Department of Electrical and Communication Engineering
Multimedia university of Kenya
P.O.BOX 15653-00503,Nairobi,
KENYA
Abstract: - The non-invasive and non-ionizing properties of Magnetic Resonance Imaging (MRI) in addition to
the associated good image quality as well as high resolution make MRI more attractive than many other medical
imaging techniques. However, during the acquisition, transmission, compression and storage processes, the
Magnetic Resonance (MR) images are corrupted by various types of noise and artifacts that degrade their visual
quality. Most of the existing MR images denoising techniques give good quality images only when the noise
density is low with their performances deteriorating as the noise power increases. The few methods that yield
high quality images for all noise densities involve multiple complex and time-consuming processes. This paper
proposes a computationally simple MR images denoising technique that consistently gives good denoising results
for low as well as high noise densities. The proposed procedure fuses an MR image that is denoised by a Modified
Discrete Fast Fourier Transform (MDFFT) filter with one that is denoised using a non-local means filter in
frequency domain to yield a high quality output image. The main contribution of this proposed method is the
employment of a novel image fusion approach that greatly improves the quality of the denoised image. The
performance of the proposed technique is compared with those of the Wiener, median, adaptive median and the
MDFFT filters. Objective metrics such as the Peak Signal-to-Noise Ratio (PSNR) and the Structural Similarity
(SSIM) index were used in the performance assessments. The outcomes of these assessments showed that the
proposed algorithm yielded images of higher quality in terms of the PSNR measure than the existing denoising
techniques by at least 7.11 dB for a noise density of up to 0.5.
Key-Words:-MRI, Denoising, Noise, Artifacts, Non-local means filter, Modified discrete fast Fourier transform.
Received: March 28, 2021. Revised: August 12, 2022. Accepted: September 18, 2022. Published: October 4, 2022.
1 Introduction
Magnetic Resonance Imaging (MRI) is one of the
most efficient imaging techniques for medical
diagnostics because of its non-invasive and non-
ionizing capabilities [1]. However, the Magnetic
Resonance (MR) images are corrupted by various
noises such as Gaussian, salt and pepper and Rician
noise in addition to artifacts that degrade the
images. These noises and artifacts make it difficult
to extract the useful information for human
interpretation or computer- aided clinical analysis of
the images [2]. In the development of medical
imaging, various denoising techniques have been
developed but the challenge of maintaining a good
filtering performance as the noise amount increases
still persists.
The process of noise removal must not degrade the
useful features in an image. In particular, the edges
are important features for medical images and thus
the denoising must be balanced with edge
preservation [3]. The choice of the denoising
technique to be used is based on either the amount
and type of noise or the performance of the filter
itself. The objective of this paper was to develop
and test the performance of a proposed robust
denoising method for MR images. The technique
fuses the output of a low pass modified fast Fourier
transform filter with that of a spatial domain high
pass non-local means filter.
Ali compared the performances of the median,
adaptive median and adaptive Wiener filters in
removing Gaussian noise as well as salt and pepper
noise from MRI images. To evaluate the
performance of each of the three filters, noise with
densities ranging from 10% to 90% was gradually
added to ground-truth MR images. Then, the Peak
Signal-to-Noise (PSNR) for every filter output and
for every noise density was calculated [4]. The
results showed that the adaptive Wiener filter has a
poor performance in removing both salt and pepper
and Gaussian noises from the images. The median
filter was the best in removing Gaussian noise. The
adaptative median filter was better than both the
median and adaptive Wiener filters in removing the
salt and pepper noise. However, all the three filters
showed poor performance for high noise densities.
In order to improve denoising performance, Sarker
et al. combined the adaptive median filter and the
Fusion Based MR Images Denoising Technique Using Frequency
Domain and Non-Local Means Filters
CHRISTIAN RUDAHUNGA*, HENRY KIRAGU, MARY AHUNA
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non-local means filter algorithms to remove salt
and pepper noise from MR images. Salt and pepper
noise with a variance ranging from 0.1 to 0.9 was
added to ground-truth MR images prior to
denoising. The PSNR values of the denoised
images for median, adaptive median as well as the
adaptive median-based non-local means filters, at a
noise variance equal to 0.9 were 54.12 dB,
56.80 dB and 58.70 dB respectively[5].
