small noise and has the advantage of low com-
plexity, and that is why the wavelet de-noising method is combined in the proposed
method. The OBNLM filter has the disadvantage of high complexity which cannot
meet the real-time requirement of medical ultrasound imaging system, although it
has satisfactory de-speckling performances. The SAR-BM3-D filter combines the
denoising ability of the nonlocal means filter and thus obtain more satisfactory
speckle noise suppression ability. However it increases the complexity and is not
time effective. The low algorithm complexity of wavelet de-noising method and the
denoising ability of guided filter are combined in the proposed method and obtain
satisfactory speckle noise suppression performance.
4.4 Conclusions
Aiming at the problem of speckle noise in medical ultrasound image, an improved de-
speckling method is proposed in this chapter which is based on the wavelet de-noising
method and guided filter. Compared with the existing other de-noising methods, the
proposed method, which combined the wavelet de-noising method with guided filter,
has advantages of these two different methods. On one hand, the guided filter is used
to compensate for the disadvantage of wavelet de-noising method. On the other hand,
compared with the traditional wavelet de-noising method, the proposed method can
greatly improve the de-noising performance for the medical ultrasound images. In
addition, it is developed on the solid theory foundation due to the using of maximum
a posteriori probability theory and Bayesian estimation theory.
In simulation experiments and experiments for medical ultrasound images, the
proposed method is compared with other seven de-noising methods. Two simulation
experiments are carried out using PSNR, SSIM and FoM quantitative performance
measures in this chapter. By comparing these indexes, it is shown that the proposed
method perform better than other filters on speckle noise removing performance. The
102 4 Despeckle Filtering of Medical Ultrasonic Images …
de-noised results of clinical medical ultrasound image also indicate that the proposed
not only has a strong de-specking ability, but also keep the image details, such as the
edge of the lesion.
References
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10. E.K. Abd, A. Youssef, Y. Kadah, Real-Time speckle reduction and coherence enhancement in
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Chapter 5
Despeckling Method for Medical Images
Based on Wavelet and Trilateral Filter
Abstract In this chapter, an integrated despeckling approach for medical ultrasound
images based on wavelet and trilateral filter is presented. Firstly, a dynamic additive
model is developed to account for the medical ultrasound signal with speckle noise.
Secondly, in accordance with the statistical property of the additive model, an adap-
tive wavelet shrinkage algorithm is applied to the noisy medical signal. Particularly,
the algorithm is significant to the high-frequency component of the speckle noise
in the wavelet domain. Thirdly, but most importantly, the low-frequency component
of the speckle noise is suppressed by a trilateral filter. It simultaneously reduces the
speckle and impulse noise in real set data. Finally, a lot of experiments are con-
ducted on both synthetic images and real clinical ultrasound images for authenticity.
Compared with other existing methods, experimental results show that the proposed
algorithm demonstrates an excellent de-noising performance, offers great flexibility
and substantially sharpens the desirable edge.
5.1 Introduction
Speckle noise is a granular artifact in medical ultrasound images. It causes serious
problems and hinders the development of automatic diagnosis technology.
Nowadays ultrasonic imaging technology still remains challenging, mainly due
to the following circumstances [1, 2]:
1. Due to the unevenness of human organs, structures with a relatively small volume
cannot be distinguished by ultrasound.
2. Based on the hypothesis that the wavelength of the incident ultrasonic waves is
generally fixed, scattering echoes occur when the size of the body tissue structure
is close to or smaller than the wavelength. The echoes possess different phases
and therefore could potentially interfere with each other. Then the speckle noise
and impulse noise are the results.
In medical ultrasound images, there exists a large amount of intuitive noise, such
as speckle, fine particle, snowflake and cob-webbing structures, among which the
speckle noise is regarded as the most influential noise. The image quality is severely
depressed, and the details are blurred by the inherent speckle noise. It results in low
© Springer Nature Singapore Pte Ltd. 2020
J. Zhang and Y. Cheng, Despeckling Methods for Medical Ultrasound Images,
https://doi.org/10.1007/978-981- 15-0516-4_5
103
104 5 Despeckling Method for Medical Images Based on Wavelet …
contrast lesions between normal and tumor tissue and thus makes the subsequent
image processing difficult, such as feature extraction, analysis and diagnostics [3–7].
