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EXTERMINATION METHODS OF IMAGE NOISES: A
REVIEW
B. Perumal
Department of Electronics and Communication Engineering, Kalasalingam Academy of
Research and Education, Krishnankoil, Virudhunagar (Dt), (India).
E-mail: palanimet@gmail.com
ORCID: https://orcid.org/0000-0003-4408-9396
R. Sindhiya Devi
Department of Electronics and Communication Engineering, Kalasalingam Academy of
Research and Education, Krishnankoil, Virudhunagar (Dt), (India).
E-mail: sindhiyadevi14@gmail.com
ORCID: https://orcid.org/0000-0002-7529-6438
M. Pallikonda Rajasekaran
Department of Electronics and Communication Engineering, Kalasalingam Academy of
Research and Education, Krishnankoil, Virudhunagar (Dt), (India).
E-mail: mpraja80@gmail.com
ORCID: https://orcid.org/0000-0001-6942-4512
Recepción:
11/11/2019
Aceptación:
05/11/2020
Publicación:
30/11/2021
Citación sugerida:
Perumal, B., Sindhiya, R., y Pallikonda, M. (2021). Extermination methods of image noises: a review.
3C Tecnología. Glosas de innovación aplicadas a la pyme, Edición Especial, (noviembre, 2021), 243-259. https://
doi.org/10.17993/3ctecno.2021.specialissue8.243-259
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ABSTRACT
To lter an image is necessary in the preprocessing of images for the extermination of noise.
Noise is an important factor that aects the information or details in the input image and so
it is a need to remove it. Here, we examine a diversied amount of denoising approaches of
MRI images by reviewing the positivity and weakness of every method and the well – suited
method for the removal of dierent noises that tend to appear in the MRI images have
been discussed. In this paper, we study about dierent noises of MRI images like Gaussian
noise, Rician noise, Speckle noise, Salt and Pepper and the Poisson noise. Also we discuss
about some of the basic error metrics like mean squared error, mean absolute error and
the peak signal to noise ratio. Furthermore, we have presented a study about the lters like
Mean lter, Median lter, Gaussian lter, Wiener lter, Anisotropic Diusion, Lee and Frost
lter, Non Local Means lter and neural network lters in order to eliminate the noises of
the MRI images. The advanced technique using neural network tops the list as it follows
the training approach. Each of these lters is better in some specic manner and so hybrid
lters with the better features of these lters will provide greater accuracy and robustness.
KEYWORDS
Filter, Noise, positivity, Weakness, MRI Images.
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1. INTRODUCTION
Brain is a mind – boggling organ having its size of about only 3 pounds, it is responsible
for most of the functions of our human body. Any wreckage to the brain tissue will lead
to malfunction of the entire system. One such ravage is the brain tumor, which can be
detected with less diculty with the help of Magnetic Resonant Images.
1.1. MAGNETIC RESONANT IMAGE
Medical Resonant Imaging (MRI) is a technique which is non – amboyant type of
investigation either in the exploration or rectication of hindrances in the brain. An
ecacious magnetic induction with throbs of extremely high frequency waves are used
here in order to beget the embellished outlook of the organs, more precisely the abby
tissues of the human body. This is performed so as to impel the innards of human body to
be interpreted easily for the croakers. To explore the organs especially brain, it is the most
hyperaware technique.
MRI is more impregnable as it does not adopt emanation and it is quite the contrast of
x – ray procedure which is time – honored and the surveying computed tomography (CT).
Therefore, no deformation in the chemical reaction occurs in our tissues. We can get
diversied standpoints investigated from the images of these scanning processes. Also, we
can eortlessly make a distinction of the soft tissues like the gray and white matters and the
cerebrospinal uid (CSF) of the brain by means of MRI images when compared with the
CT images.
To perceive the tumefaction in the brain tissues, we can utilize an extensive self – activated
process and to make it possible, we should be particularly clear about every minute details
of the tissue image. We can get a clear image of the tissues by exiling the discordance in
the images.
1.2. MRI NOISES
Generally, noise is a signal that randomly appears onto an image and it sometimes aects the
entire result. In the medical imaging systems, it is a necessity to obtain clear and undistorted
image outputs in order to get a clear cut picture of the aected parts. There exist dierent
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types of noises in the medical images, especially in the MRI images (Tahir et al., 2016). The
major types of noises (Kumar & Nachamai, 2017) that could be seen in the MRI images are
Gaussian noise, Rician noise, multiplicative noise and the Speckle noise. Here, we discuss
about these noises that aect the quality of Magnetic Resonance Images.