Therefore, a combination of the adaptive median
filter and the non-local means filter performed
better than both the median filter and adaptive
median filters. The main limitation of this
combined filters denoising technique is the long
processing time required because it is a two-stage
method that involves a large number of
computations [5].
These related works reveal two challenges. On one
hand, the filters perform well at low noise densities
and poorly at higher noise densities. On the other
hand, the combination of adaptive median filter and
non-local means filter algorithm proved to be good
for both low and high noise densities but its
operation takes a long processing time. To address
these gaps, fusion of the outputs of a Modified
Discrete Fast Fourier Transform (MDFFT) filter
algorithm and a Non-Local Means Filter (NLMF)
was employed in the method proposed in this paper.
The MDFFT algorithm denoises the low frequency
components of the MR images while the NLMF
was used to denoise the high frequency components
of the same image. In order to reconstruct the
denoised MR image, the outputs of the two filter
algorithms were fused in the Discrete Fourier
Transform (DFT) domain. The main contribution of
this research work is a proposed frequency domain-
based image fusion technique that yields better
quality images than conventional image fusion
methods. The image fusion used in this paper
selects the high frequency components from the
high pass filtered image and discards the still noisy
low frequency components of high pass filtered
image. From the output of the low pass filter, the
low frequency components are selected while
completely removing the high frequency ones. This
is followed by combining the selected high and low
frequency components to reconstruct the denoised
image in frequency domain. This proposed fusion
procedure results in a better output quality than the
conventional image fusion techniques that are
based on combining scaled versions of the inputs
and therefore retaining significant amounts of noise
power in their fused images. The rest of this paper
is organized as follows: section 2 presents some
background theory on MRI principles, image
denoising techniques and image quality measures.
Section 3 gives a presentation of the proposed
methodology. Simulation test results and their
discussions are presented in section 4 while section
5 gives the conclusion and suggestions for future
research.
2 Theoretical Background
This section summarizes the principles of the MRI
process. Some types of the noises and artifacts that
corrupt the MR images are discussed. Also,
objective measures that are commonly used to
assess the quality of MR images are presented here.
2.1 Magnetic Resonance Imaging
The Magnetic Resonance Images (MRI) technique
is based on the phenomenon of nuclear magnetic
resonance of the hydrogen nuclei contained in the
human body in form of water, fat and other
chemical components [6]. It is a powerful tool for
imaging the structure and the function of soft tissues
in the human body because of its high image
contrast and resolution capabilities as well the
absence of ionizing radiations and the ability of
arbitrary spatial encoding [7]. The abundance of
hydrogen in the human body coupled with its
solitary proton per atom leads to the generation of
large values of net magnetization in the body.
When nuclei of certain elements are placed in a
magnetic field, they absorb energy in the Radio
Frequency (RF) range of electromagnetic waves
and emit that energy while returning to their initial
state [8]. In the absence of an external magnetic
field, the magnetic moments (μ) of the hydrogen
protons in a body tissue are oriented randomly in all
directions. Consequently, the net magnetic
moment (magnetization) is equal to zero as shown
in the following equation [9].
(1)
Where
is the net magnetization.
In the presence of an external static magnetic field
, the magnetic moments are oriented in the
longitudinal direction of
and rotate (precess)
around
at the Larmor frequency f0 given by;
fo =
(2)
where is the gyromagnetic ratio of the precessing
nucleus [10]. During the precession, the longitudinal
component of the magnetization (Mz) remains
constant whereas its transverse component (
) is
zero.
