LIBYAN ACADEMY FOR POSTGRADUATE STUDIES
SCHOOL OF APPLIED SCIENCES AND ENGINEERING
ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT
Image Restoration Techniques
Submitted by:
Abdulwahab A. Abdullah
Supervised by:
Dr. Mostafa K. Aswad
This report is submitted for Image Processing “EEM 646” subject.
Fall 2021.
Image restoration
1. Introduction
Image restoration methods used to improve the appearance of an image by application of a
restoration process that uses a mathematical model for image degradation. Examples of the types
of degradation considered include blurring caused by motion or atmospheric disturbance,
geometric distortion caused by imperfect lenses, superimposed interference patterns caused by
mechanical systems, and noise from electronic sources. It is assumed that the degradation model
is known, or can be estimated. The primary idea is to model the degradation process and then
apply the inverse process to restore the original image.
The goal of this report is to give an overview of image restoration techniques to readers, who is
just beginning in this field of image restoration. The task of developing restoration algorithms is
quite difficult, since the information should not be destroyed during image restoration. The aim of
this article is to let the readers know various methods of digital image restoration techniques with
their pros and cons. Digital image restoration is a very broad field, contains many other approaches
that have been developed from different perspectives, such as satellite imaging, optics, astronomy,
and medical imaging [1].
1.1 Image Restoration vs. Image Enhancement
Image restoration is different from Image Enhancement as Restoration is more Objective and
Enhancement is Subjective. Image Enhancement could not precisely represent by mathematical
function whereas in Image restoration related to feature extraction from the imperfect image.
Enhancement is manipulated the degraded image, increases the contrast of the image and visual
appearance can be improved
1.2 Reasons for Occurrences of degradation
There are many reasons available for degradation such as sensor noise, camera-misfocus, relative
object-camera motion, random atmospheric turbulence. Random variation of brightness or color
information in the image called noise and can be produced by sensor and circuitry of a scanner or
digital camera. While object moves to the camera or vice versa, motion blur can be caused. While
the object is out of focus of the camera during exposure, the object region in the image is also
blurred. This kind of blur is called defocus blur imaging system is affected by atmospheric
turbulence by virtue of wave propagation through a medium with non-uniform index of refraction.
1.3 Degradation Model
The degradation process can be viewed with the following system shown in Fig. 1. The degraded
function is low pass filter. The original input is a two-dimensional image f(x, y). This image is
operated on the system h(x, y) and after the addition of noise n(x, y). One can obtain the degraded
image g(x, y). Digital image restoration may be visualized as a process in which we try to obtain
an approximation to f(x, y).
Figure 1. Image degradation model
1.4 Applications of Restoration
In the area of astronomical applications characterized by poisson noise, Gaussian noise,
image restoration has played a very important role in the area of imaging.
SR technique is also useful in medical imaging such as computerized tomography (CT)
and magnetic resonance imaging (MRI) since resolution while the resolution quality is
limited the acquisition of multiple images is possible. This can help the surgeon to operate
more successfully over the exact part of the body with care.
Over the multispectral bands of satellite imagery, multispectral image restoration can be
carried out in order to improve the resolution of the captured satellite images.
To enhance the HR of the mobile camera.
In order to improve the video resolution, the motion blur estimation can be performed in
the real time video image processing applications.
1.5 System Model
Image restoration uses a priori knowledge of the degradation. It models the degradation and applies
inverse process. It formulates and evaluates the objective criteria of goodness. The distortion can
be modelled as noise or a degradation function. To restore an image from a noise model, different
filters like median filter, homomorphic filters are used. To get rid of periodic noises, lowpass filter,
butterworth band reject filters and notch filters are used. To restore an image from linear
degradation, inverse and pseudo inverse filtering, wiener filtering and blind de-convolution are
used [2].
Figure 2. Image restoration process.
2. Blur model
2.1 Gaussian blur
It is type of image blurring filter which use Gaussian function for calculating transformation
applied on each pixel. The equation of Gaussian function is
(−𝑥)2
1
𝐺(𝑥) = 𝑒 2𝜎2 (1)
√2𝜋𝜎
Where x is distance from origin in horizontal axis and σ is standard deviation of Gaussian
distribution.
2.2 Motion Blur
Motion blur occur in image due to camera misfocus and change in angle during taking of picture.
2.3 Rectangular blur
This is blurring in image with specific rectangular area. Blur in image can be identified at any
part based on this it can be circular and rectangular.
