An overview of the fundamental approaches that yield several image denoising techniques

TELKOMNIKA, Vol.17, No.6, December 2019, pp.2959~2967
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v17i6.11301 ◼ 2959
Received September 26, 2018; Revised February 2, 2019; Accepted March 12, 2019
An overview of the fundamental approaches
that yield several image denoising techniques
Bilal Charmouti*1
, Ahmad Kadri Junoh2
, Mohd Yusoff Mashor3
, Najah Ghazali4
,
Mahyun Ab Wahab5
, Wan Zuki Azman Wan Muhamad6
,
Zainab Yahya7
, Abdesselam Beroual8
1,2,4,6,7
Institute of Engineering Mathematics, Universiti Malaysia Perlis (UniMAP), Perlis, Malaysia
3
School of Mechatronic, Universiti Malaysia Perlis (UniMAP), Perlis, Malaysia
5
School of Environmental Engineering, Universiti Malaysia Perlis (UniMAP), Perlis, Malaysia
8
Department of Computer Science, International Islamic University Malaysia, Malaysia
*Corresponding author, e-mail: dybilel@yahoo.fr
Abstract
Digital image is considered as a powerful tool to carry and transmit information between people.
Thus, it attracts the attention of large number of researchers, among them those interested in preserving
the image features from any factors that may reduce the image quality. One of these factors is the noise
which affects the visual aspect of the image and makes others image processing more difficult. Thus far,
solving this noise problem remains a challenge for the researchers in this field. A lot of image denoising
techniques have been introduced in order to remove the noise by taking care of the image features;
in other words, getting the best similarity to the original image from the noisy one. However, the findings
are still inconclusive. Beside the enormous amount of researches and studies which adopt several
mathematical concepts (statistics, probabilities, modeling, PDEs, wavelet, fuzzy logic, etc.), there is also
the scarcity of review papers which carry an important role in the development and progress of research.
Thus, this review paper intorduce an overview of the different fundamental approaches that yield
the several image-denoising techniques, presented with a new classification. Furthermore, the paper
presents the different evaluation tools needed on the comparison between these techniques in order to
facilitate the processing of this noise problem, among a great diversity of techniques and concepts.
Keywords: denoising methods, digital image, image denoising, image processing, noise
Copyright © 2019 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Among the different tools of communication between people, there is the image which
carries a large amount of information. However, unfortunately, the image can be corrupted by
parasitic information, which is called noise: an alteration of image, which may be caused by
the image acquisition process or transmission [1, 2]. The main concern of the researchers in this
subject is to succeed in solving this problem by removing noise from the noisy image and
achieve the best restoration of the original one. To achieve the desired aim, they need ample
and necessary knowledge, concepts and definitions, which are inspired from the review of
relevant literature. Image processing is quite a wide field of knowledge due to its importance,
and widely applied in several fields like biology, astronomy, industrial, medical and defence.
Thus, a large amount of researches and studies have been done about this area. Where,
among the existing barriers in restoring the corrupted image is the scarcity of review papers
which carry an important role in the development and progress of research, In this paper we will
take a closer look into the necessary information restricted in the primary phase of image
processing (image pre-processing), called Image denoising, particularly the fundamental
approaches of image denoising. We seek to gather and introduce these approaches and
concepts smoothly, with good arrangement, where the readers can penetrate into the subject,
in order to facilitate the path that leads to the goal, by making this paper a starting point of other
studies concerning the image denoising. Thus, image, digital image, noise, noisy image, image
denoising, approaches for image denoising, as well as method comparison, are presented in
the rest of the paper by the following main sections. Section 2: discussion about relevant
materials and tools, which present definitions and concepts about image, noise and filtering.
Section 3: Discussion about the denoising methods, also the description of the basis of

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denoising approaches. Section 4: both the evaluation and comparison of the denoising
methods. Finally, section 5 offers the conclusion.