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2.1.1 RF Excitation and MR Image Formation
In MRI, an RF pulse is used to flip some of the
magnetization into the transverse plane. The
precession motion is then transformed into a
spinning motion of the nucleus around the axis of
the static magnetic field. Application of RF pulses
that have a frequency equal to the Larmor
frequency lead to the decrease of longitudinal
magnetization (
) and the creation of transverse
magnetization component (
). The net
magnetization (
) continues to revolve around the
magnetic field
at the Larmor frequency but with
a tilt angle (α) that is proportional to the RF pulse
duration time (). At the end of RF pulse
application, the transverse magnetization
component
(
)
starts to decrease towards
its
minimum value whereas the longitudinal
magnetization starts to increase towards its
maximum value. The increase in longitudinal
component of magnetization
when returning
back to its equilibrium value M0 is called
longitudinal relaxation which can be expressed as
follows;
(3)
Where T1 is the longitudinal relaxation time
constant, M0 is the equilibrium magnetization,
Mz(0) is the longitudinal instantaneous
magnetization after pulse excitation [11].
The decay of the transverse magnetization
is
called transverse relaxation given by;
(4)
Where T2 is the transverse relaxation time constant
and Mxy(0) is the instantaneous transverse
magnetization after pulse excitation [11]. The
collapsing of the transverse magnetization
component induces an electric voltage in the
receiver coil of the MRI equipment. This induced
signal is called the Free Induction Decay (FID)
signal given by;
=
(5)
Where S(kx, ky) is the FID signal, kx(t) and ky(t) are
the spatial frequency components in the read-out
and phase -encoding directions respectively. Fx and
Fy are the fields of view in x and y directions
respectively [12]. The MR image is obtained by
evaluating the two-dimensional inverse Fourier
transform of the FID signal.
2.1. 2 MRI Noises
Magnetic resonance images are prone to various types
of noise that degrade their quality. These noises include the
Gaussian noise and the salt and pepper noise.
Gaussian noise is
a
random noise that has the
following normal probability density function(pdf)
(6)
where P(x) is the Gaussian noise pdf, is its mean
and
is its standard deviation [13].
The salt and pepper noise is a random noise whose
value at any position in the image is either the
maximum intensity level (salt value) or the minimum
one (pepper value) [14]. It manifests itself as dark
and bright spots in the image and has the following
probability density function.
=
(7)
where P(x) is the salt and pepper noise pdf while pa
and pb are the values of the pdf for the intensity
levels a and b respectively [5].
2.1.3 Types of MRI Artifacts
Image artifacts refer to any image features that are
not inherently present in the imaged scene. They
lead to misinterpretation of medical information in
MR images [15]. Some of the artifacts associated
with MRI are: truncation, motion, aliasing and
chemical shift artifacts. The sources of these
artifacts include: body motion, magnetic field
inhomogeneities, body chemical state shift and
image processing techniques used. Truncation
artifacts occur at the boundaries with sharp contrast
in the form of multiple alternating bright and dark
lines. For example, the symmetric truncation in k-
space leads to the oscillations of sampled data or
Gibbs-ringing artifacts around the boundaries of the
tissue[16] .They can be misinterpreted as a syrinx
in the spinal cord or a mechanical tear in the knee
[17]. Motion artifacts originate from the various
movements in the body parts of the patient such as
the lungs and heart during the MRI process.
Aliasing artifacts affect the MR images when the
Field of View (FoV) is small. They result in some
body parts that are outside the FoV being mapped
at the opposite end of the image. The chemical shift
artifacts appear like dark and bright bands at the
interface between lipid and water. These artifacts
are sometimes helpful as a diagnostic aid for
confirming the presence of fat within lesions [17].
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2.2 Spatial Domain Filtering Method
Spatial domain filtering can be categorized into
linear and non-linear methods [18]. The linear
filters such as the mean and maximum filters
operate in spatial and temporal domain. They
reduce the noise by changing the value of each pixel
based on the values of the pixels in its
neighborhood. The problem associated with these
filters is that they blur the image edges and other
fine details. The non-linear filters such as the
median and non-local means filters are more
preferred over the linear ones because they reduce
noise and also preserve the image edges and
boundaries [19]. Despite the advantageous features
of non-linear filters, they still suffer from serious
drawbacks such as blurring of the filtered images.
