1.1. image acquisition. At each point noise is

1.1.                    
 Types of noises

 

a)     
Additive
noise: Unwanted signal in images are called
as an additive noise. In this noise is added in original image. It is defined
as:

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

Where g(x,y) is a
noisy image, f(x,y) is an original given  image and n(x,y) is additive noise of an
image. Eg. Gaussian noise.

 

b)    
Multiplicative
noise: Multiplicative noise is an unwanted
noise which multiplies original signals while capturing, transmission or any
other processing. It is defined as:

g(x,y)=f(x,y)×n(x,y)

Where
g(x,y) is a noisy image, f(x,y) is an original image and n(x,y) is a function
which is multiplicative degraded. Eg. Speckle noise.

 

Gaussian
Noise : The Gaussian noise is an additive noise as
a standard model. In Gaussian noise probability density function (PDE) is equal
to normal distribution. This noise occurs at a time of  image acquisition. At each point noise is  independent of intensity value of pixel. It
can be calculated as

                                   

Where z is grey level, µ is mean value
and ? is standard deviation.

 

Salt
and pepper noise: Impulse noise is also known
as a salt and pepper noise. In grey scale the bright pixels are contained in
the dark regions and the dark pixels in the bright region. This noise is mostly
caused by bit errors of transmission or converter errors. 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.          

The Probability Density Function (PDE)
is given by :

                                       

If b>a intensity b will appears as
light pixel in image, conversely intensity a will appears as dark pixel in
image. If either  or  is zero, it is unipolar.

 

 

Film
grain: The grain of a photographic film is
similar to statistical distribution. It is signal dependent noise. If film
grains are distributed uniformly the intensity of dark grains in an area is totally
random with binomial distribution and if every grain has same independent
probability to develop to a dark silver grain by photon absorption. We tends to
say film grain is a non-oriented noise source.

 

Shot
noise: Shot noise is a classification of the
electronic noise which is modelled by process of Poisson. It usually originates
by electronic charge of discrete nature. It has root mean square which is
proportional to square root of density of image. The noises at distinct pixels
are not dependent upon one another. Additional shot noise is also present in
image due to dark leakage of current in the sensor of the image which is called
dark shot noise.

 

Quantization
noise: The noise caused due to quantizing the
pixels of a detected image to different discrete levels is called as
quantization noise, that also around uniform dispersion, and it may be signal
dependence, however it will be signal free if other available noise sources are
sufficiently enormous to cause dithering, or if the dithering is expressly
connected. This blunder is either because of adjusting or truncation. The error
signal is once in a while considered as an additional random signal is referred
as quantization noise due to its stochastic conduct

 

Anisotropic
noise: Some of the noise sources appear with a
critical introduction in images. For instance, image sensors are at times
subject to push noise or section noise. Anisotropic noise surfaces are
intriguing for some perception and graphics applications. The spot tests can be
utilized as contribution for surface age, e.g., Line Integral Convolution
(LIC), yet can likewise be utilized specifically for representation without
anyone else’s input. They are particularly reasonable for the perception of tensor
fields that can be utilized to characterize a metric for the anisotropic
thickness field. We display a novel strategy for producing stochastic examples
to make anisotropic noise surfaces comprising of non-covering circles, whose
size and thickness coordinate a given metric. Our technique bolsters a
programmed pressing of the circular examples bringing about surfaces like those
created by anisotropic response dispersion.

 

Speckle
noise: The multiplicative noise is called as
an speckle noise. This noise is multiplied to the original image. It is present
in the ultrasound image. This noise occurs in all coherent systems like
acoustics or laser imagery. This noise decreases the contrast of an image and
it also observes beneficial details of an ultrasound image. This noise is an
granular noise which inherently exist and also degrade quality of SAR , active
radar, coherence tomography and medical ultrasound images.

g(x,y)=f(x,y)×h(x,y)

Where g(x,y) is a noisy image, f(x,y) is
an original image and h(x,y) is multiplicative degrade. Its Raleigh Distribution
is given by :

                                   

 

                                   

                                   

 

2.    
Image
Denoising

 

Image denoising is used for the analysation of a
image. It is used for recovery of the digital image which is impure by the
noise. A image restoration or denoising method is used to decrease the noise
and also to preserve the edges of image, sharpen the image details or
significant features. It is referred to as a recovery from digital image which
is been degraded from the noise. The methods in this are orientations towards
the degradation. Here we preserve the details of an image.

                                                                                         

Restoration filter

 

Degraded function H

 

                                                                  g(x,y)

f(x,y)                                                                                                                       f'(x,y)                                                                                     

 

      Noise  n(x,y)             

                                Degradation                                                    Restoration                                         

Here in this diagram given above f(x,y)
is referred to as an original image. n(x,y) is referred to as an noise added to
make an degraded image. The g(x,y) is referred to as an degraded image. Here restoration
filter is applied to form a approximate image f(x,y) which is represented as
f'(x,y).

 

 

 

3.    
Denoising
Techniques

 

Anisotropic
diffusion filter: In image processing
the most explode topic is image denoising. There are many methods purposed for
denoising such as wiener filter, wavelet thresholding, PDE(Partial Differential
equation), total variation minimization method, non-local methods and bilateral
filtering.

Noise
reduction using1.1.                    
 Types of noises

 

a)     
Additive
noise: Unwanted signal in images are called
as an additive noise. In this noise is added in original image. It is defined
as:

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

Where g(x,y) is a
noisy image, f(x,y) is an original given  image and n(x,y) is additive noise of an
image. Eg. Gaussian noise.

