A New Biomedical Image Denoising method using an adaptive multi-
resolution technique
LALIT MOHAN SATAPATHY1, PRANATI DAS2,
1Department of EEE, SOA Deemed to be University, Bhubaneswar, INDIA.
2Department of EE, IGIT Sarang, Odisha, INDIA.
Abstract: - In the world of digital image processing, image denoising plays a vital role, where the primary objective
was to distinguish between a clean and a noisy image. However, it was not a simple task. As a consequence of
everyone's understanding of the practical challenge, a variety of methods have been presented during the last few
years. Of those, wavelet transformer-based approaches were the most common. But wavelet-based methods have
their own limitations in image processing applications like shift sensitivity, poor directionality, and lack of phase
information, and they also face difficulties in defining the threshold parameters. As a result, this study provides an
image de-noising approach based on Bi-dimensional Empirical Mode Decomposition (BEMD). This project's main
purpose is to disintegrate noisy images based on their frequency and construct a hybrid algorithm that uses existing
de-noising techniques. This approach decomposes the noisy picture into numerous IMFs with residue, which were
subsequently filtered independently based on their specific properties. To quantify the success of the proposed
technique, a comprehensive analysis of the experimental results of the benchmark test images was conducted using
several performance measurement matrices. The reconstructed image was found to be more accurate and pleasant
to the eye, outperforming state-of-the-art denoising approaches in terms of PSNR, MSE, and SSIM.
Key-Words: -image de-noising, adaptive multi-resolution, biomedical images, BEMD, PSNR, MSE, and SSIM.
Received: February 25, 2021. Revised: October 7, 2021. Accepted: November 30, 2021. Published: January 4, 2022.
1 INTRODUCTION
One of the fundamental challenges in the field of
computer vision is image de-noising, which encourages
the suppression of noise from a noise-contaminated
image. In the presence of unwanted noise, image
processing tasks are adversely affected [1].
Furthermore, it was observed that images are inevitably
corrupted during the processes of acquisition,
compression, and transmission, which leads to the loss
of valuable image information. As denoising plays an
important role in the application areas such as video
processing, tracking, image analysis, restoration,
registration, segmentation, and classification where
visually pleasing images are essential, a special focus is
required on it [1-2].
On account of the above factors, it may be
concluded that noise removal is still a challenging task
for researchers. For a better result, numerous image
denoising techniques were developed afterwards,
including the Spatial-domain filter, the Transform-
domain filter, the Partial Differential Equation, and the
Variational approach[3]. The spatial filter performs
data operations directly on the pixels of the original
image. Mean, median, and low pass filters were some
of the most commonly used spatial-domain image
denoising techniques.The spatial domain linear
techniques are mathematically simple, but they have the
problem of introducing blurring.
In the transform-domain image denoising
approach, images are transferred from the spatial
domain to the frequency domain as a preprocessing
step. Then the coefficients of the image were modified
using various techniques. The image was retransferred
to the spatial domain using the inverse transform.After
using this approach, the noises were eliminated.Some
transform domain approaches include the Fourier
transform, Discrete Cosine Transform, Discrete
Wavelet Transform, Integer Wavelet Transform, and K-
L Transform. Fourier and wavelet transformations are
two of the most extensively utilised image denoising
methods [4-5].The Fourier transform converts an image
into sine and cosine components.During the
transformation process, very little information gets lost,
which is the strength of the Fourier Transform. Where
as the inherent tradeoff between frequency and time
resolution in the Fourier transformation is a severe
drawback.Later on, the wavelet transform became an
alternatedue to its ability to provide better time and
frequency resolution of a signal [3-7].