2.2.1 Non-Local Means Filter
The operation of a Non-Local Means (NLM) filter
is based on estimating the intensity of each pixel
from the information obtained from the entire
image. It exploits the redundancy due to the
presence of similar patterns and features in the
image [2]. The weight W(m,n) assigned to a pixel is
proportional to the similarity between the local
neighborhood of the pixel under consideration and
the neighborhood corresponding to other pixels in
the image. The limitation of non-local means filter
is that the denoised image is affected by the blurring
due to appearance of the artifacts in the smooth
regions of filtered image and loss of the fine details
when the amount of noise becomes high [20]. For a
pixel n in the image I, corrupted by noise of value
v= the estimated value of that pixel
denoised by a non-local means filter, LM[ ], is
calculated as a weighted average of all pixels in the
image.
The weight, W(m,n), depends on the similarity
between the pixels m and n as shown in the
following equation [18].
with
(8)
The advantages of spatial domain filters are their
simplicity as well as the ability to operate in real
time. Their shortcomings include lack of robustness
and the imperceptibility of their filtering effects.
The frequency domain filters can be used to address
these challenges associated with spatial domain
filters [21].
2.3 Frequency Domain Filters
In frequency domain filtering, the image to be
denoised is first transformed into frequency domain
by evaluating it two-dimensional Discrete Fourier
Transform (2D-DFT) [22].
Filtering is then achieved by multiplying the
frequency domain image by the transfer function of
an appropriate filter. The MR image to be denoised
in frequency domain is first divided into spectral
bands and the filtering mechanism is applied to
each of these bands [23]. Finally, two-dimensional
Inverse Discrete Fourier Transformation (2D-
IDFT) is performed on the product to obtain the
filtered image in spatial domain. One of the
advantages of frequency domain filtering is the
ability to concentrate most of the signal energy in
the low frequency components allowing easy
removal of high frequency noise. Other merits of
these filters are their low computation complexity as
well as the ease of visualizing and manipulating the
image in frequency domain. The challenges
associated with the frequency domain filtering are
image blurring as a result of low pass filtering as
well as image over-sharpening by high-pass filters.
One of the commonly used frequency domain
filters is the Gaussian low-pass filter whose transfer
function is given by;
(9)
where H(u,v) is the transfer function of the
filter, Do is a constant and D(u,v) is the two
dimensional spatial frequency [22].
2.4 Objective Quality Measures
Two of the widely used objective measures for
assessing the quality of an image are the Peak
signal-to-Noise Ratio (PSNR) and the Structural
similarity (SSIM) index.
2.4.1 Peak Signal-to-Noise Ratio (PSNR)
The Peak Signal-to-Noise Ratio is an objective
measure that is obtained by dividing the
maximum possible power of the ground-truth
image by the mean squared power of the noise
in the denoised image. In digital images
processing, the PSNR metric considers the
Mean Squared Error(MSE) between the
ground-truth or original image and the
denoised image [24]. It is usually expressed in
decibels as follows;
PSNR =10log10
(10)
Where MSE is mean squared error and MAX is the
maximum pixel intensity value [25].
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2.4.2 Structural Similarity (SSIM) Index
The SSIM o f an image is a quality assessment
measure t h a t i s w i d e l y u s e d f o r q u a l i t y
e v a l u a t i o n i n i m a g e s p r o c e s s i n g . I t
c o m p a r e s the similarity between two images.
This metric quantifies the difference between a
degraded image and the ground-truth image based
on the luminance, structure and contrast of the two
images [26]. The SSIM is calculated as follows;
(11)
Where is the mean of the pixel values of the
reference image (x). is the mean of the pixel
values of the degraded image (y). and are
the standard deviations of the pixel values of the
reference image and the degraded image
respectively. C1 and C2 are constants to ensure that
the value of the SSIM is always finite [12].
