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Citation: Zhao, T.; Zhang, S.-X. X-ray
Image Enhancement Based on
Nonsubsampled Shearlet Transform
and Gradient Domain Guided
Filtering. Sensors 2022,22, 4074.
https://doi.org/10.3390/s22114074
Academic Editor: Daniele Cocco
Received: 22 April 2022
Accepted: 25 May 2022
Published: 27 May 2022
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sensors
Article
X-ray Image Enhancement Based on Nonsubsampled Shearlet
Transform and Gradient Domain Guided Filtering
Tao Zhao 1,2 and Si-Xiang Zhang 1, *
1School of Mechanical Engineering, Hebei University of Technology, Tianjin 300131, China;
92zhaotao@163.com
2Department of Mechanical Engineering, Zhonghuan Information College Tianjin University of Technology,
Tianjin 300380, China
*Correspondence: 13502063552@163.com
Abstract:
In this paper, we propose an image enhancement algorithm combining non-subsampled
shearlet transform and gradient-domain guided filtering to address the problems of low resolu-
tion, noise amplification, missing details, and weak edge gradient retention in the X-ray image
enhancement process. First, we decompose histogram equalization and nonsubsampled shearlet
transform to the original image. We get a low-frequency sub-band and several high-frequency
sub-bands. Adaptive gamma correction with weighting distribution is used for the low-frequency
sub-band to highlight image contour information and improve the overall contrast of the image.
The gradient-domain guided filtering is conducted for the high-frequency sub-bands to suppress
image noise and highlight detail and edge information. Finally, we reconstruct all the effectively
processed sub-bands by the inverse non-subsampled shearlet transform and obtain the final enhanced
image. The experimental results show that the proposed algorithm has good results in X-ray image
enhancement, and its objective index also has evident advantages over some classical algorithms.
Keywords:
X-ray image; image enhancement; non-subsampled shearlet transform; adaptive gamma
correction with weighting distribution; gradient-domain guided filtering
1. Introduction
X-ray image has become widely employed in medical diagnosis, security inspec-
tion, aerospace, defect detection, machinery manufacture, and other industries since the
development of photoelectric detecting technology and image analysis technology. The
radiographic inspection system’s detecting principle, the image of the hardware equipment,
and the picture created by the X-ray instrument all suffer from low dynamic range, low defi-
nition, low contrast, and excessive noise. Defect detection and image analysis are performed
directly on the collected image. It causes significant inaccuracy in the detection results. As
a result, it is beneficial to use image enhancement algorithms to analyze X-ray images [
1
,
2
],
increase image quality and visual effects, and make subsequent detection easier.
Spatial domain pixel enhancement and transform domain multi-scale coefficient im-
provement enhancement methods are the most common image enhancement algorithms.
The spatial domain improvement is to improve the image by directly processing the pixels,
such as histogram equalization [
3
–
5
], image sharpening and grayscale stretching [
6
–
8
], and
retinex theory [
9
]. Zeng et al. [
10
] proposed a gray-level information histogram for X-ray im-
age contrast enhancement, which improves the performance of many histogram-based en-
hancement techniques dramatically. However, when the image is enhanced, there will be an
over-enhancement phenomenon that will cause the image to be distorted.
Panetta et al. [11]
introduced nonlinear unsharp masking for mammogram enhancement. This method has
good performance for enhancing the fine details in the original images. However, it also
amplifies noise and overshoots the sharp details at the same time.
Tao et al. [12]
introduced
a retinex-based framework for medical X-ray image enhancement. The framework can
Sensors 2022,22, 4074. https://doi.org/10.3390/s22114074 https://www.mdpi.com/journal/sensors
Sensors 2022,22, 4074 2 of 17
increase the contrast, eliminate the noise, and enhance the details, but the contour edges of
the image are affected by the dark area pixels in the original image, showing shadows that
did not exist at all.
The enhancement based on the transform domain first transforms the original image
into the frequency domain for multi-scale decomposition, amplifies or filters the decom-
posed sub-image, and then inversely transforms the image. The wavelet transform [
13
],
ridgelet transform [
14
], curvelet transform [
15
], wedgelet transform [
16
], contourlet trans-
form [
17
], nonsubsampled contourlet transform(NSCT) [
18
,
19
], shearlet transform [
20
,
21
],
nonsubsampled shearlet transform (NSST) [
22
], and other transformations are commonly
used. Tang et al. [
23
] proposed an algorithm based on a multiscale measure in the wavelet
domain for screening mammograms to enhance the details at different scales. However,
the wavelet transform can only capture information in three directions: horizontal, verti-
cal, and diagonal, which is poor in representing anisotropic singular features in images.
Ostojiéet al. [24]
proposed an intensity adaptive nonlinear multiscale detail and contrast
enhancement algorithm for digital radiography. The method adapts to the local exposure
level and thus reduces the artifacts’ saliency, but the adaptation of detail enhancement to
image pixel intensity needs to be strengthened. Zhou et al. [
25
] introduced a medical image
enhancement method based on improved gamma correction in the shearlet domain, which
makes the texture details of the image more prominent and the overall contrast is signifi-
cantly improved. Nevertheless, since this method does not have translation invariance, the
image will produce a pseudo-Gibbs phenomenon.
Because of the unconstrained shearing directions, images after NSST may achieve
optimal sparse representation and nonlinear error approximation. There have been many
achievements in applying the NSST to image enhancement. Zhang et al. [
26
] employed
NSST and tetrolet transform to remote sensing images, effectively retaining the details
and edges of the image and significantly improving the information entropy and mean;
Li et al. [27]
studied the NSST domain to improve blur. The contrast enhancement algo-
rithm uses the remote sensing image enhancement coefficient as an adjustable pattern
recognition task, effectively removing the pseudo-Gibbs phenomenon from the image dur-
ing the enhancement process. Tong et al. [
28
] proposed a visual sensor image enhancement
algorithm using NSST and phase stretching transformation. In this method, the author uses
nonlinear models with different thresholds to process the different scale parts after NSST
decomposition. The algorithm can suppress noise and effectively increase the contrast of
the image. However, none of the above studies have analyzed the parameters and effects
of the decomposition levels and shearing directions of NSST, and the parameter selection
has a certain degree of randomness.