1.2.1. GAUSSIAN NOISE
An important and a common type of noise that appears in the MRI images is the Gaussian
noise whose probability density function equals the Gaussian distribution (Boyat & Joshi,
2015). This type of noise tends to happen during the image acquisition by some natural
causes like poor illumination and high temperature. It is independent of the intensity of the
signal caused by thermal noise. Also it does not depend on each pixel of the image.
The Gaussian noise can be also called as the Amplier Noise as it normally present in the
area where high amplication is used rather than the weak amplication areas. This noise is
additive in nature (Suryanarayana et al., 2012). It means that this noise, as it is independent
of the signal, it simply adds over to the original signal or image to get the distribution.
The expectation of the density function of Gaussian noise is determined by the following
equation,
....(1)
where, µ denotes the mean and σ2 shows the variance
g species the gray level of the image
We know that the Gaussian noise is white. Hence it is clear that it has a at power spectral
density and it is the reason for the auto – correlation of Gaussian noise to be zero.
1.2.2. RICIAN NOISE
The Rician Noise is unprejudiced that is almost similar to the Gaussian noise except the
fact that the Rician noise depends mainly on the magnitude of the signal at the time of
its acquisition every time, whereas the Gaussian noise is independent of the original data.
Generally spoken, Rician noise originates from the complex form of the Gaussian noise
but with its original frequency domain measurements. It adheres to Rice propagation (Aja-
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Fernández, Alberola-López, & Westin, 2008) which is also called the Rice – Nakagami
distribution as the measurement of the MRI signal can be obtained from the square root of
aggregation of the squares of the non – discriminating Gaussian parameters. We can also
say this as the Rician noise with high SNR can be considered as the Gaussian noise. Rician
probability density function can be given by the following expression,
....(2)
where, v is the strength of direct component.
σ shows the noise’ orthogonal part.
I0(.) is the propositional mutated Bessel cylindrical function
The noise intensity of the Rician noise is mainly based on the brightest tissue for every
acquisition of image. In dark regions which have low intensity, the Rice distribution complies
with Rayleigh propagation and in intense zones where the high intensity is available, it
tends to Gaussian distribution.
1.2.3. SPECKLE NOISE
The Speckle Noise is of course – grained type that is commonly caused by errors during
the transmission of data. It also emerges due to ecological impact on the imaging locator
during picture procurement. It appears similar to the Gaussian noise with the exception
that its probability density function follows gamma distribution. The probability density
function of the Speckle noise can be denoted as,
....
(3)
where, a is the bright region where the gray level is less.
a
2
α is its variance.
The Speckle noise is the noise that is obtained in coherent imaging of objects and is
multiplicative in nature. These types of noises are commonly seen in case of ultrasound
images (Kushwaha & Singh, 2017) but also seen in MRI images.
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1.2.4. SALT AND PEPPER NOISE
The Salt-and-Pepper noise is a typical impulse noise as it appears grizzly with canescent
pixels. It is said to be Spike noise as it is caused by sharp and sudden disturbances in the
signal and it statistically drops the original values. This is the reason for why it is otherwise
known as data drop noise.
The Salt and Pepper noise is attributable to the impairment of its constituents in
photographic sensors, fallacious memory locale in equipments or the conveyance in a
amboyant medium. It is consistently non – discriminatory and not mutually related to
Magnetic Resonance imagery and it is randomly valued (Balamurugan, Sengottuvelan,
& Sangeetha, 2013). The density function of the Salt and Pepper noise is given by the
following expression,
....(4) where, a is the bright region
with less gray level
b is the dark region with large gray level
Pa and Pb are the density equations of region ‘a’ and region ‘b’ respectively.
We can explain the appearance of the Salt and Pepper noise in the sense of pixels. The salt
noise which are the white pixels have high frequency that comes in the range of 255200,
whereas the pepper noise which are the dark pixels have low frequency that ranges from
5-0.
1.3. ERROR METRICS
The eciency and accuracy of any lter could be measured by taking the consideration of
some error metrics (Nain et al., 2014). These metrics can be used in tracking out the errors.
There are a number of error metrics and here we discuss about some of them such as MSE,
MAE and PSNR.