3 Methodology
The proposed MR image denoising technique
presented in this section is composed of the stages
shown in Fig. 1. The algorithm separately denoises
a noisy image using both a frequency domain
Gaussian low pass filter and a spatial domain high
pass non-local means filter. Since the Gaussian
filter denoises low frequency components better
than it does for higher frequency ones, its denoised
low frequency components are extracted to form
the low frequency part of the denoised output image
of the algorithm. On the other hand, the non-local
means filter, denoises the higher frequency
components better than lower frequency ones. The
high frequency components of the output of this
filter are extracted to constitute the high frequency
components of the denoised output image. The
extracted low and high frequency components are
then combined by matrix summation to reconstruct
the denoised output image.
The process of extracting and fusing the frequency
components to reconstruct the denoised image was
carried out using the following procedure. Salt and
pepper or Gaussian noise was added gradually
(variance between 0.1 to 0.9) to a pixels
ground-truth image, to form a noisy image,
as follows;
Ground-truth image
Denoised image
Fig. 1: Flowchart of the proposed method.
(12)
Where is an noise matrix,
and . The noisy image was then
transformed into frequency domain by taking its
two-dimensional Discrete Fourier Transform (2D-
DFT).
Noise addition
AN(m, n) =
A(m, n) +
N(m, n)
Centered 2D-
DFFT evaluation
ANC(u, v) =
2D-DFT{AN(m,
n)}
Non-local
means filtering
AHF(m,n) =
NLMF{AN(m,
n)}
Frequency domain
Gaussian low-pass
filtering
ALF(u, v)=
H(u, v). ANCD(u,
v)
Centered 2D-
DFFT evaluation
AFC(u, v)=
2D-DFT{AHF(m,
n)}
High frequency
components
extraction
AH(u, v)=
B(u, v) . AFC(u,
v)
Matrix addition
A0(u, v) =
AL(u, v) + AH(u, v)
Low frequency
components
extraction
AL(u, v)=
L(u, v). ALF
(u, v)
2D-IDFT
evaluation
A1(m, n)=
2D-IDFT{A0(u, v)}
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The 2D-DFT was centered in order to put the low
frequency components of the noisy image at the
center of matrix as follows;
(13)
Where , and
denotes the centered 2D-DFT. The centered
frequency domain image was low pass filtered by
multiplying it element-wise by the transfer
function of a Gaussian low pass filter as follows;
(14)
Where {.*} denotes element-by-element matrix
multiplication, is the low pass filtered
image in frequency domain and is the
transfer function of the modified Gaussian low pass
filter given by;
(15)
Where and are constants while is
the two-dimensional spatial frequency given by;
(16)
The low frequency components of the filtered
image were extracted by element-wise
multiplication of by a low pass filter
mask as follows;
(17)
Where is a matrix containing only the low
frequency components of and is
the low pass mask defined as follow;
(18)
Where K is the highest frequency extracted by the
mask. The value of K used was obtained as follows;
(19)
The same noisy image () was also
denoised by the non-local means filter to produce
the image as follows;
(20)
where denotes non local means filtering.
The filtered image () was transformed
into frequency domain by evaluating its centered
2D-DFT so that its high frequency components are
at the periphery of matrix as;
(21)
The high frequency components of the filtered
image were extracted using element-wise
multiplication of by a high pass filter
mask as follows;
(22)
Where is a matrix containing only the
high frequency components of and
is the high pass mask defined as follow;
(23)
The 2D-DFT of the denoised image was
reconstructed as matrix by combining the
extracted low and high frequency components as
follows;
(24)
Finally, the denoised output image was obtained by
taking the two-dimensional Inverse Discrete
Fourier Transform (2D-IDFT) of as;
(25)
where denotes the 2D-IDFT and
is the denoised output image.
4 Results and Discussions
The test results of the proposed algorithm are
presented in this section. The results were
generated by computer simulation of the algorithm
using maths works MATLAB 2018a software. The
t e s t MR images were obtained from the Kenya
Sonar Imaging Center and t h e Siemens
Healthineers website [27]. The values of the
constants used are:
.