2.4 Defocus blur
Defocus blur occurs in image when camera is improperly focused on image. The resolution of
image medium depends on amount of defocus. If there is more tolerance of image, there is low
resolution in image. For good resolution of image defocus in image should be minimize.
3. Noise Models
Noise tells unwanted information in digital images. Noise produces undesirable effects such as
artifacts, unrealistic edges, unseen lines, corners, blurred objects and disturbs background scenes.
The principal sources of noise in digital images arise during image acquisition and/or transmission.
The performance of imaging sensors is affected by a variety of factors, such as environmental
conditions during image acquisition, and by the quality of the sensing elements themselves. For
instance, in acquiring images with a CCD camera, light levels and sensor temperature are major
factors affecting the amount of noise in the resulting image. Images are corrupted during
transmission principally due to interference in the channel used for transmission. For example, an
image transmitted using a wireless network might be corrupted as a result of lightning or other
atmospheric disturbance [3]. To reduce these undesirable effects, prior learning of noise models is
essential for further processing. Probability density function (PDF) or Histogram is also used to
design and characterize the noise models. Here we will discuss few noise models, their types and
categories in digital images [4].
3.1 Gaussian Noise Model
It is also called as electronic noise because it arises in amplifiers or detectors. Gaussian noise
caused by natural sources such as thermal vibration of atoms and discrete nature of radiation of
warm objects [5].
Gaussian noise generally disturbs the gray values in digital images. That is why Gaussian noise
model essentially designed and characteristics by its PDF or normalizes histogram with respect to
gray value. This is given as:
−(𝑧−µ)2
1 −
𝑝(𝑧) = 𝑒 2𝜎2 (2)
√2𝜋𝜎
Where g = gray value, 𝜎 = standard deviation and μ = mean. Generally, Gaussian noise
mathematical model represents the correct approximation of real world scenarios. In this noise
model, the mean value is zero; variance is 0.1 and 256 gray levels in terms of its PDF, which is
shown in Fig. 3.
Figure 3. PDF of Gaussian noise
Due to this equal randomness, the normalized Gaussian noise curve look like in bell shaped. The
PDF of this noise model shows that 70% to 90% noisy pixel values of degraded image in between
μ−𝜎 and μ+𝜎. The shape of normalized histogram is almost same in spectral domain.
3.2 Impulse Valued Noise (Salt and Pepper Noise)
This is also called data drop noise because statistically its drop the original data values. This noise
is also referred as salt and pepper noise. However, the image is not fully corrupted by salt and
pepper noise instead of some pixel values are changed in the image. Although in noisy image,
there is a possibilities of some neighbors does not changed [6]. This noise is seen in data
transmission. Image pixel values are replaced by corrupted pixel values either maximum ‘or’
minimum pixel value i.e., 255 ‘or’ 0 respectively, if number of bits are 8 for transmission.
Let us consider 3x3 image matrices, which are shown in the Fig. 4. Suppose the central value of
matrices is corrupted by Pepper noise. Therefore, this central value i.e., 212 is given in Fig. 3 is
replaced by value zero.
In this connection, we can say that, this noise is inserted dead pixels either dark or bright.
Therefore, in a salt and pepper noise, progressively dark pixel values are present in bright region
and vice versa.
Figure 4. The central pixel value is corrupted by Pepper noise
Inserted dead pixel in the picture is due to errors in analog to digital conversion and errors in bit
transmission. The percentagewise estimation of noisy pixels, directly determine from pixel
metrics. The PDF of this noise is shown in the Fig. 5.
Figure 5. The PDF of Salt and Pepper noise
𝑃𝑎 𝑓𝑜𝑟 𝑧 = 𝑎
𝑝(𝑧) = { 𝑃𝑏 𝑓𝑜𝑟 𝑧 = 𝑏 (3)
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Fig. 4 shows the PDF of Salt and Pepper noise, if mean is zero and variance is 0.05. Here we will
meet two spike one is for bright region (where gray level is less) called ‘region a’ and another one
is dark region (where gray level is large) called ‘region b’, we have clearly seen here the PDF
values are minimum and maximum in ‘region a’ and ‘region b’, respectively [5]. Salt and Pepper
noise generally corrupted the digital image by malfunctioning of pixel elements in camera sensors,
faulty memory space in storage, errors in digitization process and many more.
3.3 Rayleigh Noise
Unlike the Gaussian distribution, the Rayleigh distribution is not symmetric [7].