2. Materials and Tools
2.1. Image
An image is a scene representation through painting, sculptures, drawing, photography,
and so on. It is also a structured set of information that, after the display on the screen, gives
meaning to human. It may be defined as a two-dimensional function I (x, y) analog brightness
continuous, defined in a bounded domain, x and y as the spatial coordinates of a point of
the image and I is a function of luminance intensity and color. In this aspect, the image is
unusable by the machine, which requires digitization [3].
The digital image, in its broadest sense, refers to any image acquired, processed and
stored in a coded form which may be represented by numbers (numerical values). Digitization is
the process which permits the image to move from the physical state (optical image)
represented by continuous signal (an infinity of intensity value), to the digital image state which
is characterized by the discrete aspect (intensity take their values in a finite number of points).
This is the digital form which permits a further exploitation by computer software tools. Thus,
the digital image is a bounded set of elements, where each one of them is determined by
location coordinate and value. These elements are named image elements, picture elements,
pixels, and pels, whereas, the most widely used term to denote the digital image elements is
''pixel''. According to the luminance intensity value, digital image is classified into three types
(color-coding): black and white gray scales and coloured scales.
The binary images are an array of integers (k = 1 bit), pixel that can take one of
the values: 0 or 1. White is denoted by 0 and Black by 1. This is the simplest types of images
and usually this kind is used to scan texts when the latter is composed of one color. The gray
level is the value of the luminance intensity at one point. This image consists of only 8 bytes,
and the pixel color can take values ranging from black to white through various levels of
brightness [0, 1, 2, ..., 255]. Usually color images are based on three primary colours: Red,
Green and Blue (RGB), and each of these colours use 8 bits for one pixel which takes a value
from the range [0, 1, 2, ...,255], so each pixel in the color image requires 3×8=24 bits to encode
three components.
2.2. Noise
Noise is an alteration of image (parasites information) that may be created in one of
these phases, during the acquisition process (conversion operation from optical signals to
the electrical then from electrical to digital signal) through the transmission, sensor status and
environmental conditions [1, 4]. The noise has different origins, but it causes similar effects such
as the loss of sharpness in the details or the appearance of grains, where the amount of noise
in noisy image is assigned by the number of corrupted pixels. In terms of removing this noise
from the corrupted image, the researchers of this field have made some in-depth studies to
know the nature and types of noise. The image is corrupted due to the fact that there are
various types of noise such as the Gaussian noise, Poisson noise, Speckle noise, Salt and
Pepper noise and many more fundamental noise types in the case of digital images [5].
Noise is integrated in the image 𝑢(𝑥, 𝑦) through three forms of noise 𝑛(𝑥, 𝑦), namely
additive, multiplicative, and impulse noise [6, 7], to give a noisy image denoted by 𝑣(𝑥, 𝑦).
The additive noise formula is shown by (1) :
v(x, y) = u(x, y) + n(x, y) (1)
the multiplicative noise formula is modeled by (2):
v(x, y) = u(x, y) × n(x, y) (2)
3. Denoising Methods
Image denoising is a phase, which precedes the image processing (image
pre-processing); in other words, a set of operations occuring on the image, which aims to
améliorate the visual aspect of the image by means of reducing or removing noise from image.

TELKOMNIKA ISSN: 1693-6930 ◼
An overview of the fundamental approaches that yield several image... (Bilal Charmouti)
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This is in order to facilitate other processes such as the compression, analyses, classification,
segmentation, and extraction of information [8]. Denoising methods are based on the main idea
which is to replace each corrupted pixel value (noise) in the noisy image with another value,
making that image closer to the original one (noise free image) as much as possible, using
the necessary knowledge about noise and image cited in the previous section. In other words,
the denoising methods aim to achieve the version closest to the original image. Several
methods have been developed in this way, although each method has its advantages and
disadvantages. These denoising methods may be classified into two main categories,
the spatial domain and transform domain filtering which merged together in some cases to yield
hybrid filters.