To generate the results, salt and pepper or Gaussian
noise was added gradually (from a variance of 0.1
to 0.9) to one of a sample of ten MR images at a
time. The Peak Signal to Noise Ratio (PSNR) and the
Structural Similarity(SSIM) index were calculated for every
salt and pepper or Gaussian noise density and for every filter.
The proposed algorithm was used to denoise the
MR images and its results compared with those of
other denoising techniques such as: modified
discrete fast Fourier transform, median, adaptive
median and Wiener filters. The comparison was
done both qualitatively and quantitatively using
objective measures such as the Peak Signal-to-
Noise Ratio (PSNR) and the Structural Similarity
(SSIM) index.
The statistical summary was used to represent
graphically the denoising performance of every
filter and to compare the filtering activities of all
the filter algorithms.
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4.1 Qualitative analysis
In Fig. 2, a subjective comparison of the
performances of the proposed method to that of the
modified discrete fast Fourier transform filter is
presented. Column (a) shows the ground-truth
pixels head MR image. Column (b) from
top to bottom shows the image corrupted by salt
and pepper noise of variances 0.1, 0.3, 0.5 and 0.7
respectively. More the noise density increases from
top downward, more the Head MR image gets
corrupted. For example, at 0.3 and 0.5 salt and
pepper noise variances, the Head image is much
corrupted in such way it is very difficult to
recognize it. Results of denoising the noisy image
using the MDFFT filter as well as the proposed
algorithm are presented in columns (c) and (d)
respectively. By visual observation, the proposed
algorithm yielded images of higher quality than the
MDFFT filter for all the noise variances tested.
In fig. 3, another subjective comparison of the
performances of the proposed method to that of the
modified discrete fast Fourier filter is presented.
Four different MR images (Head, Ankle, Shoulder
and Neck) are corrupted by salt and pepper noise.
Column (a) shows four different ground-truth MR
images. The images corrupted by a salt and pepper
noise of variance 0.3 are presented in column (b).
Results of denoising the images using the MDFFT
filter as well as the proposed algorithm are
presented in columns (c) and (d) respectively. By
observation, the proposed algorithm produced
images of better quality than the MDFFT filter.
A qualitative comparison of the performances of
the proposed and the MDFFT methods for images
corrupted by Gaussian noise is presented in fig. 4.
Column (a) shows a ground-truth Neck MR image.
From top to bottom of column (b), the MR image
corrupted by Gaussian noise of variances 0.1, 0.3,
0.5 and 0.7 respectively is given. The Gaussian
noise is added increasingly from top downward and
more the noise density increases more the Neck MR
image get corrupted. Denoising results of the
MDFFT filter and the proposed algorithm are
shown in columns (c) and (d) respectively. By
subjective comparison, the proposed algorithm
yielded images of higher quality than the MDFFT
filter for low noise variances. For higher noise
variances, the visual quality for MDFFT and the
proposed methods are similar. This means that the
denoising performance of the proposed algorithm is
better than that of MDFFT filter for low Gaussian
noise densities. But for high Gaussian noise
densities, the denoising performances of MDFFT
filter and proposed algorithm are almost equal.
Original
image
Noisy
image
MDFFT
Filter
Proposed
Method
(a) (b) (c) (d)
Fig. 2: Comparison between the MDFFT filter and
the proposed method. (a) Original image. (b) Salt
and pepper noise corrupted image. (c) MDFFT
filter denoised image. (d) Proposed method
denoised image.
In fig. 5, a comparison of the Gaussian noise
removal capabilities of the proposed method and
the MDFFT filter is presented. The MR images
used are those of a Head, Ankle, Shoulder and Neck
as presented in column (a). Column (b) presents the
four MR images corrupted by Gaussian noise of
variance 0.3. Results of denoising the noisy images
using the MDFFT filter as well as the proposed
algorithm are presented in columns (c) and (d)
respectively. By visual observation, it was found
that the proposed algorithm produced images of
better quality than the MDFFT filter for low
Gaussian noise variances. However, there is no
perceptible difference between the noise removal
efficacies of the two methods when the Gaussian
noise variance is higher than 0.3. This is evident
from the denoising results presented in third and
fourth rows of fig. 4 for noise variances equal to 0.5
and 0.7 respectively.