He et al. [
29
] proposed a linear edge-preserving guided image filtering algorithm. The
filtered image can avoid a blurring effect on detailed information. Li et al. [
30
] introduced a
weighted guided image filter by incorporating an edge-aware weighting into an existing
guided image filter to address the problem of abiding by halo artifacts. Kou et al. [
31
]
proposed gradient-domain guided filtering to reduce the effect of image edge smoothing
and introduced first-order edge-aware constraints to processing images, which can better
preserve image edges. However, using intensity domain constraints for edges and details
can over-smooth edges and reduce edge retention.
To address the above issues, we propose an image enhancement method. It is based on
NSST and gradient-domain guided filtering and applies it to X-ray images. The algorithm
combines the advantages of NSST for sparse image representation with gradient-domain
guided filtering for image detail enhancement. The low-frequency sub-band uses adaptive
gamma correction with a weighted distribution to enhance contrast, highlighting tiny
details in the background. The high-frequency sub-bands use gradient-domain guided
filtering to filter out image noise and extract edge and texture information by analyzing the
image quality of the four-levels direction decomposition under different scale decomposi-
tion levels, and the image quality of various direction decomposition sequences under the
four-levels scale decomposition. We compare the running times of different decomposi-
Sensors 2022,22, 4074 3 of 17
tions and obtain optimal NSST decomposition parameters. The enhancement experiments
on medical and industrial X-ray images show that the proposed algorithm can enhance
the image contrast, details, and texture information and obtain high-quality images for
subsequent research and analysis.
2. Related Works
2.1. Nonsubsampled Shearlet Transform
The nonsubsampled shearlet transform is extended based on the shearlet transform.
The shearlet transform is an algorithm that combines synthetic dilated affine systems
with multiscale analysis. It can decompose the image more sparsely and achieve optimal
approximation. Its construction is simple and anisotropic, and in dimension
n=
2, the
affine systems with composite dilations are collections of the form:
ΛAB (ψ) = nψj,l,k(x) = |detA|j/2ψ(BlAjx−k):j,l∈Z,k∈Z2o(1)
A=a0
0√a,B=1s
0 1(2)
Among them,
ψ∈L2(R2)
represents the basis function,
A
is a 2-dimensional in-
vertible matrix of anisotropic expansion, which is related to scale transformation.
B
is
a 2-dimensional shear invertible matrix, related to rotation or shear transformation, and
|detB|=
1,
j
,
l
,
k
represents the scale parameter, shearing parameter, and translation param-
eter. If the system
ΛAB (ψ)
forms a Parseval frame (also called a tight frame) for
L2(R2)
,
then
ψ
in the system is called a synthetic wavelet, and the following formula holds for all
f∈L2(R2):
∑
j,l,k
Df,ψj,l,kE
2=kfk2(3)
This synthetic wavelet is called a shear wave when
a=
4,
s=
1. As shown in Figure 1,
the three-levels NSST decomposition structure diagram, in which the scale parameter
j=
3
and the numbers of the shearing parameters of each level are set to [
2
–
4
] respectively, then
the corresponding shearing directions of each level are [4,8,16].
Sensors 2022, 22, x FOR PEER REVIEW 4 of 20
Figure 1. NSST of the three-levels decomposition process.
2.2. Adaptive Gamma Correction with Weighted Distribution
Gamma correction can expand the bright part in the X-ray image to make the image
contrast more obvious, and the simple form of the transform-based gamma correction is
derived by
max max
() ( / )Tv v v v
γ
= (4)
where v is the grayscale of the input image and ma x
v is the maximum intensity of the
input image, and
γ
is the varying adaptive parameter.
Define the probability density function of each gray level in the image as pdf ap-
proximated by
() /( )
v
pdf v n MN= (5)
where v
n is the number of pixels whose gray level is v,
M
N is the total number of
image pixels, and its cumulative distribution function cdf is defined as
0
() ()
v
k
cdfv pdfv
=
= (6)
The weighted distribution function is defined as
min
max
max min
()
() ( )
pdf v pdf
pdf v pdf pdf pdf
α
ω
−
=− (7)
Adjust the histogram of statistics with a weighted distribution function, where
α
is
the adjustment parameter, max
pdf is the maximum pdf of the statistical histogram, and
min
pdf is the minimum of the statistical histogram. Applying ()cdf v and ()pdf v
ω
to the
normalized gamma function, the formula of adaptive gamma correction with weighting
distribution (AGCWD) [32] is obtained as
NSP
j=1
Image
SF
l=4
NSP
j=2
NSP
j=3
SF
l=3
SF
l=2
Figure 1. NSST of the three-levels decomposition process.
Sensors 2022,22, 4074 4 of 17
2.2. Adaptive Gamma Correction with Weighted Distribution
Gamma correction can expand the bright part in the X-ray image to make the image
contrast more obvious, and the simple form of the transform-based gamma correction is
derived by
T(v) = vmax(v/vmax )γ(4)
where
v
is the grayscale of the input image and
vmax
is the maximum intensity of the input
image, and γis the varying adaptive parameter.
Define the probability density function of each gray level in the image as
pd f
approxi-
mated by
pd f (v) = nv/(MN)(5)
where
nv
is the number of pixels whose gray level is
v
,
MN
is the total number of image
pixels, and its cumulative distribution function cd f is defined as
cd f (v) =
v
∑
k=0
pd f (v)(6)
The weighted distribution function is defined as
pd fω(v) = p d fmax(pd f (v)−p d fmin
pd fmax −p d fmin )
α
(7)
Adjust the histogram of statistics with a weighted distribution function, where
α
is
the adjustment parameter,
pd fmax
is the maximum
pd f
of the statistical histogram, and
pd fmin
is the minimum of the statistical histogram. Applying
cd f (v)
and
pd fω(v)
to the
normalized gamma function, the formula of adaptive gamma correction with weighting
distribution (AGCWD) [32] is obtained as
T(v) = vmax(v/vmax )γA(8)
where
γA=1−
vmax
∑
v=0
pd fω(v)/Σp d fω(9)
with
Σpd fω=
vmax
∑
v=0
pd fω(v)(10)
Since most of the pixels of the X-ray image are densely distributed in the low grayscale
area, the AGCWD algorithm can gradually increase the low pixel intensity of the image
based on the weight distribution function, smooth the fluctuation phenomenon, and thus
reduce the excessive enhancement of the image by gamma correction.