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The wavelet is a time-frequency analysis
method that adaptively selects the appropriate
frequency band based on the signal's characteristics [3-
7]. The frequency band is then matched to the spectrum,
improving the time-frequency resolution. At this stage,
many authors have applied some mathematical
operation such as thresholding to suppress the noise [7-
10]. Then denoising is accomplished by reversing the
wavelet coefficients into the spatial domain. The whole
process is known as the wavelet-based denoising
technique [9-12]. In maximum denoising cases, wavelet
thresholds are applied to remove the Gaussian
noise. Soft thresholding and hard thresholding are the
two most commonly used wavelet-based thresholding
techniques [13]. But in the case of soft thresholding,
over smoothing affects the reconstructed image. On the
other hand, in hard thresholding, many coefficients are
made zero. This causes blur and artifacts.Therefore,
even though threshold-based image denoising methods
present favourable results, the artefacts are still
noticeable [14-16]. In addition, the wavelet transform
has lower singularity and directional effect issues. From
an operational point of view, DWT decomposes an
image into a set of mutually orthogonal wavelet basis,
for which a constant set of filters are used. These filters
are not image-dependent. Moreover, the inverse DWT
increases the computational complexity. It is quite
difficult to choose a suitable mother wavelet.
When dealing with images with low noise
density, the partial differential equation has a greater
effect. However, when dealing with images with high
noise density, the effect is poor and it takes a longer
processing time. The advantages of image
denoising using the total variational method are that it
determines the energy function of the image. It
outperforms basic approaches like linear smoothing or
median filtering while smoothing out edges to a greater
extent [6].
This motivated us towards an image-dependent
denoising method using bi-dimensional empirical mode
decomposition (BEMD) [17]. The BEMD is a time-
domain approach well suited for non-linear and non-
stationary signal analysis. By applying EMD, the image
is decomposed adaptively into integral oscillatory
components, named Intrinsic Mode Functions (IMF)
and residue. In this investigation, the BEMD
decomposed images are filtered using the classical
filters. The key issues addressed in this study are the
Smoothing of flat regions,
Protection of edge information without
blurring,
Preservation of internal texture,
Suppression of new artefacts.
To outline the paper's objective, Section 2
demonstrates the detailed methodology in algorithm
form. Section 3 describes the experimental results as
well as comparisons with other state-of-the-art methods
with proper evidence. The conclusion and future work
are given in section 4.
2 METHODOLOGY
In this section, some of the fundamental issues related
to image denoising with different types of noises having
zero mean and finite variance are considered and their
characteristics are elaborately discussed.
2.1 Noise Model
In digital image processing, noise is generally classified
as additive or multiplicative, depending on how it is
distributed. The best additive noise used in the most
common type of image denoising work is Gaussian
noise. The white Gaussian noise is spatially
uncorrelated, which means that the noise for each pixel
is independent and identically distributed. In this
process, each pixel of a digital image changes by a small
amount from its actual value. As a result, the image is
soft and slightly blurred. Equation (1) demonstrates the
additive Gaussian noise model.
I(x ,y)= M(x ,y) +n(x ,y) (1)
Where I (x, y) is the noise-contaminated image
function, M (x, y) is the original noise-free image, and
n(x, y) represents the signal-independent additive
Gaussian random noise with zero variance.
In some cases, noise arises due to environmental
conditions such as voltage spikes in the circuits or
random changes in the physical properties of materials.
This kind of noise is categorised as "multiplicative
noise" and is also known as "speckle" noise. The
multiplicative noise model can be depicted in Equation
(2).
I(t) = (I - e) M (t) + n (t) (2)
Where e has a probability of p and lies between 0 and 1,
I(t) is the noisy image at a specific time (t), M(t) is the
original signal, and N(t) is the speckle noise introduced
during image capture, transmission, or other processing.
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2.2 Image Decomposition
Image decomposition is an image processing technique
where the image is segregated into multiple images
based on its features and frequency. In this paper, we
have used frequency-based decomposition using
BEMD [17]. The EMD can decompose the image into
n levels based on the frequency of the input signal. In
this model, we have used a four-level decomposition as
illustrated in fig.1.
Fig. 1: Image decomposition using BEMD
2.3 Image Denoising Model
The proposed denoising model is presented in Figure 2.