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1.3.1. MSE
MSE is the Mean Squared Error which can be otherwise referred to as the mean squared
deviation. To observe the eminence of the adjudicator, the value of this error is calculated.
The MSE is estimated by measuring the mean of squares of the error. When we take the
square root of the MSE, we get the error or deviation estimation of the root mean square.
This is what we called as Root Mean Square Error which is the RMSE or Root Mean
Square Deviation which is RMSD as an alternate. Since the MSE is generally think out as
the variance, the RMSE can be called as the Standard Deviation as it is derived by taking
the square root of its variance.
The MSE of the ltered image with respect to the original image can be expressed as
the summation of the absolute squared erratum in the image which is prorated by the
multiplied values of the number of rows and columns in the image.
MSE = (abs (squared error)) / (M*N) ....(14)
where M and N are the number of rows and columns of the image respectively.
Squared error is nothing but the absolute value of variation amongst the original and the
recreated images.
1.3.2. PSNR
PSNR is dened as the proportionality between the original signal or image and the
reconstructed signal. It is often used to gure out the eminence of the recreated image. The
reconstructed image quality is said to be good, if the PSNR value computed is high.
PSNR is a quality measuring test, which is equivalent in the guesstimate of the humanoid
assessment of the excellence of the renovated image. The value of PSNR can be demarcated
easily without diculty by considering the MSE. The PSNR can be mathematically
articulated by considering the MSE in the following way:
PSNR = 10 log_10 (2552 / MSE) ....(15)
Equation (15) represents the calculation of the PSNR from the known MSE values, when
each pixel is quantized by 8 bits. The MSE and the PSNR values are related in such a way
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that when the MSE lean towards zero, then the PSNR tends to innity. It means that if
there is no error in the image, then the PSNR is innite explaining that the renovated image
is of high quality.
If the MSE gets lower in its errata, the peak ratio of the reference imagery to the noisy
replica increases representing the high portrait quality with exact details.
1.3.3. MAE
The mean absolute error is another term that is responsible for guring out the quality of
the reconstructed image. It is the error detected by calculating the mean of the absolute
errata. It is used to estimate the precognition error in its relativity to the reference image.
The mean absolute error can be calculated as follows:
MAE = (sum (Reference – Reconstructed))/N …. (16)
where N is the pair of forecast and observation images. This error should be small to get
good quality of images.
2. METHODOLOGY
De – noising is quintessential for the maneuvering of images. We can adopt this de – noising
functioning as the chief task or as the supplementary of other procedures. There is an
existence of several methodologies for the extermination of noise. Yet, it is still bothersome
to choose a highly consistent work for a reserved implementation. Here, we discuss some
methodologies such as Mean lter, Median lter, Gaussian lter, Wiener lter, Anisotropic
Diusion, Lee and Frost lter and the Non Local Means lter for the noisy imagery acquired
from the MRI.
2.1. MEAN FILTER
Mean lter is contiguous by speculating the spatial behavior and this can be done with
untroublesome implementation of smoothing images. This lter replenishes the halfway
point of the kernel by taking the mean of all the other values. Hence it can be also called
as the Average lter. It can do the job of a lter that is an LPF (Chandel & Gupta, 2013),
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in which the elements of the image are summed up and then divided by the total number
of elements.
The formula for this lter could be denoted as follows,
....(5)
where, Sxy is the match of counterparts in a window of size mxn centralized at (x,y).
The working of the mean lter is done by marching throughout the image completely
exchanging the value of each dot with the average of neighborhood pixels including it as
it is the method of smoothing which is done by lessening the measure of discrepancy of
intensity amongst the neighborhood pixels.
The mean lter could be used to remove Gaussian noise and Speckle noise, whereas
unsuccessful in Salt and Pepper noise. It is because, when the neighbor of the pixel bestrides
a border, then the lter may introduce recently found values for the picture elements on that
border which may numb the border.
2.2. GAUSSIAN FILTER
The corrosive Gaussian lter does not induce lofty frequency inheritance. It is deliberated
to be the exemplary type of lter in time domain (Singh, 2017). It promises its favor to the
extent of time on an equal footing with its favor to the extent in frequency. The cuto may
not be sharp at some pass band frequencies. This is due to the fact that this lter has its
Fourier transformation as Gaussian.