2.3. Gradient Domain Guided Filtering
The output of any pixel in the filtered image can be expressed as the following lin-
ear model: ∧
Z(p) = ap0G(p) + bp0,∀p∈Ως1(p0)(11)
Among them,
∧
Z(p)
is the output image,
G(p)
is the guide image,
Ως1(p0)
is a local
square window with the point
p0
as the center and
ς1
as the radius in the guide image
G(p)
,
ap0
and
bp0
are the constant term coefficients in the window
Ως1(p0)
. To compute
ap0
and
bp0
, we define
E(ap0
,
bp0)
(hereafter abbreviated as
E
) as the noise-dependent loss function
within the window Ως1(p0)as follows:
E=∑
p∈Ως1(p0)
[(ap0G(p) + bp0−X(p))2+λ
∧
ΓG(p0)
(ap0−γp0)2](12)
Sensors 2022,22, 4074 5 of 17
Among them,
X(p)
is the image to be filtered,
λ
is the regularization parameter to
prevent
ap0
from being too large, and
∧
ΓG(p0)
is the edge perception weight, which is defined
as follows:
∧
ΓG(p0)=1
N
N
∑
p=1
χ(p0) + ε
χ(p) + ε(13)
χ(p0) = σG,1(p0)×σG,ς1(p0)(14)
where
σG,1(p0)
and
σG,ς1(p0)
represent the standard deviation within the window 3
×
3 and
within the window
(
2
ς+
1
)×(
2
ς+
1
)
, centered on the point
p0
.
ε
defined as
(0.001 ×L)2
,
L
is the dynamic range of the input image.
γp0
is the edge image factor, defined as follows:
γp0=1−1
1+eη(χ(p0)−µχ,∝)(15)
where
µχ,∝
is the mean of
χ(p)
, and
η
is calculated as 4
/(µχ,∝−min(χ(p)))
. It can be
known from formula (15) that if the pixel
p0
is in the smooth area of the image, the value of
γp0is close to 0, and if it is at the edge of the image, the value of γp0is close to 1.
To minimize the noise of the filtered image, take the minimum value of
E
, and the
linear regression is used to solve the formula (12) to obtain
ap0=
µGX,ς1(p0)−µG,ς1(p0)µX,ς1(p0) + λ
∧
ΓG(p0)
γp0
σ2
G,ς1(p0) + λ
∧
ΓG(p0)
(16)
bp0=µX,ς1(p0)−ap0µG,ς1(p0)(17)
where
is the dot product between the two matrices,
µGX,ς1(p0)
,
µG,ς1(p0)
and
µX,ς1(p0)
are the mean values of
GX
,
G
, and
X
. Bringing formulas (16) and (17) into formula (11),
the final calculation formula of ∧
Z(p)is simplified as
∧
Z(p) = −
apG(p) + −
bp(18)
where −
apand −
bpare the mean values of ap0and bp0in the window Ως1(p).
Gradient-domain guided filtering preserves its detailed features while smoothing the
image. To further enhance the edge and texture information of the image, the smoothed
image is subtracted from the original image to obtain a different image, which is added to
the smoothed image to obtain an enhanced one, and the specific formula is as follows
Genhanced =∧
Z(p) + ξ(X(p)−∧
Z(p)) (19)
where
ξ
is the scale coefficient of the differential gain effect of the image gradient-domain
guided filtering.
3. Implementation of the Algorithm
3.1. Algorithm Implementation Steps
The flow of the enhancement algorithm is shown in Figure 2. The high-frequency sub-
bands of the image contain noise, and as the decomposition scale increases, they become
almost invisible. We use gradient-domain guided filtering to process the high-frequency
sub-bands to reduce noise interference. The detailed information in the image can be well
preserved. To display the high-frequency images more clearly, both the high-frequency sub-
bands and the images enhanced by the gradient domain guided filtering have undergone a
linear grayscale transformation.
Sensors 2022,22, 4074 6 of 17
Sensors 2022, 22, x FOR PEER REVIEW 7 of 20
Figure 2. The proposed method for enhancing X-ray images is depicted schematically.
Step 1: Perform histogram equalization on the X-ray image, stretch the overall gray-
scale range of the image, and improve the image layering.
Step 2: Perform NSST scale decomposition on the image processed in Step 1 to obtain
one low-frequency sub-band and multiple high-frequency sub-bands.
Step 3: Use adaptive gamma correction with weighted distribution to enhance the
contrast of the low-frequency sub-band to highlight a small amount of detailed infor-
mation in the background.
Step 4: Use gradient-domain guided filtering for the high-frequency sub-bands to fil-
ter out image noise and subtract the smoothed image from the original image to obtain a
differential image, which was added to the smoothed image by scale coefficient
ξ
to per-
form image enhancement.
Step 5: Perform inverse NSST on the processed low-frequency sub-band and high-
frequency sub-bands and output the final enhanced image.
3.2. Decomposition Levels Analysis of NSST
The key parameters of NSST decomposition are the decomposition levels and shear-
ing directions of each level. To analyze the effect of decomposition levels on image quality,
five X-ray images of different sizes and different grayscales were selected for the experi-
ments.
Experiments were performed on the 64-bit operating system of Windows 10 (Intel
Core i7-8750H CPU2.20GHz), and the experimental tool was MATLAB R2016b. The scale
decomposition levels are set to 1-5, respectively, the number of shearing parameter of each
level is set to 4, and the corresponding shearing directions of each level are 16. The win-
dow radius of the gradient domain guided filtering
ς
is 16, the regularization parameter
λ
is 0.5, the scale coefficient
ξ
is 5, and the parameters of other experimental conditions
are kept the same.
Figure 2. The proposed method for enhancing X-ray images is depicted schematically.
Step 1: Perform histogram equalization on the X-ray image, stretch the overall
grayscale range of the image, and improve the image layering.
Step 2: Perform NSST scale decomposition on the image processed in Step 1 to obtain
one low-frequency sub-band and multiple high-frequency sub-bands.
Step 3: Use adaptive gamma correction with weighted distribution to enhance the
contrast of the low-frequency sub-band to highlight a small amount of detailed information
in the background.
Step 4: Use gradient-domain guided filtering for the high-frequency sub-bands to
filter out image noise and subtract the smoothed image from the original image to obtain
a differential image, which was added to the smoothed image by scale coefficient
ξ
to
perform image enhancement.
Step 5: Perform inverse NSST on the processed low-frequency sub-band and high-
frequency sub-bands and output the final enhanced image.