Fig.2: Image denoising using BEMD
Initially, the input image, the data acquisition system,
and external sources of noise are modelled to generate
a noisy image. In this experiment, Gaussian noise, salt
and pepper noise, and speckle noise with zero mean and
different variances are considered. The behaviour of the
mentioned noises is additive or multiplicative. The
noisy image is then segmented into four pieces based on
their frequency using a four-level emperical mode
decompsition. The breakdown images are named
IMF1, IMF2, IMF3, and residue. IMF1, IMF2, IMF3
and residue maintain frequencies ranging from high to
low.
The objective of this proposal is to remove noise from
homogeneous areas of a noisy image while preserving
structures such as edges and corners. On the other hand,
considering the decomposed images separately, the
valuable hidden information has to be preserved [17–
18]. Moreover, noise is widely known as high-
frequency in nature. So the high-frequency components
of digital images are filtered to eliminate the unwanted
noise. Additionally, the low-frequency component
contains information about hidden structures as its pixel
values fluctuate slowly over time. Thus, the residual
image is left unfiltered.
2.4 Bidimensional Empirical Mode
Decomposition (BEMD)
The complicated two-dimensional model data set
(Image) can be decomposed into a finite number of
unique frequency components, which are known as
intrinsic mode functions (IMF) [19]. These IMFs are
extracted by applying a sifting process that repeats the
steps until fewer than 2 maxima points occur. The
uniqueness of the BEMD is similar to that of the EMD,
which is used for one-dimensional signals. If I (x,y) is
defined as the image which is to be decomposed into a
series of BIMFs and a residue (eq.3),
I(x,y) =
+Res (x, y) (3)
Where the IMFi (x, y) is the ithIMF component. The
frequency of IMF1 is higher than the other IMFs. The
detailed process is demonstrated in Figure 3.
2.5 Noise
Noise is treated as an external energy that corrupts the
signal and changes its characteristics. In digital image
processing, noise may be treated as any type of random
variation in brightness that changes the pixel data. This
generally happens during the use of a digital camera,
sensor, or scanner.
The noise generated by the electronic data acquisition
systems and communication channels varies
substantially, with different effects. Salt and pepper,
Gaussian, and speckle noise are common sources of
visual distortion.
Image (I)
BEMD
IMF1
IMF2
IMF3
RESIDUE
Original
Image (M)
Data
Acquisition
System
Noise(n)
Noisy
Image (I)
Bi-dimensional empirical mode
Decomposition (BEMD)
Residu
e
IMF1….n
Filter
Reconstruction
Filtered Image (N)
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Fig. 3: Flowchart of BEMD
2.5.1 Salt & Pepper Noise:
Salt-and-pepper noise is also known as impulse noise,
which is a form of white and black pixel that can
sometimes be seen on images. In most of the image
applications for suppressing the above noise, traditional
filters such as the Median filter or morphological filter
are used. This type of noise is generally caused by both
software and hardware (camera sensor) faults during
image photographing or transmission. The probability
density function "S" of a Gaussian random variable
"u" is formulated as
S(u) = SPfor u =0 (Pepper)
= Ssfor u = 2n – 1 (Salt) (4)
= 1-(Sp-Ss) for u= k (0<k< 2n-1)
2.5.2 Gaussian Noise:
Gaussian noise is statistical noise that is identically
distributed at any pair of times. Sensor noise, which is
caused by temperature and poor lighting, is the primary
source of Gaussian noise.
(a) (b)
Fig. 4: (a) Input MRI brain images (b) image with Salt
and Pepper noise and 0.01 variance
(a) (b)
Fig. 5: (a) Input MRI brain images (b) image with
Gaussian noise and 0.01 variance
Gaussian noise is reduced using spatial filters. The
probability density of a Gaussian random variable is
given by:
h(z)=
(5)
Where the parameters z, µ represent the gray-
level, mean and standard deviation.
2.5.3 Speckle Noise:-
Speckle noise is modelled as a multiplicative noise that
arises due to the effect of environmental conditions.
This type of noise is mostly noticed in medical images
and radar images. In speckle noise, the signal and the
noise are statistically independent and directly
proportional to the local grey level of any image area.
This can be represented as follows (eq. 6)
F(b) =
(6)
Where b is the Grey level and αisthe Variance.