 

b)    
Multiplicative
noise: Multiplicative noise is an unwanted
noise which multiplies original signals while capturing, transmission or any
other processing. It is defined as:

g(x,y)=f(x,y)×n(x,y)

Where
g(x,y) is a noisy image, f(x,y) is an original image and n(x,y) is a function
which is multiplicative degraded. Eg. Speckle noise.

 

Gaussian
Noise : The Gaussian noise is an additive noise as
a standard model. In Gaussian noise probability density function (PDE) is equal
to normal distribution. This noise occurs at a time of  image acquisition. At each point noise is  independent of intensity value of pixel. It
can be calculated as

                                   

Where z is grey level, µ is mean value
and ? is standard deviation.

 

Salt
and pepper noise: Impulse noise is also known
as a salt and pepper noise. In grey scale the bright pixels are contained in
the dark regions and the dark pixels in the bright region. This noise is mostly
caused by bit errors of transmission or converter errors. 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.          

The Probability Density Function (PDE)
is given by :

                                       

If b>a intensity b will appears as
light pixel in image, conversely intensity a will appears as dark pixel in
image. If either  or  is zero, it is unipolar.

 

 

Film
grain: The grain of a photographic film is
similar to statistical distribution. It is signal dependent noise. If film
grains are distributed uniformly the intensity of dark grains in an area is totally
random with binomial distribution and if every grain has same independent
probability to develop to a dark silver grain by photon absorption. We tends to
say film grain is a non-oriented noise source.

 

Shot
noise: Shot noise is a classification of the
electronic noise which is modelled by process of Poisson. It usually originates
by electronic charge of discrete nature. It has root mean square which is
proportional to square root of density of image. The noises at distinct pixels
are not dependent upon one another. Additional shot noise is also present in
image due to dark leakage of current in the sensor of the image which is called
dark shot noise.

 

Quantization
noise: The noise caused due to quantizing the
pixels of a detected image to different discrete levels is called as
quantization noise, that also around uniform dispersion, and it may be signal
dependence, however it will be signal free if other available noise sources are
sufficiently enormous to cause dithering, or if the dithering is expressly
connected. This blunder is either because of adjusting or truncation. The error
signal is once in a while considered as an additional random signal is referred
as quantization noise due to its stochastic conduct

 

Anisotropic
noise: Some of the noise sources appear with a
critical introduction in images. For instance, image sensors are at times
subject to push noise or section noise. Anisotropic noise surfaces are
intriguing for some perception and graphics applications. The spot tests can be
utilized as contribution for surface age, e.g., Line Integral Convolution
(LIC), yet can likewise be utilized specifically for representation without
anyone else’s input. They are particularly reasonable for the perception of tensor
fields that can be utilized to characterize a metric for the anisotropic
thickness field. We display a novel strategy for producing stochastic examples
to make anisotropic noise surfaces comprising of non-covering circles, whose
size and thickness coordinate a given metric. Our technique bolsters a
programmed pressing of the circular examples bringing about surfaces like those
created by anisotropic response dispersion.

 

Speckle
noise: The multiplicative noise is called as
an speckle noise. This noise is multiplied to the original image. It is present
in the ultrasound image. This noise occurs in all coherent systems like
acoustics or laser imagery. This noise decreases the contrast of an image and
it also observes beneficial details of an ultrasound image. This noise is an
granular noise which inherently exist and also degrade quality of SAR , active
radar, coherence tomography and medical ultrasound images.

g(x,y)=f(x,y)×h(x,y)

Where g(x,y) is a noisy image, f(x,y) is
an original image and h(x,y) is multiplicative degrade. Its Raleigh Distribution
is given by :

                                   

 

                                   

                                   

 

2.    
Image
Denoising

 

Image denoising is used for the analysation of a
image. It is used for recovery of the digital image which is impure by the
noise. A image restoration or denoising method is used to decrease the noise
and also to preserve the edges of image, sharpen the image details or
significant features. It is referred to as a recovery from digital image which
is been degraded from the noise. The methods in this are orientations towards
the degradation. Here we preserve the details of an image.

                                                                                         

Restoration filter

 

Degraded function H

 

                                                                  g(x,y)

f(x,y)                                                                                                                       f'(x,y)                                                                                     

 

      Noise  n(x,y)             

                                Degradation                                                    Restoration                                         

Here in this diagram given above f(x,y)
is referred to as an original image. n(x,y) is referred to as an noise added to
make an degraded image. The g(x,y) is referred to as an degraded image. Here restoration
filter is applied to form a approximate image f(x,y) which is represented as
f'(x,y).

 

 

 

3.    
Denoising
Techniques

 

Anisotropic
diffusion filter: In image processing
the most explode topic is image denoising. There are many methods purposed for
denoising such as wiener filter, wavelet thresholding, PDE(Partial Differential
equation), total variation minimization method, non-local methods and bilateral
filtering.

Noise
reduction using PDE: a paradigm used for noise reduction is by using non linear
diffusions to remove the noise from images. The Gaussian filter to denoise the
image is achieved by convolving the Gaussian kernel K? with noisy image u0. PDE: a paradigm used for noise reduction is by using non linear
diffusions to remove the noise from images. The Gaussian filter to denoise the
image is achieved by convolving the Gaussian kernel K? with noisy image u0.