The Gaussian lter has the formula as given in the expression,
....(6)
where, x – level stretch from outset
y – erect stretch from outset
σ2 – variance of Gaussian distribution
The kernel coecients of the Gaussian lter depend on σ where the larger values of σ
produce more blurring in the image. These kernels are rotationally symmetric and have no
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directional bias. Gaussian lter is a dynamic, baseband lter whose kernels are separable
which results in faster computation.
The Gaussian lters remove the speckle noise which is the spike noise by smoothing the
image. Also, Gaussian smoothing could be used in removing the Gaussian noise, a common
sort of noise in medical MRI images.
2.3. ANISOTROPIC DIFFUSION FILTER
Anisotropic diusion lter is a mechanism which reduces noise from the imagery by keeping
the noteworthy parts of the image untouched. It can be also called as Perona – Malik
dispersion as it is presented by Perona and Malik (1990). It is highly space – variant and is
locally adaptable.
The Anisotropic Diusion lter is based on the following equation,
....(7)
where, |
u|2 measures the larger likelihood of locations to be edges.
The Anisotropic diusion lter is one of the eective non – linear lters which simultaneously
enhances the contrast and also reduces the noise. It depends mainly on the direction of
application so that it soothes the homogeneous image regions and retains the edges of the
image. Hence, it is one of the well – suited lters for the removal of Rician noise.
2.4. WIENER FILTER
Wiener ltering works with the term of the error of squared mean and is determined to be
the unsurpassed tradeo amongst inverse lter and the smoothing lter. It is splendiferous
as an endorsement frame. The Wiener ltering provokes the yield by using the rectilinear
time invariant ltering of the imagery (Kazubek, 2003). It is a renement process of
rehabilitation.
The approximated formulation for the Wiener lter in the expatriation of noise is specied
by,
....(8)
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where, K is chosen manually to obtain the best visual result.
The Wiener lter is normally a beeline lter which is considered to be stationary. It considers
the frequency details instead of the spatial details and it uses the discrete Fourier transform
to get the high quality replica. It uses the analytical style of processing. The noise variance
can be reduced by the Wiener lter thereby making the blurred images clearly visible. The
Wiener lter can be used to nd the power spectra of dierent images and make it useful in
other images by taking the average of all the data where a huge set of data exist. This gives
a further smoothened imagery.
During rectication purposes, it speculates the province of decadence as well as the noise. It
is the process from which we can enumerate the eectiveness of the system by considering
various criteria. The image refurbishment with the Wiener lter gives excellent results as it
is an outstanding restoration lter. The designing of the Wiener lter is a rectilinear process
and is used in removing the Gaussian and the speckle noise, but it is not much better than
the median lter.
2.5. NON – LOCAL MEANS FILTER
The Non – Local Means lter calculates the neutral value of all the picture elements in the
given image, whose weightage is made in such a way that it nds out the level of similarity
of these pixels with the intend dot (Wiest-Daesslé et al., 2008). This provides more clarity
after ltering with a very little loss percentage of details in contrast to the local means
algorithm.
The NL means lter formula is expressed by the following equation,
....(9)
where, u(x) – ltrated estimate of picture at spot ‘x’
v(y) – unltrated estimate of picture at spot ‘y’
f(x,y) – weighing functionate
The level of similarity of the pixels not only depends on the homogeneity of the gray
level intensity, but also the geometrical conguration in the neighborhood pixels. The main
function of the NL means lter is the dismissal of Rician noise.
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2.6. MEDIAN FILTER
The Median lter is probably a spatial lter and is indiscriminate in nature. It is useful for
the smoothing of the images. In this lter, the output is obtained from the middle value of
the input exemplars in the interface, after the input sampled values are sorted.
The lter formula for the median lter is expressed as follows,
....(10)
where, ω describes the vicinity established by the user, rested with the location [x,y] of the
imagery.
Hence, from the above equation, it is clear that the main principle of the median lter is to
restock the value of every single picture element with the middle value of the surrounding
pixels, instead of averaging the pixel values (Kazubek, 2003).
Most commonly, the kernel covers odd number of pixels and so the median is the middle
value. But, if it is even, then the mean of the duo middle values can be taken as the median.
Prior to the start, the voids are inlaid on every margin which makes the squinching to be
presented at the borders.