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(a) (b)
Fig. 6: (a) Input image MRI brain images (b) image
with Speckle noise and 0.01 variance
2.6 Filtering:
Filtering is an algorithm that converts the pixel values
of an image or a small part of it by applying some
process. These are used for noise (unwanted artifacts)
reduction, contrast enhancement, and brightness
preservation purposes. Nowadays, filters are mostly
used for the suppression of high-frequency components
of an image. As a result, the image is smoothed and the
edge is preserved.Compared with the frequency-
domain, in the spatial domain, noise removal is easier
because it requires much less processing time. The
filters are broadly divided into two categories: (i) linear
filters and (ii) non-linear. Both have some advantages
as well as disadvantages. If we consider the linear filter,
it has the advantage of faster processing but fails to
preserve the edge. Where a nonlinear filter can preserve
the edge with the compromise of processing speed.
2.6.1 Median filter:
The Median Filter is a non-linear filter having the
ability to remove salt and pepper type noise. It uses a
pre-defined window size. During the filtering process,
the median filter replaces the pixel values with the
median value of neighbouring pixels. Because edge
information is the crucial data for an image, the median
filter plays a vital role in preserving the edges during
the smoothing process.
2.6.2 Gaussian filter:
A Gaussian filter is a linear filter whose impulse
response is a Gaussian function. This filter is commonly
used for smoothing, noise reduction, and computing
image derivatives. Furthermore, this classic filter
effectively reduces noise while significantly blurring
the edges. The standard deviation used in the Gaussian
function plays a vital role in its behavioural
features. The two-dimensional Gaussian filter is
represented as
G(p,q) =
(7)
Where p and q are the horizontal and vertical distances
of the pixel from the origin. σ is the standard deviation.
A Gaussian filter reduces the contrast and preserves the
brightness of the filtered image. As per its
characteristics, it is designated as the ideal time-
domain filter.
2.6.3 Wiener filter:
The Wiener filter is a stationary linear filter used for
inverse filtering and noise smoothing. In inverse
filtering, the filter works as a high-pass filter by using
de-convolution. In compression mode, it functions as a
low-pass filter to remove noise. In the process of
filtering, it minimises the overall mean square error.
This technique gives a better result in the case of
additive white Gaussian noise (AWGN). This filter is
applicable to noise having a zero mean and uses a
stochastic framework to provide the linear estimation.
The limitation of Wiener filtering is that it requires
knowledge of the power spectra of the noise and the
original image. The Wiener filter can be mathematically
expressed as follows:
W (f1, f2) =
(8)
Where,
is the power spectral of the
original image, S
is the power spectral of
additive Gaussian noise,
is the blurring filter.
3 EXPERIMENTAL RESULTS
The performance of the proposed method is evaluated
subjectively using performance metrics such as Mean
Square Error (MSE), Peak Signal to Noise Ratio
(PSNR), and Structural Similarity Index Measure
(SSIM). In this paper, a set of standard MRI brain
images with a 256x256 size was investigated. For this
study, Matlab 14a, with an Intel (R) 2.40 GHz CPU and
4 GB of memory, was used. During the experiment, the
original image is added with noise (salt and pepper
noise, Gaussian noise, speckle noise) having different
variances. The noisy images with a variance of 0.01 are
shown in Figs. 4-6. The proposed denoising technique
is compared with three state-of-the-art filtering methods
like the Median Filter, Gaussian Filter, and Wiener
filter. The comparative results are demonstrated in Fig.
7-9.
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3.1 Metrics of Performance measures
3.1.1 Mean Square Error:
The MSE represents the aggregate of the square of the
error between the de-noised image and the reference
image. The lower the value of MSE, the closer the two
images are. The equation (9) is used for MSE
calculation.
(9)
Where, p q: Dimension of the image.
M (a, b): Intensity of pixels (a, b) of original image.
N(a,b):Intensityof pixels (a, b) after de-noising.
3.1.2 Peak signal-to-noise ratio
The peak signal-to-noise ratio (PSNR) is the ratio of
the signal power of the processed image to the referral
image. The higher value of PSNR represents a better
quality of performance. PSNR is denoted as:
(10)
=
MAX is the maximum possible pixel value of the image
which is 255 in 8-bit image systems.