3.2. Decomposition Levels Analysis of NSST
The key parameters of NSST decomposition are the decomposition levels and shearing
directions of each level. To analyze the effect of decomposition levels on image quality, five
X-ray images of different sizes and different grayscales were selected for the experiments.
Experiments were performed on the 64-bit operating system of Windows 10 (Intel Core
i7-8750H CPU2.20GHz), and the experimental tool was MATLAB R2016b. The scale
decomposition levels are set to 1-5, respectively, the number of shearing parameter of each
level is set to 4, and the corresponding shearing directions of each level are 16. The window
radius of the gradient domain guided filtering
ς
is 16, the regularization parameter
λ
is 0.5,
the scale coefficient
ξ
is 5, and the parameters of other experimental conditions are kept
the same.
Select two representative medical images for analysis: Image 1 with the size of
440 ×440
and image 2 with the size of 1024
×
1024. The enhanced X-ray images obtained
under different decomposition levels are shown in Figures 3and 4where (a) is the original
image, and (b–f) corresponds to the decomposition levels
j
equal to 1–5. When the number
of scale decomposition levels is
j
, NSST decomposition requires 2
j
times of image and
filter convolution; the running time of the algorithm gradually increases. Observing the
image, the image contrast has been significantly improved after histogram equalization.
When the decomposition scale
j≤
3, with the increase of the NSST decomposition scale,
the boundary and texture features of the image are gradually obvious, and the detailed
Sensors 2022,22, 4074 7 of 17
information is enhanced. When 5
≥j>
3, the enhancement effect is further improved; the
change is not significant.
Sensors 2022, 22, x FOR PEER REVIEW 8 of 20
Select two representative medical images for analysis: Image 1 with the size of
440 440×
and image 2 with the size of
1024 1024×
. The enhanced X-ray images obtained
under different decomposition levels are shown in Figures 3 and 4 where (a) is the original
image, and (b–f) corresponds to the decomposition levels
j
equal to 1–5. When the num-
ber of scale decomposition levels is j, NSST decomposition requires 2j times of image
and filter convolution; the running time of the algorithm gradually increases. Observing
the image, the image contrast has been significantly improved after histogram equaliza-
tion. When the decomposition scale 3j≤,with the increase of the NSST decomposition
scale, the boundary and texture features of the image are gradually obvious, and the de-
tailed information is enhanced. When 53j≥>, the enhancement effect is further im-
proved; the change is not significant.
(a) (b) (c)
(d) (e) (f)
Figure 3. The enhanced effects of different decomposition levels on the X-ray image 1. (a) is the
original image, and (b–f) corresponds to the decomposition levels
j
equal to 1–5.
Figure 3.
The enhanced effects of different decomposition levels on the X-ray image 1. (
a
) is the
original image, and (b–f) corresponds to the decomposition levels jequal to 1–5.
Sensors 2022, 22, x FOR PEER REVIEW 9 of 20
(a) (b) (c)
(d) (e) (f)
Figure 4. The enhanced effects of different decomposition levels on the X-ray image 2. (a) is the
original image, and (b–f) corresponds to the decomposition levels
j
equal to 1–5.
The subjective evaluation of the enhancement effect purely from the visual aspect has
a certain one-sidedness. Therefore, five indicators of average gradient (AG), information
entropy (H), spatial frequency (SF), edge intensity (EI), and running time (RT) are selected
to objectively analyze the enhancement effect.
The average gradient (AG) can reflect the sharpness of the image and is defined as:
1
22
2
(( (, ) ( 1, )) ( (, ) (, 1)))
ij
fij fi j fij fij
AG MN
−+ + − +
=
(20)
The larger the average gradient of an image, the higher the image clarity.
The information entropy (H) is an important indicator to measure the richness of im-
age information and is defined as:
1
0
() ()log ()
L
l
Hp Pl Pl
−
=
=
(21)
where
L
refers to the number of gray levels, and
()Pl
represents the distribution prob-
ability of each gray level. The information entropy value indicates the average amount of
information contained in the enhanced image. The larger the value, the richer the infor-
mation contained in the enhanced image.
Figure 4.
The enhanced effects of different decomposition levels on the X-ray image 2. (
a
) is the
original image, and (b–f) corresponds to the decomposition levels jequal to 1–5.
Sensors 2022,22, 4074 8 of 17
The subjective evaluation of the enhancement effect purely from the visual aspect has
a certain one-sidedness. Therefore, five indicators of average gradient (AG), information
entropy (H), spatial frequency (SF), edge intensity (EI), and running time (RT) are selected
to objectively analyze the enhancement effect.
The average gradient (AG) can reflect the sharpness of the image and is defined as:
AG =∑i∑j(( f(i,j)−f(i+1, j))2+ ( f(i,j)−f(i,j+1))2)
1
2
MN (20)
The larger the average gradient of an image, the higher the image clarity.
The information entropy (H) is an important indicator to measure the richness of
image information and is defined as:
H(p) =
L−1
∑
l=0
P(l)log P(l)(21)
where
L
refers to the number of gray levels, and
P(l)
represents the distribution probability
of each gray level. The information entropy value indicates the average amount of infor-
mation contained in the enhanced image. The larger the value, the richer the information
contained in the enhanced image.
Spatial frequency (SF) can reflect the overall activity of an image in the spatial domain.
The higher the spatial frequency, the better the quality of the enhanced image. Its formula
is defined as follows:
SF =pRF2+CF2(22)
Among them,
RF
represents the spatial row frequency and
CF
represents the spatial
column frequency; the definitions of RF and CF are as follows:
RF =v
u
u
t
1
MN
M
∑
i=1
N
∑
j=2
[fi,j−fi,j−1]2(23)
CF =v
u
u
t
1
MN
N
∑
j=1
M
∑
i=2
[fi,j−fi−1,j]2(24)
The edge intensity (EI) reflects the image clarity degree. The more abundant the image
detail and edge, the higher the image clarity.
EI =∑
i
∑
jqG2
x(i,j) + G2
y(i,j)(25)
where
Gx(i
,
j)
,
Gy(i
,
j)
represent the first-order partial derivative in horizontal and vertical
directions and is defined as:
Gx(i,j) = f(i,j)⊗gx(26)
Gy(i,j) = f(i,j)⊗gy(27)
where
⊗
is the convolution symbol,
gx
and
gy
are the horizontal template and vertical
template for the Sobel operator. When the kernel size is 3, they are defined as:
gx=1
4
−101
−202
−101
,gy=1
4
−1−2−1
000
121
(28)
Having analyzed the effects of the decomposition levels on image enhancement, the
statistical data is shown in Tables 1and 2.