In this chapter, based on the wavelet shrinkage algorithm and trilateral filter, an
integrated optimization algorithm is investigated to deal with the noisy image. The
novel idea here is the combination of an improved wavelet algorithm and a high
efficiency trilateral filter.
Firstly, a dynamic additive model is developed to account for the medical ultra-
sound signal with speckle noise. Secondly, in accordance with the statistical property
of the additive model, an adaptive wavelet shrinkage algorithm is applied to the noisy
medical signal. Particularly, the algorithm is significant to the high-frequency com-
ponent of the speckle noise in the wavelet domain. Thirdly, but most importantly, the
low-frequency component of the speckle noise is suppressed by a trilateral filter. It
simultaneously reduces the speckle and impulse noise in real set data. Finally, a lot
of experiments are conducted on both synthetic images and real clinical ultrasound
images for authenticity. Compared with other existing methods, experimental results
show that the proposed algorithm demonstrates an excellent de-noising performance,
offers great flexibility and substantially sharpens the desirable edge.
5.2 A Despeckling Approach for Medical Ultrasound
Images Based on Wavelet and Trilateral Filter
In order to continuously improve the de-noising performance of medical images, we
have made many attempts. Combine various filters with wavelet transform de-noising
methods and see how they work. In this chapter, a novel and integrated approach is
introduced to address the de-noising problem by using wavelet transformation and
trilateral filter.
5.2.1 Model for Medical Ultrasound Images
As described in previous chapters, the envelope signal, which is collected by medical
ultrasound imaging systems, consists of two aspects, namely the reflected signal
in body tissue and the noisy signal. The noisy signal can further be classified into
multiplicative noise and additive noise. The multiplicative noise mainly derives from
random scattering signal and the additive noise generally belongs to system noise
that can usually be ignored, in contrast to the multiplicative noise. Hence, the generic
model for the envelope signal s(x, y) is simply expressed as
s
(
x, y
)
= r
(
x, y
)
n
(
x, y
)
(5.1)
5.2 A Despeckling Approach for Medical Ultrasound Images Based … 105
where (x, y) ∈ Z
2
represents the 2D spatial coordinate, r(x , y) denotes the noise-
free signal, and n(x, y) denotes the multiplicative noise.
In order to adapt to the dynamic display range, which is exhibited by ultrasound
imaging system on the screen, the model in Eq. (5.1) is transformed into the additive
form in Eq. (5.2) via the logarithmic transformation processing.
log
(
s
(
x, y
))
= log
(
r
(
x, y
))
+ log
(
n
(
x, y
))
(5.2)
At this point, log(s (x , y)) is the general medical ultrasound image. By applying
2D discrete wavelet transformation t o Eq. (5.2), a new model is obtained:
S
j
l,k
= R
j
l,k
+ N
j
l,k
, j = 1, 2, ···, J (5.3)
where S
j
l,k
, R
j
l,k
, N
j
l,k
denote the wavelet coefficients of the noisy image, the noise-free
image and the speckle noise, respectively. The superscript j indicates the decompo-
sition layers of wavelet transformation, and the s ubscript (l, k ),
(
l, k
)
∈ Z
2
means
the wavelet domain coordinate. J denotes the largest decomposition layer.
5.2.2 Some Backgrounds
In this chapter, we still suppose that in Eq. (5.3), the wavelet coefficient R
j
l,k
of
noise-free signal obeys the generalized Laplace distribution and is in accord with the
formulation provided by Gupta et al.
p
R
(r) =
b
2aΓ
1
b
exp
−
r
a
b
a, b > 0(5.4)
where Γ(v) =
∞
0
x
v−1
exp(−x )dx denotes Gamma function, a represents the scale
parameter, and b means the shape parameter. To simplify calculation, we choose
b = 1sothatEq.(5.4) obeys the Laplace distribution, as Eq. (5.5), which is a special
case of the generalized Laplace distribution.
p
R
(r) =
1
2 a
exp
−
r
a
a > 0 (5.5)
Furthermore, we suppose that the wavelet coefficient of speckle noise N
j
l,k
submits
to zero mean Gaussian distribution:
p
N
(n) =
1
√
2πσ
N
exp
−
n
2
2σ
2
N
(5.6)
where σ
N
denotes the standard deviation of the speckle noise in wavelet domain.