3.1.3 Structural similarityindex
The SSIM is a perceptual metric used for
quantifying the image quality which has been degraded
by the processes of data compression, data transmission,
and data acquisition. It is a full-reference metric
comparison method that requires a minimum of two
images: the reference image and a processed image. The
range of the SSIM is between -1 and 1, to indicate the
similarity. The closer the value is to one, the more
similar the structure.
(11)
Where,
(12)
(13)
(14)
Where,
= cross co-variance for image a,b
If α = β = γ = 1 and C3= C2/2 then the above index is
simplifying to:
SSIM =
(15)
(a) (b) ( c)
(d) (e) ( f)
Fig.7: (a) Input MRI brain image (b) Image with Salt
and pepper noise with density 0.1 (c) median filtered
image (d)wiener filtered image(e) Applying
Gaussianfiltered image (f) Proposed BEMD with
Gaussian filter method.
(a) (b) ( c)
(d) (e) ( f)
Fig. 8 (a) Input image (b) Image with Gaussian noise
and variance 0.01 (c) median filtered image (d) wiener
filtered image (e) Applying Gaussianfiltered image (f)
Proposed BEMD with Gaussian filter method.
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(a) (b) ( c)
(d) (e) ( f)
Fig. 9: (a) Input MRI brain image (b) Image with
Speckle noise with variance 0.1) (c) Median filtered
image (d) wiener filtered image(e) Applying
Gaussianfiltered image (f) Proposed BEMD with
Gaussian filter method.
3.2 Result and Discussion
The proposed system was verified in this section using
four-level empirical mode decomposition techniques,
as discussed in the previous section. MSE, PSNR, and
SSIM were the three measuring parameters for each
test. Table 1-3 shows the performance of each of these
matrices. The range of noise variance considered in
each experiment is from 0.001 to 0.1. Figure 7-9 depicts
a few samples of MRI brain images for visual
evaluation, where the images are modelled with 0.1
variance using various noises
This method incorporates the traditional filters with
BEMD. Separately, the median filter with BEMD, the
Gaussian filter with BEMD, and the wiener filter with
BEMD are studied. In every evaluation, the
hybridization outcome was found to be much better than
the straight filtration procedure. In Figure 7, the brain
MRI image is considered and was affected by salt and
pepper noise with a density of 0.1. The noisy image was
filtered by the median filter, wiener filter, and Gaussian
filter. The resulting images are presented in Figures 7
(c) to 7 (e). Figure 7 (f) illustrates the proposed BEMD
with a gaussian filter. The median filter is quite good at
reducing "salt and pepper" noise. After thoroughly
testing the effect of salt and pepper noise, it was
discovered that the proposed method outperforms the
median filter (Figure 7). Experiments on Gaussian and
speckle noise were also conducted, with the results
displayed in Figs. 8 and 9. The comparison of PSNR
values is depicted in fig. 10 as a bar graph.Separately,
considering the graphs, it was found that the PSNR
value of the denoised images increases when filters are
applied in combination with BEMD. The graphic
performance of MSE is depicted in fig. 11. The
proposed method presents a lower error when a hybrid
filer is applied. At present, there is no MSE value that
has been fixed as a proper value. Simply put, the lower
the value, the better. While the greater the MSE, the less
similar they are, it will be more difficult to detect
anything if the MSE between image sets differs at
random. SSIM, on the other hand, uses a scale of -1 to
1 to rate everything. The structural similarity index of
the proposed method as a comparison isdepicted in fig.
12.
Fig. 10: Comparision of PSNR value for Gaussian
noise affected image filtered by different methods and
the proposed method
Fig. 11: Comparision of MSE value for Gaussian noise
affected image filtered by different methods and the
proposed method
By using equations 9, 10, and 15, the values of MSE,
PSNR, and SSIM of a set of images are calculated. The
average value of each noise is recorded in Table I to
Table III. Table 1 shows the Gausian noise affected
image and its filtering both in the classical method and
the proposed method. The result supports the claims of
the proposed method numerically.