Sensors 2022,22, 4074 9 of 17
Table 1. An objective evaluation of the NSST decomposition levels for Figure 3.
Figure Levels (j)Directions (2l)AG H SF EI RT
Figure 3a / / 1.0209 6.7705 3.2987 11.0071 0
Figure 3b 1 16 3.7609 7.5542 9.5269 38.7133 2.6598
Figure 3c 2 16,16 4.9984 7.5516 11.8834 51.0562 3.7920
Figure 3d 3 16,16,16 5.6034 7.5394 12.7895 58.1641 5.3340
Figure 3e 4 16,16,16,16 5.7891 7.4672 13.1481 60.6308 6.9986
Figure 3f 5
16,16,16,16,16
5.7363 7.2994 13.2229 60.5058 8.5886
Table 2. An objective evaluation of the NSST decomposition levels for Figure 4.
Figure Levels (j)Directions (2l)AG H SF EI RT
Figure 4a / / 2.3300 7.5341 10.3475 24.0514 0
Figure 4b 1 16 4.5223 7.2774 17.1468 42.1044 18.4116
Figure 4c 2 16,16 6.3055 7.2848 19.5768 61.0428 35.8895
Figure 4d 3 16, 16,16 6.8069 7.3293 20.1561 67.3551 53.7948
Figure 4e 4 16,16,16,16 6.9036 7.4187 20.2654 68.8586 75.4546
Figure 4f 5
16,16,16,16,16
6.8085 7.4351 20.1713 68.1701 86.2375
The larger the above four parameters are, the better the enhancement effect. Observing
the data in Tables 1and 2and Figure 5, under the condition of a certain number of shearing
parameter in each level, with the increase of the decomposition scale, the information
entropy slightly increases, but the overall fluctuation effect is not large. The average
gradient, spatial frequency, and edge intensity of the image increase significantly, reaching
their extreme value when the decomposition scale is 4. If the decomposition scale is
increased again, the image enhancement effect is not obvious. Therefore, the primary
decomposition scale is set to 4.
Sensors 2022, 22, x FOR PEER REVIEW 12 of 21
Table 2. An objective evaluation of the NSST decomposition levels for Figure 4.
Figure
Levels (
j
)
directions (
2l
)
AG
H
SF
EI
RT
4a
/
/
2.3300
7.5341
10.3475
24.0514
0
4b
1
16
4.5223
7.2774
17.1468
42.1044
18.4116
4c
2
16,16
6.3055
7.2848
19.5768
61.0428
35.8895
4d
3
16, 16,16
6.8069
7.3293
20.1561
67.3551
53.7948
4e
4
16,16,16,16
6.9036
7.4187
20.2654
68.8586
75.4546
4f
5
16,16,16,16,16
6.8085
7.4351
20.1713
68.1701
86.2375
The larger the above four parameters are, the better the enhancement effect. Observ-
ing the data in Tables 1 and 2 and Figure 5, under the condition of a certain number of
shearing parameter in each level, with the increase of the decomposition scale, the infor-
mation entropy slightly increases, but the overall fluctuation effect is not large. The aver-
age gradient, spatial frequency, and edge intensity of the image increase significantly,
reaching their extreme value when the decomposition scale is 4. If the decomposition scale
is increased again, the image enhancement effect is not obvious. Therefore, the primary
decomposition scale is set to 4.
(a)
(b)
Figure 5. The effects of different decomposition levels: (a) are for Table 1 and (b) are for Table 2.
3.3. Shearing Directions Analysis of NSST
Performing
l
-level directional decomposition on the high-frequency sub-band im-
age can obtain a
2l
-directional sub-band image of the same size as the source image,
achieving more accurate directional decomposition in the frequency domain. The time
taken by the 4-level directional decomposition of the NSST algorithm is much longer than
that of the 2-level directional one. The shearing directions experiment was carried out on
the same batch of pictures by selecting two representative medical images for analysis.
The enhanced X-ray images obtained under different shearing directions are shown in
Figures 6 and 7. Having analyzed the effects of the shearing directions on image enhance-
ment, the statistical data is shown in Tables 3 and 4.
Figure 5. The effects of different decomposition levels: (a) are for Table 1and (b) are for Table 2.
3.3. Shearing Directions Analysis of NSST
Performing
l
-level directional decomposition on the high-frequency sub-band image
can obtain a 2
l
-directional sub-band image of the same size as the source image, achieving
more accurate directional decomposition in the frequency domain. The time taken by the
4-level directional decomposition of the NSST algorithm is much longer than that of the
2-level directional one. The shearing directions experiment was carried out on the same
batch of pictures by selecting two representative medical images for analysis. The enhanced
X-ray images obtained under different shearing directions are shown in Figures 6and 7.
Having analyzed the effects of the shearing directions on image enhancement, the statistical
data is shown in Tables 3and 4.
Sensors 2022,22, 4074 10 of 17
Sensors 2022, 22, x FOR PEER REVIEW 12 of 20
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 6. The enhanced effects of different shearing directions on X-ray image 1. In (a), the shear-
ing parameters of each level are set to (4,4,4) and the shearing directions are (16,16,16). For (b–h),
the decomposition scale was set to 4 levels, the shearing parameters of each level are set from
(2,2,2,2) to (4,4,4,4), and the shearing directions are from (4,4,4,4) to (16,16,16,16). The number of
shearing directions of each level was gradually increased.
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 7. The enhanced effects of different shearing directions on X-ray image 2. In (a), the shear-
ing parameters of each level are set to (4,4,4) and the shearing directions are (16,16,16). For (b–h),
the decomposition scale was set to 4 levels, the shearing parameters of each level are set from
(2,2,2,2) to (4,4,4,4), and the shearing directions are from (4,4,4,4) to (16,16,16,16). The number of
shearing directions of each level was gradually increased.
Figure 6.
The enhanced effects of different shearing directions on X-ray image 1. In (
a
), the shearing
parameters of each level are set to (4,4,4) and the shearing directions are (16,16,16). For (
b
–
h
), the
decomposition scale was set to 4 levels, the shearing parameters of each level are set from (2,2,2,2)
to (4,4,4,4), and the shearing directions are from (4,4,4,4) to (16,16,16,16). The number of shearing
directions of each level was gradually increased.