Rayleigh noise presents in radar range images. In Rayleigh noise, probability density function is
given as:
−(𝒛−𝒂)𝟐
𝒃
𝑷(𝒛) = 𝟐
(𝒛 − 𝒂)𝒆 𝒇𝒐𝒓 𝒛 ≥ 𝒂 (4)
𝒃
{𝟎 𝒇𝒐𝒓 𝒛 < 𝒂
𝜋𝑏 𝑏(4−𝜋)
Where mean 𝜇 = 𝑎 + √ 4 and variance 𝜎 2 = are given as, respectively.
4
Figure 6. Rayleigh distribution
3.4 Gamma Noise
Gamma noise is generally seen in the laser-based images. It obeys the Gamma distribution.
Which is shown in the Fig. 7 and given as:
𝑎𝑏 𝑧 𝑏−1 𝑒 −𝑎𝑧
𝑓𝑜𝑟 𝑧 ≥ 0
𝑃(𝑧) = { (𝑏−1)! (5)
0 𝑓𝑜𝑟 𝑧 < 0
𝑏 𝑏
Where 𝜇 = and variance 𝜎 2 = are given as, respectively.
𝑎 𝑎2
Figure 7. Gamma distribution
3.5 Exponential noise
The PDF of exponential noise is given by:
𝑎𝑒 −𝑎𝑧 𝑓𝑜𝑟 𝑧 ≥ 0
𝑝(𝑧) = { (6)
0 𝑓𝑜𝑟 𝑧 < 0
Where 𝑎 > 0. The mean and variance of this density function are:
1
𝜇=
𝑎
and
1
𝜎2 =
𝑎2
Note that this PDF is a special case of the Erlang PDF, with b = 1.
3.6 Uniform Noise
The PDF of uniform noise is given by:
1
𝑖𝑓 𝑎 ≤ 𝑧 ≤ 𝑏
𝑝(𝑧) = { 𝑏−𝑎 (7)
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
The mean of this density function is given by
𝑎+𝑏
𝜇=
2
and its variance by
(𝑏 − 𝑎)2
𝜎2 =
12
Figure 8. Uniform noise distribution
Fig.9 shows a test pattern well suited for illustrating the noise models just discussed. This is a
suitable pattern to use because it is composed of simple, constant areas that span the gray scale
from black to near white in only three increments. This facilitates visual analysis of the
characteristics of the various noise components added to the image.
Figure 9. Test pattern used to illustrate the characteristics of the noise PDFs
Fig.10 shows the test pattern after addition of the six types of noise discussed thus far in this
section. Shown below each image is the histogram computed directly from that image. The
parameters of the noise were chosen in each case so that the histogram corresponding to the three
intensity levels in the test pattern would start to merge. This made the noise quite visible, without
obscuring the basic structure of the underlying image.
Figure 10.Images and histograms result from adding Gaussian, Rayleigh, and gamma noise to the image in Fig. 9.
Figure 10. (Continued) Images and histograms resulting from adding exponential, uniform, and salt-and-pepper
noise to the image in Fig. 9.
We see a close correspondence in comparing the histograms in Fig. 10 with the PDFs. The
histogram for the salt-and-pepper example has an extra peak at the white end of the intensity scale
because the noise components were pure black and white, and the lightest component of the test
pattern (the circle) is light gray. With the exception of slightly different overall intensity, it is
difficult to differentiate visually between the first five images in Fig. 10, even though their
histograms are significantly different. The salt-and-pepper appearance of the image corrupted by
impulse noise is the only one that is visually indicative of the type of noise causing the degradation.
3.7 Periodic noise
Periodic noise in images is typically caused by electrical and/or mechanical systems. This type of
noise can be identified in the frequency domain as impulses corresponding to sinusoidal
interference (see Figure 11). During image acquisition, mechanical jitter or vibration can result
in this type of noise appearing in the image. The vibration can be caused by motors or engines,
wind or seas, depending on the location of the image sensing device. Electrical interference in
the system may also result in additive sinusoidal noise corrupting the image during acquisition. If
this type of noise can be isolated, it can be removed with band-reject and notch filters.
Figure 11. Image corrupted by periodic noise. On the top are the original image and its spectrum; under it are the
image with additive sinusoidal noise, and its spectrum. Note the four impulses corresponding to the noise appearing
as white dots—two on the vertical axis and two on the horizontal axis.