The median lter is mainly used for expatriating the Salt and Pepper noise. In such type of
noise, the squinched signal varies from the original and so is its mean value from the true
value. Hence Salt and Pepper noise could not be reduced by conventional lters like mean
or Gaussian lter successfully, but median lter is well – suited as it removes the drop – out
noise eectively and preserves even the small details and edges in a better way. In case
of Speckle noise, it is better than the Wiener and the mean lters. It can also be used in
removing the Gaussian noise, as it is a spatial lter.
2.7. LEE AND FROST FILTER
The Lee lter and the Frost lter are mainly designed to remove the multiplicative noise.
The Lee lter was developed by Jong Sen Lee in 1981, whereas the Frost lter was invented
by Frost in the year 1982.
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The Lee lter is mainly developed for the generative speckle pattern which utilizes localized
enumeration in order to maintain the ne points. It drives in line with the variance. It
means that if performs the smoothening operation for the area where the variance is low
but not for high variance areas.
The Lee lter formula for the removal of noise is given by the following equation,
....(11)
where, Yxy is the despeckled image
K ̅ is the mean of Kernel
C is the central element in the kernel
W is the lter window
The lter window value is given by,
....(12)
where, σ² is the variance of the reference image
σ
k² is the variance of pixels in kernel of speckled image.
The Frost lter is a linear, convolution lter. This lter is related to the gure of variance
i.e., the proportion of localized deviation to the localized mean of corrupted image. Here,
the image factor decreases when we abscond from the concerned pixels while increases
when near at hand.
....(13)
where,
|t| = |X − X0| + |Y − Y0|
K – Normalized coecient
I ̅ – Localized mean
Σ – Localized variance
σ ̅ – Image factor of deviation
N – Dimension of roaming kernel
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The Lee lter and the Frost lter are mainly responsible for the removal of Speckle noise
(Jaybhay & Shastri, 2015) and they are better in performance than the other lters like
Wiener, mean and the median lter.
2.8. NEURAL NETWORK FILTER
The image denoising is recently being done by using neural network approaches. The salient
point in the depiction of a neural network image lter is to link an image over another with
some features that are extracted in order to form a function in a neural network. Bermudez et
al. (2018) used dierent degrees of Gaussian noise to test their proposed method which uses
a skip connection based autoencoder for denoising and proved that their method towered
above the FSL SUSAN software. A combination of deep neural networks with spatio –
temporal denoising and bolus injection of contrast agent (CA) has been proposed by Benou
et al. (2017) for reducing noise. Here, the training of data is performed by adopting a Tofts
pharmacokinetic (PK) model and noise realizations. They used concatenated noisy time
curves from the surrounding pixels of the frontline for further betterment. Golkov et al.
(2016) recommended “q-space deep learning” approach, with model-tting steps to get the
scalar properties of voxels directly from the subsampled diusion weighted images.
3. RESULTS
The error metrics MSE and MAE can be compared so as to get a clear pictorial view. The
MSE and the MAE are the errors and are to be lower in each and every case (Saladi &
Prabha, 2017). With this comparative evaluation of all the lters, we get a vibrant outlook
that explains the mediocre values of mean square error and the mean absolute error that
are the main distinctive features of an image.
From the review of various ltering methods’ positivity and weakness, the basic lters such
as mean, Wiener and the Gaussian lters are well and good in the removal of speckle and
Gaussian noise, but median lter is better than these by providing clear and sharp edges
with details. Lee and Frost are better far from the other local lters. Rician noise could
be reduced with Anisotropic diusion and non local means lter. Comparing to the basic
lters, the advanced neural network could be more comfortable in the removal of noises as
it adopts the proper training of data. However, hybrid techniques are improving nowadays
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which involve the combination of two or more lters in order to improve the accuracy and
robustness.
4. CONCLUSIONS
Good quality of images is necessary in every eld that involves image processing as its part,
especially in medical eld. Since brain is a complex organ with soft tissues, expatriation of
noise is vital. In this paper, by considering the error metrics, we nd that the Gaussian noise
could be reduced by using the spatial lters like mean lter, Wiener lter and Median lter.
We can also use Gaussian smoothing which can considerably reduce the noise. Salt and
Pepper noise can be reduced eciently by employing median lter. The lters, anisotropic
diusion and NL means are better in removing Rician noise and the Speckle noise reduction
can be eectively done by Lee and Frost lters. However, the lter based on neural network
is found to be more ecient in ltering noises by mapping of noisy images with the training
samples and hybrid methods are far better.
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