Sensors 2022, 22, x FOR PEER REVIEW 12 of 20
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 6. The enhanced effects of different shearing directions on X-ray image 1. In (a), the shear-
ing parameters of each level are set to (4,4,4) and the shearing directions are (16,16,16). For (b–h),
the decomposition scale was set to 4 levels, the shearing parameters of each level are set from
(2,2,2,2) to (4,4,4,4), and the shearing directions are from (4,4,4,4) to (16,16,16,16). The number of
shearing directions of each level was gradually increased.
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 7. The enhanced effects of different shearing directions on X-ray image 2. In (a), the shear-
ing parameters of each level are set to (4,4,4) and the shearing directions are (16,16,16). For (b–h),
the decomposition scale was set to 4 levels, the shearing parameters of each level are set from
(2,2,2,2) to (4,4,4,4), and the shearing directions are from (4,4,4,4) to (16,16,16,16). The number of
shearing directions of each level was gradually increased.
Figure 7.
The enhanced effects of different shearing directions on X-ray image 2. In (
a
), the shearing
parameters of each level are set to (4,4,4) and the shearing directions are (16,16,16). For (
b
–
h
), the
decomposition scale was set to 4 levels, the shearing parameters of each level are set from (2,2,2,2)
to (4,4,4,4), and the shearing directions are from (4,4,4,4) to (16,16,16,16). The number of shearing
directions of each level was gradually increased.
Sensors 2022,22, 4074 11 of 17
Table 3. An objective evaluation of the NSST shearing directions for Figure 6.
Figure Levels (j)Directions (2l)AG H SF EI RT
Figure 6a 3 16,16,16 5.6034 7.5394 12.7895 58.1641 5.3340
Figure 6b 4 4,4,4,4 5.8223 7.4581 13.2668 61.2474 2.9424
Figure 6c 4 4,4,8,8 5.8528 7.4573 13.2985 61.4832 3.5790
Figure 6d 4 8,8,4,4 5.782 7.4581 13.1731 60.7947 3.6289
Figure 6e 4 8,8,8,8 5.8122 7.4612 13.2097 61.0277 4.1941
Figure 6f 4 8,8,16,16 5.8356 7.4599 13.2460 61.2155 5.6572
Figure 6g 4 16,16,8,8 5.7650 7.4683 13.1010 60.4517 5.5436
Figure 6h 4 16,16,16,16 5.7891 7.4672 13.1481 60.6308 6.9986
Table 4. An objective evaluation of the NSST shearing directions for Figure 7.
Figure Levels (j)Directions (2l)AG H SF EI RT
Figure 7a 3 16,16,16 6.8069 7.3293 20.1561 67.3551 53.7948
Figure 7b 4 4,4,4,4 7.3331 7.4109 21.0909 73.0702 22.6136
Figure 7c 4 4,4,8,8 7.1990 7.4119 21.0370 72.0519 30.6810
Figure 7d 4 8,8,4,4 7.2375 7.4133 20.9472 71.9375 30.6267
Figure 7e 4 8,8,8,8 7.1001 7.4142 20.8958 70.8976 38.6901
Figure 7f 4 8,8,16,16 7.0193 7.4163 20.4215 70.2705 54.8658
Figure 7g 4 16,16,8,8 6.9897 7.4174 20.7423 69.5446 55.5662
Figure 7h 4 16,16,16,16 6.9036 7.4187 20.2654 68.8586 75.4546
To prove the effectiveness of the proposed algorithm in this paper, 30 chest X-ray
images obtained from [
33
] are selected to simulate, and the average metrics are shown
in Table 5. Five indicators of average gradient (AG), information entropy (H), spatial
frequency (SF), edge intensity (EI), and running time (RT) are introduced to objectively
analyze the enhancement effect. The line charts of the average values of the objective
metrics data in Table 5are given in Figure 8. To display the data in the same graph, the
value of EI has taken one-ninth of the original value, the value of SF has taken half of the
original value, and the value of T has taken one-fifth of the original value.
Observing the experimental data, under the condition of a certain decomposition scale,
with the increase of the shearing parameter of each level, the operation time gradually
increases due to the low efficiency of the iterative filtering operation during the direction
division process. However, the average gradient, information entropy, spatial frequency,
and edge intensity are not obvious, indicating that the number of clipping directions will
increase the complexity of the operation and make the running time of the algorithm longer,
but the enhancement effect on the image is not obvious. In the final algorithm scheme, the
decomposition scale of NSST is set to four levels, the shearing parameters of each level are
set to (2,2,2,2), and the shearing directions are (4,4,4,4).
Table 5. The average objective evaluation of the methods on the 30 chest X-ray images.
Figure Levels (j)Directions (2l)AG H SF EI RT
Figure 8a 3 16,16,16 8.3583 7.4553 20.4879 84.1216 31.3269
Figure 8b 4 4,4,4,4 8.7476 7.4315 21.4071 88.3668 15.2641
Figure 8c 4 4,4,8,8 8.6903 7.4313 21.2207 88.0425 19.6420
Figure 8d 4 8,8,4,4 8.6895 7.4350 21.2853 87.7092 20.5452
Figure 8e 4 8,8,8,8 8.6322 7.4351 21.1022 87.3851 24.9692
Figure 8f 4 8,8,16,16 8.5567 7.4352 20.8234 86.7944 33.6135
Figure 8g 4 16,16,8,8 8.5685 7.4401 20.9832 86.6336 35.4185
Figure 8h 4 16,16,16,16 8.4898 7.4401 20.7023 86.0090 42.0250
Sensors 2022,22, 4074 12 of 17
Sensors 2022, 22, x FOR PEER REVIEW 15 of 21
Table 5. The average objective evaluation of the methods on the 30 chest X-ray images.
Figure
Levels (
j
)
Directions (
2l
)
AG
H
SF
EI
RT
a
3
16,16,16
8.3583
7.4553
20.4879
84.1216
31.3269
b
4
4,4,4,4
8.7476
7.4315
21.4071
88.3668
15.2641
c
4
4,4,8,8
8.6903
7.4313
21.2207
88.0425
19.6420
d
4
8,8,4,4
8.6895
7.4350
21.2853
87.7092
20.5452
e
4
8,8,8,8
8.6322
7.4351
21.1022
87.3851
24.9692
f
4
8,8,16,16
8.5567
7.4352
20.8234
86.7944
33.6135
g
4
16,16,8,8
8.5685
7.4401
20.9832
86.6336
35.4185
h
4
16,16,16,16
8.4898
7.4401
20.7023
86.0090
42.0250
Figure 8. The effects of different shearing directions for Table 5.