4. RESTORATION TECHNIQUES
There are various restoration techniques as well as spatial domain filter for noise removal. In
spatial domain methods, the technique operates directly on the pixels of an image. The spatial
domain methods are used for removing additive noise only. Sometimes blur helps to increase
photo’s expressiveness but it decreases the quality of image unintentionally. In image restoration,
the improvement in the quality of the restored image over the recorded blurred one is measured by
the signal-to-noise ratio improvement [8]. Image restoration techniques are used to make the
corrupted image as similar as that of the original image. Figure.3 shows classification of restoration
techniques. Basically, restoration techniques are classified into blind restoration techniques and
non-blind restoration techniques [9]. Non-blind restoration techniques are further divided into
linear restoration methods and nonlinear restoration method [10].
Figure 12. Classification of restoration techniques
4.1 Noise Removal Using Spatial Filters
Spatial filters can be effectively used to remove various types of noise in digital images.
These spatial filters typically operate on small neighborhoods, 3 × 3 – 11 × 11, and some can be
implemented as convolution masks. We will use the degradation model defined in Fig. 2, with the
assumption that h(r,c) causes no degradation, so the only corruption to the image is caused by
additive noise, as follows:
𝑑(𝑟, 𝑐) = 𝐼(𝑟, 𝑐) + 𝑛(𝑟, 𝑐) (8)
Where
𝑑(𝑟, 𝑐) = degraded image.
𝐼(𝑟, 𝑐) = original image.
𝑛(𝑟, 𝑐) = additive noise image.
The two primary categories of spatial filters for noise removal are order filters and mean
filters. The order filters are implemented by arranging the neighborhood pixels in order
from smallest to largest gray-level value, and using this ordering to select the “correct” value,
while the mean filters determine, in one sense or another, an average value. The mean
filters work best with Gaussian or uniform noise, and the order filters work best with saltand-
pepper, negative exponential, or Rayleigh noise.
The mean filters have the disadvantage of blurring the image edges, or details; they are
essentially lowpass filters. Where much of the high frequency energy in noisy
images is from the noise itself, so it is reasonable that a lowpass filter can be used to mitigate noise
effects.
Order filters such as the median can be used to smooth images, thereby attenuating high frequency
energy. However, the order filters are nonlinear, so their results are sometimes unpredictable.
In general, there is a tradeoff between preservation of image detail and noise elimination. To help
understand this concept consider an extreme case where the entire image is replaced with the
average value of the image. In one sense, we have eliminated any noise present in the image, but
we have also lost all the information in the image. Practical mean and order filters also lose
information in their quest for noise elimination, and the trick is to minimize this information loss
while maximizing noise removal. Ideally, a filter that adapts to the underlying pixel values is
desired. A filter that changes its behavior based on the gray-level characteristics (statistics) of a
neighborhood is called an adaptive filter, and these filters are effective for use in many practical
applications.
4.2 Mean Filters
4.2.1 Arithmetic Mean Filters
The Arithmetic mean filter is also called Linear Filter. It averages all the values of pixels within
the window. The arithmetic filter is the simplest form of the mean filter. This filter helps in
smoothing the variations in an image and it blurs the image. It normally blurs the edges. This may
be a problem if sharp edges are required in the desired output. The arithmetic mean filter finds the
arithmetic average of the pixel values in the window, as follows:
1
Arithmetic mean = 𝑁2 ∑(𝑟,𝑐)∈𝑊 𝑑(𝑟, 𝑐) (9)
Where 𝑁 2 = the number of pixels in the N × N window, W. The arithmetic mean filter smoothes
out local variations within an image, so it is essentially a lowpass filter. It can be implemented
with a convolution mask where all the mask coefficients are 1/N2. This filter will tend to blur an
image, while mitigating the noise effects. Fig. 13 show the results of an arithmetic mean applied
to an image with Gaussian noise. It can be seen that the larger the mask size, the more pronounced
the blurring effect. This type of filter works best with Gaussian, gamma, and uniform noise.
(a) Original image (b) Image with added Gaussian noise
, variance = 800, mean = 0
(c) Result of arithmetic mean filter on image (d) Result of arithmetic mean filter on image
with Gaussian noise, mask size = 5 with Gaussian noise, mask size = 3
Figure 13. Arithmetic Mean Filter. As the mask size increases more noise mitigation occurs, but at the price of
increased blurring. (a) Original image (b) Image with added Gaussian noise, variance = 800, mean = 0, (c) Result of
arithmetic mean filter on image image with Gaussian noise, mask size = 3, (d) Result of arithmetic mean filter on with
Gaussian noise, mask size = 5.