3.1. Spatial Domain Filtering
Spatial domain filtering is considered as a traditional way to remove corrupted pixels
(noise) from the image [9]. It is a set of mathematical operations that deal directly with the pixel
in the image plane, because in this domain, the signal is represented by pixels, or in other
words, image elements are pixels. The filtering operations are applied into these pixels, based
on mathematics concepts, through which we apply the filtering window to each pixel in
the whole noisy image (overall processing), in the case that the detection phase is absent, or to
some pixels of noisy image (partial processing), or in the case that we firstly pass through
the detection phase (Noise detection) using several detector techniques such as the fuzzy
techniques as shown in Figure 1. Generally, the filter treats the noisy image through two ways,
linear or non-linear as shown in Figure 1.
Figure 1. Basic path of spatial filtering process
3.1.1. Linear Filtering
The linear filter transforms an input data set into a set of output data according to
a mathematical operation called convolution. It allows for each pixel in the area to which it
applies, to change its value through a linear combination of its neighbors. The linear filtering
operation is easy to implement for removing noise but usually it produces blurred images, which
are the main defect of this filter [10, 11]. Many well known linear filters have been introduced like
the mean filter and Wiener filter.
3.1.2. Non-linear Filtering
They are designed to solve the problems of the linear filter, especially with regard to
the poor preservation of edges [10, 11]; Their principle is the same as the linear filters, where it

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always replaces the value of each pixel with the calculated value from a mathematical operation
applied to its neighbors’ values, including itself. The difference is that this operation is no longer
linear. There are many popular non-linear filters such as the median and its extensions (order
statistic filters), bilateral filter, Total variation (TV), morphological filter, anisotropic filter and so
on. Other characteristic filtering may differ between several denoising approaches, such as
statistical/deterministic, adaptive/non-adaptive and local/non-local. In [12-15], some examples
are presented.
3.2. Transform Domain Filtering
The transform domain filtering is the second category of image denoising approaches,
which gained enormous interest from scholars and studies. It may be defined as a set of filtering
operations that treats the image in another form (other domains) such as frequency domain
(Figure 2), rather than the original form (original domain), in order to gain further information
from the signal and reach a successful filtering through this new form. The new domain may
differ from the original one in the dimensions (e.g. from 2D to 3D) or in the characteristics
(e.g. from spatial to frequency domain). This transform is a mathematical conversion that is
achieved through a clever mathematical tool (basis function). The image filtering process in
the transform domain can split into two branches according to the type of this basis function [9];
adaptive to processed data and non-adaptive. For the adaptive approaches there are two
effective techniques namely the Principal component analysis (PCA) [16],which treats only
the data information given by the second-order statistics, and the Independent component
analysis (ICA) [17] which comes as an extension to PCA to give better performance, by living up
to high order statistics ( the case of the most natural images) [18]. The main idea of both
statistical techniques, PCA and ICA, is to use an orthogonal decomposition to separate linearly
as much as possible the correlated data into independent sub-sets [19]. In the non-adaptative
aproaches there are many methods due to the variety of basic functions such as, wavelets [20],
wave atoms [21], curvelets [22], contourlets [23], wedgelets [24], and bandelets [25], which
transform the image to the frequency domain. From those, the oldest, the most popular, and
the dominant one (''wavelet'') [26], are highlighted in the following sections. Recently in
the transform domain, a new efficient method (BM3D) is developed by Dabov et al. [27] using
sparse 3D transform by grouping similar 2D-Blocks in the image into a 3D-arrays (grouped), in
this case the image is represented in the transform domain by many 3D-groups. Then,
the spectrum is shrunken to separate the noise from other features [28]. This method has
shown great efficiency in removing image compared to several techniques, but in the case of
high level of noise it gives less performance, and for that, in [29] a bounded BM3D method was
proposed based on the basis BMED to exceed this limitation. Furthermore, many techniques
were derived from the BM3D such as in [29], which focuses on the optimal choice of shrinkage
operator, and the two algorithms in [30],CD-BM3D and iterative CD-BM3D used the complex
domain. The several fundamental techniques of image denoising in transform domain are
presented by the below diagram in Figure 3.
