## Image are as follows: · Introduction to Digital Image

Image
denoising plays a great significance role in the digital image processing. We
use denoising process to achieve final noise free estimates by removing the
unnecessary noise from the image. Various fields in which Image denoising plays
an important role are as Astronomy field, Medical field, SAR Images etc. to analyse
and extracting various features of images. There are various approaches to
perform denoising and each approach have their own merits and demerits. In the
following research work, we have discussed and analysed some of the denoising
techniques on the MRI images.

Topics
explored in this chapter are as follows:

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·
Introduction to Digital Image and Noise

o
Noise

o
Types of noises

·
Image Denoising

·
Denoising Techniques

1.
Introduction
to Digital Images and Noise

An
image is a Two-Dimensional Function f(x,y) where x and y are spatial
coordinates, and the amplitude of f at any pair of coordinate (x,y) is called
grey level or intensity value of image at that point. When x,y and intensity
value of f are all discrete finite quantities , we  call that image as digital image .

1.1.
Noise

Noise is something which distorts the digital image. Noise
can cause changes in brightness or color in an image. There are many reasons by
which a noise can occur in an image such as variation in brightness of
surrounding or environmental conditions. It
is unwanted information that lower the quality of an image. Noise adds
irrelevant information and also depicts undesired information in an image. Digital
images are liable to suffer from various types of  noises. Different sources of noises are
below  :

a)      Gaussian
images occurs in digital images by image acquisition i.e noise is produced by
poor illuminations and by high temperature .

b)      Inference
in transmission channel leads to noise in images .

c)      Atmospheric
disturbance causes noise in images while transmission through wireless network.

1.

1.1.

1.2.
Types of noises

a)
noise: Unwanted
signal are called as an additive noises. Here the noise is added to original
image. The additive noise of an image is defined as:

g(x,y)=f(x,y)+n(x,y)

Where g(x,y) is referred to as an noisy image, f(x,y)
is referred to as an original given image and n(x,y) is referred to as additive
noise of an image. Gaussian noise is an example of the additive noise

Multiplicative noise:
Multiplicative noise is an unwanted noise which multiplies original signals
while transmission, capturing or any other processing. The multiplicative noise
of an image is defined as:

g(x,y)=f(x,y)×n(x,y)

Where
g(x,y) is referred to as an noisy image, f(x,y) is referred to as an original
given image and n(x,y) is referred to as function which is multiplicative

Gaussian Noise : The
Gaussian noise has additive as a standard model. In this the probability
density function is equal to normal distribution or it is called as Gaussian
distribution. This noise is found in the image acquisition. At each point the
intensity of pixel value is independent by the noise. It can be calculated as

Where
z is referred as grey level, µ is called mean value and ? is the standard
deviation.

Salt and pepper noise:
Impulse noise is also sometimes called as a salt and pepper noise. In a gray
scale the bright pixels are contained in the dark regions and the black and
white pixels in the bright region. This noise is mostly caused by a converter
errors or bit errors of transmission. This type of noise is eliminated by dark
or bright pixels in a large part. In this only pixel parts are corrupted but
rest is noise free.

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