4.2.2 Geometric mean filter
The geometric mean filter works best with Gaussian noise, and retains detail information
better than an arithmetic mean filter. It is defined as the product of the pixel values within
the window, raised to the 1/𝑁 2 power:
1
Geometric mean = ∏[𝑑(𝑟, 𝑐)]𝑁2 (10)
(𝑟, 𝑐) ∈ 𝑊
(a) (b)
(c) (d)
Figure 14. Geometric mean filter. (a) Image with Gaussian noise, variance = 300, mean = 0, (b) Result of geometric
mean filter, mask size = 3, on image with Gaussian noise, (c) Image with pepper noise, probability = 0.04, (d) Result
of geometric mean filter, mask size = 3, on image with pepper noise. Note this filter is counterproductive with pepper
noise.
As shown in Figure 14.d, this filter is ineffective in the presence of pepper noise—with zero (or
very low) values present in the window, the equation returns a zero (or very small) number.
4.2.3 Harmonic mean filter
The harmonic mean filter also fails with pepper noise, but works well for salt noise. It is defined
as follows:
𝑁2
Harmonic mean = 1 (11)
∑(𝑟,𝑐)∈𝑊
𝑑(𝑟,𝑐)
This filter also works with Gaussian noise, retaining detail information better than the arithmetic
mean filter. In Figure 15 are the results from applying the harmonic mean filter to an image with
Gaussian noise (Figure 15 a and b), and to an image corrupted with salt noise (15 c and d).
(a) Image with Gaussian noise, (b) Result of harmonic mean filter,
variance = 300, mean = 0 mask size = 3, on image with Gaussian noise
(c) Image with salt noise, probability = .04 (d) Result of harmonic mean filter, mask size = 3, on
image with salt noise
Figure 15. Harmonic mean filter.
4.2.4 Contra harmonic mean filter
The contra-harmonic mean filter works well for images containing salt OR pepper type noise,
depending on the filter order, R:
∑(𝑟,𝑐)∈𝑊 𝑑(𝑟,𝑐)𝑅+1
Contra-harmonic mean = ∑(𝑟,𝑐)∈𝑊 𝑑(𝑟,𝑐)𝑅
(12)
Where W is the N × N window under consideration. For negative values of R, it eliminates salt-
type noise, while for positive values of R; it eliminates pepper-type noise. If choose wrong values
then the filter can behave as a dragon. The Fig. 16 (A) and Fig. 16 (B) shows the negative impact
of this filter. The filter removes pepper noise and for its negative value, it destroys salt noise. If
choose a wrong value then filter gives the worst results.
Figure 16. (A) Pepper noise filtered by R = -1.5 (B) Salt noise filtered by R= +1.
Table 1. Classification of Mean Filters
4.3 Order Statistic Filter
In these type of filters, the values of the pixels of an image are ranked in order. Only those pixel
values are ranked whose area or region is enclosed in the filter.
4.3.1 Median Filter
This filter first calculates the median of the intensity levels of the pixels suppose the pixel values
are from 1-9, so the median will be 5, that is, the midpoint of the pixel values. Then after calculating
the median, it replaces the corrupted pixel value with the new value (median value). This filter is
more robust because single pixel in the neighborhood never affects median value. It is much better
at preserving sharp edges than another filter. However, it is more expensive and complex to
execute. It is taking much time to calculate a median value for each window.
Note that with this technique the outer [(N + 1)/2] –1 rows and columns are not replaced. In
practice, this is usually not a problem due to the fact that the images are much larger than the
masks, and these “wasted” rows and columns are often filled with zeros (or cropped off the
image). For example, with a 3 × 3 mask, we lose one outer row and column, a 5 × 5 loses two
rows and columns—this is not usually significant for a typical 640 × 480 or larger image. Results
from using the median filter for salt-and-pepper (impulse) noise are shown in Figure 17.
(a) (b) (c)
Figure 17. Median filter. (a) Image with added salt-and-pepper noise, the probability for salt = probability for
pepper = 0.08, (b) after median filtering with a 3 × 3 window, all the noise is not removed, (c) after median filtering
with a 5 × 5 window, all the noise is removed, but the image is blurry acquiring the “painted” effect.
4.3.2 Max and Min Filter
These filters are used to find the brightest and darkest points in the image. The Max filter
replaces the pixel value with the brightest point and the Min filter replaces the pixel with the
darkest point. Max filter helps to find light colored pixels in an image while Min filter helps to
find dark points in the image.