Figure 2. The above images transformed to the frequency domain below

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Figure 3. Image denoising approaches
3.3. Hybrid Filtering
Hybrid filtering may be considered as the third image-denoising category. It is a diverse
combination of several approaches from the spatial or transform domain or both together
as shown in Figure 3. This kind of image filtering, exploits the advantages of different existing
filters to build a new filter which includes a mixture of these advantages, in order to overcome
the limitations of conventional techniques and give better performance. This has been used by
many researchers and studies in the image denoising. Thus, numerous hybrid filters have been
proposed, whereby the point which attracts much attention, is the considerable attendance of

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the wavelet in these hybrid filters. For example, in [31] the filter decomposes the image by
(DT-CWT) then, it applies an adaptive wavelet thresholding to the detailed coefficients, while
the approximation coefficients are treated by Non-Local Means (NLM) technique, and finally
the denoised image is obtained by the inverse DT-CWT. As well, in [32] the undecimated
wavelet transform (UDWT) and NLM is performed. In [33], a denoising technique based on
the combination of wavelet transform and anisotropic filtering was presented. Many other hybrid
filters use the mixture of wavelet and total variation has been introduced in [34-37].
The principle component analysis (PCA) was merged with the wavelet and NLM in [38] and [39],
respectively. A hybrid neighborhood filter is applied in [40], based on the Gaussian filter with
the correlation of wavelet coefficients. Wiener filtering was combined with DT-CWT and
continuous wavelet transform (CWT) (to a seismic signal) in [41] and [42], respectively.
The area in the image may be defined as a texture, edge or smooth (homogeneous) region [43].
If for each of these areas we chose the filter which gives good result among the existing filters,
eventually we get three diverse filters for the image. This is the concept which is adopted in [43]
by using the combination of three different multiresolution techniques, namely wave atoms
(textures), curvelet (edges) and wavelet (smooth regions). Meanwhile, these last two techniques
were blended in [44]. In [45], a hybrid filter including a mix of HMF (hybrid median filter) and
total variation (TV) is proposed.
4. Evaluation and Comparison
The common objective of these introduced denoising methods is to remove noise from
image by way of preserving its features, or in other words, reaching the restored image which is
the most similar to the original one, taking into account certain strict and crucial criteria such as
the simplicity of filter implementation and the cost merit [46]. Seeking to overcome filtering
limitations and to achieve the optimality, a great number of denoising techniques have been
introduced in these last years. Thus, many disparities and differences can be observed between
these filters. Getting a comparison and evaluation from this large number proves to be an
arduous task, especially as it shares many characteristics such as linear/non-linear,
statistical/deterministic, etc. (network of features), therefore it is quite necessary to rely on some
points linked with the three parts of the filtering process (Table 1) which are:
a. The noisy image (input): the type of noise (additive, multiplicative, impulse noise, mixed
noise), amount of noise (high, low), structure of image (texture, smooth, edge), pixels
intensity.
b. Filter (denoising tool): computational cost (acceptable, high), filter implementation (simple,
complex).
c. Restored image (output): the image quality is one of the evaluation criteria of denoising
techniques performance, so the question is how do we assess this quality? The way by
which the image quality is evaluated (evaluation criteria) may be divided into two ways:
- The first one is the visual evaluation determined by the observer, where the human
judgment is interested in the image components appearance, if it contains any
degradation factors or otherwise, such as artifacts, discontinuities and blur [47].