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Original
image
Noisy
image
MDFFT
filter
Proposed
method
(a)
(b)
(c)
(d)
Fig. 3: Performance comparison for different
images. (a) Original image. (b) Salt and pepper
noise corrupted images. (b) MDFFT filter denoised
image. (d) Proposed method denoised.
Original
image
Noisy
image
MDFFT
filter
Proposed
method
(a)
(b)
(c)
(d)
Fig. 4: Gaussian noise removal comparison. (a)
Original image. (b) Gaussian noise corrupted
image. (c) MDFFT filter denoised image. (d)
Proposed method denoised image.
Original
image
Noisy
Image
MDFFT
filter
Proposed
Method
(a)
(b)
(c)
(d)
Fig. 5: Performance comparison for different
images. (a) Original image. (b) Noisy image with
0.3 noise variance. (c) MDFFT filter denoised
image. (d) Proposed method denoised image.
4.2 Quantitative analysis
For objective quality analysis, five filter algorithms
were used to remove salt and pepper and Gaussian
noises from MR images. The algorithms used are
the Wiener, median, adaptive median and the
MDFFT filters in addition to the proposed method.
The PSNR and SSIM measures were used to
compare their filtering performances. Table 1
shows the denoising performances of the five
algorithms in removing salt and pepper noise in
terms of the mean PSNR for ten MR images.
The proposed method produced images of higher
quality than the other algorithms for both low and
high noise densities (variances). For example, the
mean PSNR of the proposed method is 9.73 dB and
5.72 dB higher than for any of the other filters at 0.2
and 0.7 noise densities respectively. For Gaussian
noise removal, the performances of the proposed
method and four other algorithms are presented in
table 2 in terms of mean PSNR. The other four
methods are the Wiener, median, adaptive median
and the MDFFT algorithms.
The proposed method out-performs all the other
four filters when the Gaussian noise density is low.
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For example, at a noise of density of 0.1, the mean
PSNR of the proposed method is at least 1.86 dB
higher than those of the other four filters. At higher
noise densities, the performance of the proposed
method is comparable to that of the MDFFT filter
but better than those of the Wiener, median and
adaptive median filters. In terms of the SSIM index,
table 3 gives a comparison of the denoising
performances of the proposed method and the
MDFFTF in removing salt and pepper noise. The
SSIM values were averaged for ten MR images at
different noise densities.
Table 1. Mean PSNR for salt and pepper noise
removal
Salt
and
pepper
noise
density
Denoising algorithms
Wiener
Median
Adaptive
median
MDFF
filter
Proposed
method
PSNR
in dB
PSNR
in dB
PSNR
in dB
PSNR
in dB
PSNR
in dB
0.1
45.25
61.82
66.86
64.87
71.13
0.2
42.78
58.78
62.32
61.79
72.05
0.3
40.88
56.66
59.45
59.97
69.14
0.4
39.20
54.22
57.25
58.65
66.68
0.5
37.80
52.05
54.92
57.61
64.72
0.6
36.55
49.33
52.80
56.76
63.11
0.7
35.37
46.55
50.66
56.03
61.75
0.8
34.38
43.26
45.75
55.39
60.57
0.9
33.47
39.13
40.19
54.82
59.53
Table 2. Mean PSNR for Gaussian noise removal
Gaussian
noise
density
Denoising algorithms
Wiener
Median
Adaptive
.median
MDFFT
Proposed
method
PSNR
in dB
PSNR
in dB
PSNR
in dB
PSNR
in dB
PSNR
in dB
0.1
43.21
51.98
38.98
66.17
68.03
0.2
40.72
50.00
36.61
61.65
62.21
0.3
39.40
48.81
35.53
58.54
58.78
0.4
38.54
47.90
34.94
56.26
56.38
0.5
37.92
47.27
34.55
54.50
54.56
0.6
37.46
46.77
34.28
53.13
53.14
0.7
37.05
46.27
34.08
52.09
52.08
0.8
36.78
45.94
33.93
51.39
51.37
0.9
36.53
45.54
33.79
50.98
50.97
Table 3. Mean SSIM for salt and pepper
noise removal
Salt and
Pepper
noise
density
Denoising algorithms
MDFFTF
Proposed