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Fig.12: Comparison of SSIM value for Gaussian noise
affected image filtered by different methods and the
proposed method
Table 1.Comparison of PSNR, MSE, SSIM of
different filters concerningthe proposed method for
Gaussian noise affected image
PSNR
MSE
SSIM
Noisy Image
20.45507
0.009067
0.369267
Median Filter
25.93197
0.002567
0.634567
Gaussian Filter
25.1281
0.003167
0.763433
wiener filter
24.74497
0.003433
0.708
Proposed method
with Median
Filter
25.97003
0.002533
0.636967
Proposed method
withGaussian
Filter
25.15897
0.003152
0.763467
Proposed method
with wiener filter
25.62447
0.0028
0.7288
Table 2. Comparison of PSNR, MSE, SSIM of
different filters with respect to the proposed method
for Speckle noise affected image
PSNR
MSE
SSIM
Noisy Image
20.45507
0.009067
0.369267
Median Filter
21.61433
0.007033
0.5184
Gaussian Filter
23.6321
0.0048
0.742633
wiener filter
23.00047
0.005533
0.6599
Proposed
method with
Median Filter
21.75607
0.0068
0.5251
Proposed
method
withGaussian
Filter
23.6626
0.004767
0.742367
Proposed
method with
wiener filter
23.59537
0.0048
0.675
In table II, the performance of speckle noise is
presented. By comparing the median filter with the
bemd-median filter, it was found that the PSNR value
increased by 0.65% and the MSE decreased by 3.31%.
In the case of the Gaussian filter and the bemd-gaussian
filter, the results do not show any significant deference.
Considering Table III, where salt and pepper noise are
considered, the median filter gives a detrimental result.
As per Z. Wang and A.C. Bovik in some cases, the MSE
and PSNR give adverse results, even if the result is
visually good [20].
Table 3.Comparison of PSNR, MSE, SSIM of
different filters with respect to the proposed method
for salt and peeper noise affected image
PSNR
MSE
SSIM
Noisy Image
20.45507
0.009067
0.369267
Median Filter
30.27383
0.0019
0.731
Gaussian Filter
23.54703
0.004567
0.681833
wiener filter
22.48283
0.005767
0.610133
Proposed
method with
Median Filter
27.53493
0.001833
0.740333
Proposed
method
withGaussian
Filter
23.56583
0.0045
0.682
Proposed
method with
wiener filter
22.82073
0.0053
0.614733
4. CONCLUSION
This paper has analysed the process of noise generation
and the characteristics of common image noises, studied
the different filtering techniques used in the spatial and
transfer domains, discussed the methods to choose the
structural decomposition technique, studied the
fundamental theories of empirical mode decomposition
(EMD) and its mathematical morphology, exploited the
advantages of empirical mode decomposition with a
multi-resolution structure, investigated the selection
criteria for filters, and proposed a filtering algorithm
with structural decomposition combined with image
denoising. Experiments on a set of benchmark images
demonstrate that the proposed technique outperforms
similar types of denoising algorithms, particularly in
terms of PSNR, MSE, SSIM index, and visual effect.
The future work of this paper is as follows:
(1) Before filtration, a threshold factor is applied to the
coefficients of each decomposed image.
(2) The threshold factors must be noise-dependent.
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(3) A new algorithm will be proposed, combining
BEMD with soft computing techniques (deep learning,
fuzzy logic, artificial neural networks, genetic
algorithms, particle swarm optimization algorithms) to
improve the denoising performance.
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Contribution of individual authors to the
creation of a scientific article (Ghostwriting
Policy)
L.M. Satapathy carried out conceptual framework;
system design, analysis, simulations, discussion,
writing, proofreading and editing.
Prof. P. Das Supervised the project.
Sources of funding for research presented in a
scientific article or scientific article itself
There is no funding source for this project.
Creative Commons Attribution License 4.0
(Attribution 4.0 International , CC BY4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2022.17.2
Lalit Mohan Satapathy, Pranati Das
E-ISSN: 2224-2856
24
Volume 17, 2022