Observing the experimental data, under the condition of a certain decomposition
scale, with the increase of the shearing parameter of each level, the operation time gradu-
ally increases due to the low efficiency of the iterative filtering operation during the direc-
tion division process. However, the average gradient, information entropy, spatial fre-
quency, and edge intensity are not obvious, indicating that the number of clipping direc-
tions will increase the complexity of the operation and make the running time of the algo-
rithm longer, but the enhancement effect on the image is not obvious. In the final algo-
rithm scheme, the decomposition scale of NSST is set to four levels, the shearing parame-
ters of each level are set to (2,2,2,2), and the shearing directions are (4,4,4,4).
Figure 8. The effects of different shearing directions for Table 5.
4. Experimental Results and Discussion
4.1. Subjective Analysis
To demonstrate the effectiveness of the algorithm in this paper, experiments were
carried out on five X-ray images, as is shown in Figure 9, in which (1) and (2) are medical
images mentioned before, (3) and (5) are industrial images with a size of 2048
×
2048, and
(4) is a thermal battery image with a size of 1000
×
1000. The enhancement effect of the
algorithm in this paper is compared with the FLM method [
34
], the AGCWD method [
32
],
the TSSR method [
9
], and the LCM-CLAHE method [
8
] in terms of subjective visual effects
and objective evaluation indicators.
To facilitate the observation and analysis of the detailed information in the image, we
zoomed in on part of the image, as shown in the red box in the experimental results. It
can be seen from Figure 9that the FLM method may appear excessively enhanced, such
as the bone background in (b)(2) being too bright, and the single-cell stack of the battery
in (b)(4) being too bright, making the image lose a large amount of detail information; the
AGCWD method has a certain enhancement effect on the image clarity, but the enhancement
of details and texture information is not obvious in (c)(1) and (2); the TSSR algorithm
enhances the contrast, but it will make the black areas in the image connect to produce
a blurring effect, such as (d)(3)–(5); the LCM-CLAHE method can improve the texture
information of the image, such as (e)(1), (2) and (5), but because the image is dark and the
contrast is low, it is not conducive to the observation of image details. Figure 9f shows
the results of the algorithm used in this paper, which suggests that the method proposed
in this paper is very effective for X-ray image enhancement. Dealing with medical X-
ray images like Figure 9((1),(2)), we can see that the sharpness of bone and soft tissue
information is significantly increased, image noise is suppressed, and contrast in local areas
is also improved. The algorithm makes the texture information more prominent, which is
beneficial to the doctor’s diagnosis and follow-up treatment of the patient’s disease. When
applied to the industrial X-ray images in Figure 9((3)–(5)), we can see that the local details
in the enhanced image are clearly visible, and the contrast between the battery texture
information and the component edge information is obvious. The overall brightness of the
image is moderate, and the noise components in the image are not seriously amplified so
that the processed image is more in line with the visual effect of the human eye.
Sensors 2022,22, 4074 13 of 17
Sensors 2022, 22, x FOR PEER REVIEW 15 of 20
4. Experimental Results and Discussion
4.1. Subjective Analysis
To demonstrate the effectiveness of the algorithm in this paper, experiments were
carried out on five X-ray images, as is shown in Figure 9, in which (1) and (2) are medical
images mentioned before, (3) and (5) are industrial images with a size of 2048 × 2048, and
(4) is a thermal battery image with a size of 1000 × 1000. The enhancement effect of the
algorithm in this paper is compared with the FLM method [34], the AGCWD method [32],
the TSSR method [9], and the LCM-CLAHE method [8] in terms of subjective visual effect s
and objective evaluation indicators.
(a) (b) (c) (d) (e) (f)
Figure 9. Comparison of different enhancement algorithms. (a) Original image, (b) FLM, (c)
AGCWD, (d) TSSR, (e) LCM-CLAHE, (f) Proposed method.
Figure 9.
Comparison of different enhancement algorithms. (
a
) Original image, (
b
) FLM, (
c
) AGCWD,
(d) TSSR, (e) LCM-CLAHE, (f) Proposed method.
4.2. Objective Analysis
Four evaluation indicators, average gradient (AG), information entropy (H), spatial
frequency (SF), and edge intensity (EI), were selected to objectively analyze the image
enhancement effect. From the aggregated data in Table 6, we can see that the algorithm
proposed in this paper has achieved the optimal values in the three indicators of average
gradient, spatial frequency, and edge intensity compared with the other four enhancement
algorithms, and the information entropy also ranks in second place. From the average
index data of the five pictures, we can see that the proposed method has achieved the best
results in all four indicators.
The algorithm in this paper can improve the local contrast and sharpness, making
it easier for people to obtain useful information about the target area from the enhanced
image. To verify the robustness and general adaptability of the algorithm, experimental
statistics were performed on 30 COVID-19 X-ray images with a size of 1024
×
1024 collected
from [33]. The average metrics of their objective evaluation are given in Table 7.
Sensors 2022,22, 4074 14 of 17
Table 6. Objective index analysis of methods for image enhancement.
Input Index Original FLM AGCWD TSSR LCM-
CLAHE Proposed
(1)
AG 1.0209 3.7850 1.4918 1.4474 2.7640 5.8223
H 6.7705 7.6702 6.7923 7.0087 7.1667 7.4581
SF 3.2987 10.0261 3.6482 3.8214 6.2908 13.2668
EI 11.0071 38.4831 15.8314 15.4658 28.8997 61.2474
(2)
AG 2.3300 3.2646 2.7096 2.5508 4.3032 7.3331
H7.5341 6.6296 7.2817 6.2981 7.3906 7.4109
SF 10.3475 20.3085 13.1887 12.1677 12.5993 21.0909
EI 24.0514 31.7895 28.0340 26.3186 43.4980 73.0702
(3)
AG 2.7952 3.8904 3.0928 3.7314 3.9837 6.3108
H 6.0726 6.2112 6.2114 5.1526 6.4169 6.7970
SF 10.4788 16.4859 10.6596 13.6344 11.9184 23.6223
EI 30.4747 39.5424 34.0402 40.6691 42.9675 67.1452
(4)
AG 1.3866 2.5508 1.5810 1.7410 2.5079 4.1480
H 6.9763 5.9883 5.9370 6.5906 7.0725 7.5378
SF 5.3728 12.9020 6.4922 7.5981 7.3069 12.9766
EI 14.9979 25.8824 17.1513 18.8056 26.7857 42.5292
(5)
AG 2.3483 2.4361 2.6111 2.4574 3.1436 4.5574
H 6.3407 5.3683 5.9630 4.0854 6.2908 6.5791
SF 7.7697 9.0802 8.1054 10.0210 9.3806 14.3243
EI 25.9900 26.2052 28.8516 27.4110 33.3082 47.2777
Table 7. Objective index analysis of the methods on the 30 COVID-19 X-ray images.