method
SSIM
SSIM
0.1
0.81
0.94
0.2
0.66
0.95
0.3
0.55
0.91
0.4
0.45
0.85
0.5
0.37
0.78
0.6
0.30
0.70
0.7
0.24
0.61
0.8
0.19
0.52
0.9
0.14
0.43
The proposed method yielded a better salt and
pepper noise removal capability than the MDFFT
filter. This superiority of the proposed method to
MDFFT filter holds for both low as well as high
noise densities. For example, at a noise density of
0.2, the mean SSIM indexes of the images denoised
using the proposed method and MDFFT filter are
0.95 and 0.66 respectively. When the noise density
is 0.8, the proposed method produced an output
image with a mean SSIM index of 0.52 compared
to the value of 0.19 obtained using the MDFFT
filter. This is a confirmation of the mean PSNR
results presented in table 1.
4.3 Statistical Summary
A statistical summary of the performance of the
proposed method in comparison with other
denoising methods is graphically presented in
fig.6. In part (a), plots of the mean PSNR values of
Wiener, median, adaptive median, MDFFT and the
proposed algorithms versus the noise density of salt
and pepper noise are shown. For every filter, the
mean PSNR reduces as the noise density increases.
The proposed method has the highest mean PSNR
for all the noise densities tested. At 0.2 and 0.7
noise variances, the proposed algorithm out-
performs the other four methods by at least 9.73 dB
and 5.72 dB respectively. Hence, it exhibits better
salt and pepper filtering performance than the other
four algorithms.
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(a)
(b)
(c)
Fig.6: Statistical summary.
(a) Mean PSNR versus Salt and pepper noise
density. (b) Mean PSNR versus Gaussian
noise density. (c) Mean SSIM mean versus
Salt & pepper density.
A performance comparison of the five denoising
techniques for images corrupted by Gaussian noise
is presented in part (b) of the figure. The mean
PSNR values of the denoised images are plotted
against the noise density. When the noise variance
is 0.3 or lower, the proposed method portrays a
better noise removal performance than the other
four filters. For example, at a noise density of 0.1,
the proposed method yielded a mean PSNR of
68.03 dB while all the other four methods gave
PSNR values that are lower than 66.20 dB. For
noise densities above 0.3, the quality performance
of the proposed technique is comparable to that of
the MDFFT filter but better than those of the other
three filters.
In part (c), plots of the mean SSIM index versus
salt and pepper noise density for the MDFFT filter
as well as the proposed method are presented. The
mean SSIM index values for the proposed method
are higher than those of the MDFFT filter. These
results reaffirm the findings of part (a) that the
proposed method is superior to the MDFFT filter in
removing salt and pepper noise from MR images.
5 Conclusion
In this Paper, a proposed novel MR images
denoising technique has been presented. The
performance of the method has been compared with
the Wiener, median, adaptive median and modified
discrete fast Fourier transform filters for the removal
of salt and pepper as well as Gaussian noise. Objective
quality assessments showed that the proposed
method performed better than the others in
removing salt and pepper noise for both low and
high noise densities. For example, the proposed
method yielded average PSNR values that were
higher than those of the other filters by at least 9.73 dB
and 5.72 dB for noise variances of 0.2 and 0.7
respectively. Further research work will be focused
on optimizing the performance of the proposed
algorithm by adjusting the parameters of the
Gaussian filter.
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