The maximum and minimum filters are two order filters that can be used for elimination of salt or
pepper (impulse) noise. The maximum filter selects the largest value within an ordered window of
pixel values, so is effective at removing pepper-type (low values) noise. The minimum filter selects
the smallest value and works when the noise is primarily of the salt-type (high values). In Figure
18a and b, the application of a minimum filter to an image contaminated with salt-type noise is
shown, and in Figure 18c and d a maximum filter is applied to an image corrupted with pepper-
type noise is shown.
(a) (b)
(c) (d)
Figure 18. Minimum and maximum filters. (a) Image with added “salt” noise, probability of salt = 0.04, (b)
result of minimum filtering image (a); mask size = 3 × 3, (c) Image with “pepper” noise, probability of
pepper = 0.04, (d) result of maximum filtering image (c), mask size = 3 × 3
For certain types of pepper noise selecting the second highest value works better than
selecting the maximum value. This type of ordered selection is very sensitive to the type
of images and their use—it is application specific.
The final two order filters are the midpoint and alpha-trimmed mean filters. They are
actually both order and mean filters since they rely on ordering the pixel values, but are
then calculated by an averaging process.
4.3.3 Midpoint Filter
The Midpoint filter computes the midpoint between the maximum and minimum values of the
image. The midpoint filter is widely used for noises like Gaussian noise and uniform noise. But it
works well only for randomly distributed noise. The midpoint filter is the average of the maximum
and minimum within the window, as follows:
Ordered set → 𝐼1 ≤ 𝐼2 ≤ 𝐼3 ≤ ⋯ ≤ 𝐼𝑁2
𝐼1 +𝐼𝑁2
Midpoint = (13)
2
(a) (b)
(c) (d)
Figure 19. Midpoint filter. (a) Image with Gaussian noise, variance = 300, mean = 0, (b) result of midpoint
filter, mask size = 3, (c) Image with uniform noise, variance = 300, mean = 0, (d) result of midpoint filter,
mask size = 3.
4.3.4 Alpha-trimmed Mean Filter
The alpha-trimmed mean is the average of the pixel values within the window, but with some of
the endpoint ranked values excluded. It is defined as follows:
Ordered set → 𝐼1 ≤ 𝐼2 ≤ 𝐼3 ≤ ⋯ ≤ 𝐼𝑁2
1 2
Alpha-trimmed mean = 𝑁2 −2𝑇 ∑𝑁 −𝑇
𝑖=𝑇+1 𝐼𝑖 (14)
Where T is the number of pixel values excluded at each end of the ordered set, and can range from
0 to(𝑁 2 − 1)/2.
The alpha-trimmed mean filter ranges from a mean to median filter, depending on the value
selected for the T parameter. For example, if T = 0, the equation reduces to finding the average
gray-level value in the window, which is an arithmetic mean filter. If T=(𝑁 2 − 1)/2, the equation
becomes a median filter. This filter is useful for images containing multiple types of noise, for
example Gaussian and salt-and-pepper noise. In Figure 20 are the results of applying this filter to
an image with both Gaussian and salt-and-pepper noise.
(a) (b)
(c) (d)
Figure 20. Alpha-trimmed mean filter. This filter can vary between a mean filter and a median filter, so can be useful
with multiple types of noise. (a) Image with added noise: Gaussian noise, variance = 200, mean = 0, and saltand-pepper
noise with probability of each = 0.03, (b) result of alpha-trimmed mean filter, mask size = 3, T = 1, (c) result of alpha-
trimmed mean filter, mask size = 3, T = 2, (d) result of alpha-trimmed mean filter, mask size = 3, T = 4. As the T
parameter increases the filter becomes more like a median filter, so is more effective at removing salt-and-pepper
noise.
5 CONCLUSION
Restoration of images is a difficult problem to resolve. The main objective of this work is to carry
out a comparative study. However, every technique has its own way of dealing with the problem
and have their own pros and cons. It is concluded from the above explanations that usage of the
techniques is governed by the understanding, requirement and the standard of the output needed.
Before the application of the any filtering technique, it is supposed to have the better understanding
that is it requires proper analysis.
Enhancement and restoration is necessary task in the digital image processing. There are various
noise models available that can distort the images up to any extent. In order to restore
such noisy images there are many image restoration and filtering techniques available that can
recover the original image from the degraded image. Various sources of noises and applications
of image restoration are also discussed. Apart from noise a detailed comparative study of image
restoration and filtering techniques is also given that helps the new researchers to understand the
various aspects of the image restoration that will create interest and lead them to work in specified
hybrid technique.
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