- The second one is the quantitative evaluation (quality metric) by using the measurement
parameters, which include: 1) Signal to Noise Ratio (SNR), which measures the amount
of noise n in the noisy image I(i, j) using the standard deviation of the noise σ(n) and
image σ(I) (σ(I) = 60 indicating good image quality) [48], it is given by (3); 2) Mean
Squared Error (MSE), that measures the dissimilarity between the restored image Î(i, j)
and the original one I(i, j) as shown below in (4), thus whenever the MSE is lower, the
image denoising achieves more success [49]; 3) Peak Signal to Noise Ratio (PSNR) [50],
a well-known parameter that has an inverse relationship with MSE, as denoted in (5).
It is not necessary to be an entailment relation between the visual and quantitative
assessment, because sometimes an image, even with high PSNR or low MSE, does not seem
clean. This means that these indexes (MSE, PSNR) are not well matched to perceived visual
quality [51]. Thus, there are many quality assessment (QA) methods developed in the last
decades, which take into account the human visual system (HVS), such as the Structural
SIMilarity (SSIM) index [51].

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SNR =
σ(I)
σ(n)
(3)
MSE =
1
N
∑ (I[i, j] − Î[i, j])2
i,j (4)
PSNR = 10 log10 (
2552
MSE
) (5)
𝑁 the number of pixels in image.
By using these above three guidance points, the several techniques of image denoising
can be evaluated and compared briefly according to their classification in Table 1 (field ''types of
filters''), as follows: The performance of filtering method rises from the left column to the right
column and from the first row to the last row, where the performance of denoising method is
denoted by the blue triangle, where it is rises from the head to the base of this triangle. For
example, the adaptive denoising methods in the transform domain are more efficient compared
to the non-adaptive methods in the transform domain or with adaptive methods in the spatial
domain. In addition, the linear filters are simple to implement than non-linear ones, whereas
the statistical filters are expensive and complex compared to the deterministic filters.
5. Conclusion
This paper presents an overview of the fundamental approaches from which the several
denoising algorithms are derived, as a starting point of future studies and researches in this
subject. Through this study, it is found that there is an enormous number of denoising
algorithms which makes the evaluation and the comparison between them difficult to be
attainable. In order to overcome this situation by facilitating the understanding, the evaluation
and the comparison between the significant number of diverse techniques of
image denoising, this paper proposes seven categories to classify these
algorithms (Linear/Nonlinear-Deterministic/Statistical-Non-Adaptive/Adaptive-Local/Non-Local-
without Noise Detection (treat all pixels)/with Noise Detection (treat corrupted pixels)-Spatial
Domain/Transform Domain-Unmixed/Hybrid), where the characteristics of any category affect
the efficiency of the denoising filter. To achieve this goal, we also present the evaluation tools
which permit the estimation of the efficiency and the disparity among these techniques. All these
categories and evaluation tools are summarised in Table 1.
Table 1. The Comparison between Several Fundamental Denoising Methods
Evaluation Tools
Filtering TypesThe noisy image
(input)
Filter
(denoising tool)
Restored image
(output)
- Type of noise
(additive,
multiplicative,
impulse noise,
mixed noise)
- Amount of noise
(high, low)
- Structure of image
(texture, smooth,
edge), pixels
intensity
- Computational cost
(acceptable, high)
- Filter
implementation
(simple, complex)
- Measurement of
noise (SNR, MSE,
PSNR, etc.)
- Visual quality
(blur, artifacts,
information loss,
etc.)
Linear Non-Linear
Deterministic Statistical
Non-Adaptive Adaptive
Local Non-Local
Without Noise Detection
(treat all pixels)
With Noise
Detection
(treat corrupted
pixels)
Spatial Domain Transform Domain
Unmixed Hybrid
ACKNOWLEDGEMENT
This work was financially supported by Ministry of Education Malaysia (MOE) under
Fundamental Research Grant Scheme (FRGS) ((Ref: FRGS/1/2019/STG06/UNIMAP/02/3).

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