Input Index Original FLM AGCWD TSSR LCM-
CLAHE Proposed
30
AG 1.9192 3.6877 2.6340 2.6047 3.9789 8.7476
H 7.2153 6.5179 7.3022 7.1615 7.4034 7.4315
SF 6.4099 14.5301 8.4112 8.4708 9.7797 21.4071
EI 19.6104 35.4322 26.8381 26.6882 40.3258 88.3668
RT 0 4.3355 0.0539 0.2668 5.5797 14.8398
The line charts of the average values of the objective metrics data in Table 7are given
in Figure 10. To display the data in the same graph, the value of EI has taken one-eighth of
the original value. It can be seen from Figure 10 that the four evaluation indicators (AG, H,
SF, and EI) obtained by the algorithm in this paper have achieved the optimal values among
all the five algorithms. These results indicate that the proposed X-ray image enhancement
algorithm can achieve a better enhancement effect.
Compared with existing enhancement methods, the proposed algorithm does not show
significant advantages in terms of running time. The image enhancement model based on
shearlet transform has relatively high computational complexity. The choice of the number
of decomposition layers influences the effect of image enhancement, and the increase in the
number of decomposition layers will bring higher computational complexity. This results in
a long time for image enhancement. The different processing of sub-bands after multi-scale
decomposition also affects the image enhancement effect and running time. Therefore, how
to select a better sub-band processing method to obtain the optimal enhancement effect
while reducing the number of decomposition layers is the next problem we will study.
In addition, some parameter values in the algorithm need to be determined by empirical
values. For X-ray images of different initial conditions, the algorithm parameters need to
be changed accordingly. Future research will focus on the adaptability of this method.
Sensors 2022,22, 4074 15 of 17
Sensors 2022, 22, x FOR PEER REVIEW 19 of 21
Figure 10. The average index of different enhancement algorithms on the 30 chest X-ray images was
calculated.
Compared with existing enhancement methods, the proposed algorithm does not
show significant advantages in terms of running time. The image enhancement model
based on shearlet transform has relatively high computational complexity. The choice of
the number of decomposition layers influences the effect of image enhancement, and the
increase in the number of decomposition layers will bring higher computational complex-
ity. This results in a long time for image enhancement. The different processing of sub-
bands after multi-scale decomposition also affects the image enhancement effect and run-
ning time. Therefore, how to select a better sub-band processing method to obtain the
optimal enhancement effect while reducing the number of decomposition layers is the
next problem we will study. In addition, some parameter values in the algorithm need to
be determined by empirical values. For X-ray images of different initial conditions, the
algorithm parameters need to be changed accordingly. Future research will focus on the
adaptability of this method.
5. Conclusions
Due to the influence of the X-ray detection hardware system and other factors, the
quality of the X-ray image will decline, and the visual effect will become worse, causing
certain difficulties in the process of X-ray image detection. Therefore, it is necessary to
perform enhancement processing on the radiographic image to obtain higher quality im-
ages for subsequent analysis. This paper proposes a new image enhancement algorithm
combining NSST and gradient-domain guided filtering. The innovation is that the image
is decomposed in the NSST domain. AGCWD is used to enhance the contrast of the low
frequency. Gradient-domain guided filtering is performed on the high-frequency sub-
bands to improve image details and texture features. The final enhanced image is obtained
through NSST coefficient reconstruction. The algorithm makes full use of the image sparse
representation characteristics of NSST, the advantages of adaptive gamma correction in
image contrast enhancement, and the advantages of the gradient domain guided filter in
image detail enhancement. The algorithm proposed in this paper has an obvious effect on
image enhancement, not only improving the contrast and clarity of the image but also
Figure 10.
The average index of different enhancement algorithms on the 30 chest X-ray images
was calculated.
5. Conclusions
Due to the influence of the X-ray detection hardware system and other factors, the
quality of the X-ray image will decline, and the visual effect will become worse, causing
certain difficulties in the process of X-ray image detection. Therefore, it is necessary
to perform enhancement processing on the radiographic image to obtain higher quality
images for subsequent analysis. This paper proposes a new image enhancement algorithm
combining NSST and gradient-domain guided filtering. The innovation is that the image
is decomposed in the NSST domain. AGCWD is used to enhance the contrast of the
low frequency. Gradient-domain guided filtering is performed on the high-frequency
sub-bands to improve image details and texture features. The final enhanced image is
obtained through NSST coefficient reconstruction. The algorithm makes full use of the
image sparse representation characteristics of NSST, the advantages of adaptive gamma
correction in image contrast enhancement, and the advantages of the gradient domain
guided filter in image detail enhancement. The algorithm proposed in this paper has an
obvious effect on image enhancement, not only improving the contrast and clarity of the
image but also improving the image quality, as demonstrated by experiments on 30 X-ray
images compared to the other four advanced image enhancement methods at home and
abroad. From the experimental results, we can see that the evaluation indicators AG, H, SF,
and EI have all achieved optimal value. This demonstrates that the proposed algorithm can
obtain a better enhancement effect for both medical and industrial radiographic images.
It will provide a basis for later medical X-ray image diagnosis and industrial X-ray defect
identification and detection.
Author Contributions:
The experimental measurements and data collection were carried out by T.Z.
and S.-X.Z. The manuscript was written by T.Z. with the assistance of S.-X.Z. All authors have read
and agreed to the published version of the manuscript.
Funding:
This work is supported by the Scientific research project of the Tianjin Education Commis-
sion under Grant No. 2020KJ077.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Sensors 2022,22, 4074 16 of 17
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