106 5 Despeckling Method for Medical Images Based on Wavelet …
Fig. 5.1 Histogram
distribution of wavelet
subband in lena image (Real
Line), Laplace probability
density function (dashed
line)
To verify the model distribution, the histogram distribution of a high frequency
subband of a classical Lena image and Laplace density function and its simulation
are both given in Fig. 5.1.
5.2.3 Steps of the Proposed Despeckling Approach
for Medical Ultrasound Images Based on Wavelet
and Trilateral Filter
For medical ultrasound images, we present a de-speckling approach based on wavelet
and trilateral filter, by making three aspects of improvements on the traditional
wavelet transformation. The main steps of the proposed algorithm are listed as fol-
lows:
• Step A: Modifying the general threshold function i n order to further deal with the
de-noising processing of medical ultrasonic images.
• Step B: According to the statistical model of the signal and the noise in the wavelet
domain, designing an adaptive wavelet shrinkage algorithm based on the Bayesian
maximum a posteriori estimation method [8].
• Step C: Applying the trilateral filter to deal with the low-frequency component
after wavelet transformation.
• Step D: Utilizing the inverse wavelet transformation to obtain the de-noised image.
The schematic diagram of the proposed algorithm is shown in Fig. 5.2.
5.2 A Despeckling Approach for Medical Ultrasound Images Based … 107
Fig. 5.2 Schematic diagram of the proposed de-speckling approach for medical ultrasound images
based on wavelet and trilateral filter
5.2.4 Main Aspects of the Despeckling Approach for Medical
Ultrasound Images
(1) Adaptive Wavelet Threshold Function Setting
As early as 1994, Donoho suggested a layout named the universal wavelet shrinkage
threshold function T = σ
N
√
2logM, where M denoted the number of the wavelet
coefficients in the corresponding wavelet domain. However, the algorithm had been
proved to perform poorly in the de-noising process of medical ultrasonic images [9,
8, 10, 11].
As we known, the threshold function T will be greatly influenced by the number of
wavelet coefficients. The larger M is, the bigger threshold value T becomes, and the
108 5 Despeckling Method for Medical Images Based on Wavelet …
big value T will smooth out some useful information, so that the threshold function
becomes ineffective in the noise removal process of medical ultrasonic images.
In this chapter, we select the wavelet shrinkage threshold function which has
same structure as the wavelet shrinkage threshold function we have used in previous
chapter. Its formula will be showed in follows:
T
j
= t
j
σ
N
2logM (5.7)
where j (= 1, 2, …, J ) denotes the decomposition layers of wavelet transformation,
J denotes the largest decomposition layer. In this chapter, we choose t
j
= 2
J −j +1
.
But it should be noted that t
j
denotes the adaptive parameter of the j layer, and it is
determined experimentally. After the waveletdecomposition, the wavelet coefficients
in different decomposition layers have different distribution. Thus, the selection
of t
j
should be based on j. But this choice of t
j
is not optimal, because if t
j
is
selected appropriately, t he method we are introducing in this chapter will reflect
more advantageously.
(2) Steps of the Adaptive Wavelet Shrinkage Algorithm
• Bayesian maximum a posteriori estimation is utilized to obtain the estimation of
the signal in the wavelet domain. Set
p
R
|
S
(
r
|
s
)
=
1
p
S
(
s
)
p
N
(
s − r
)
p
R
(
r
)
(5.8)
• Applying Eqs. (5.5) and (5.6), (5.8) can be restated as:
p
R
|
S
(
r
|
s
)
=
1
2
√
2πaσ
N
p
S
(
s
)
exp
−
2σ
2
N
|
r
|
+ a
(
s − r
)
2
2aσ
2
N
(5.9)
• Calculate the first-order derivative of ln
p
R
|
S
(
r
|
s
)
with respect to r and then the
consequential algebraic expression is set to 0 in order to get the maximum posteriori
probability. Such that ˆr = sgn
(
s
)
max
|
s
|
−
σ
2
N
a
, 0
, where ˆr is the estimation of
r.
• Finally, the synthetic wavelet shrinkage formula is replaced by
ˆr =
0 s ≤ T
j
sgn
(
s
)
max
|
s
|
−
σ
2
N
a
, 0
s > T
j
(5.10)
Parameter estimations are listed in Table 5.1.