Chapter – 1 Introduction

1

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 filed, Medical field, SAR Images etc. to

analyze 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 analyzed some of the denoising

techniques on the MRI images.

Topics

explored in this chapter are as follows:

·

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)

Additive

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

degraded. Speckle noise is an example of the additive noise.

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.

The Probability Density Function

(PDE) is given by :

If

b>a intensity then b will appear as light pixel in a image, or intensity a

will appears as a dark pixel in image. If either

or

is zero, then it is unipolar.

Film grain:

The grain of photographic film is same as statistical distribution. It is a

signal dependent noise. The number of dark grains in an area is random with

binomial distribution if film grains are distributed uniformly and if every grain

has same independent probability to develop to a dark silver grain by photon

absorption. We usually regard film grain as a non-oriented noise source.

Shot noise:

shot noise is a classification of the electronic noise which is modeled 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 by quantizing the pixels of a detected image to various

discrete levels is has known as quantization noise, around uniform dispersion,

and it can 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 called noisy image, f(x,y) is the original image and h(x,y) is a multiplicative

degrade. Its Raleigh Distribution is given by equation as:

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.

With

standard deviation ? , is equivalent to

the solution of the diffusion equation in two dimensions.

Where

is

the 2-D image. In general form this can be written as:

,

where I0 is the original image. In general form this can be written

as

,

Where c(x,y,t) is the diffusion

conductance or diffusivity of the equation,

Wiener

filter: wiener filter is a filter in a signal

processing. This filter is used to create approximate of a target arbitrary

process by linear time-invariant (LTI) filtering of a observed process of an

noise image, thinking of known noise spectra, stationary signal and also

additive noise. This filter also minimizes mean square error in desired process

and in estimated random processes.

Total

Variation Minimizing: this method was used to

minimize a total variation norm for removing noise in an image. A new

constrained minimization algo was derived like time dependent nonlinear where

noise statistics were used to determine the constraints. It is used to reduce

incompatible local oscillations from images. It is a quantity used to measure

the oscillations form functions.

Non-local

Means: Non-local means

is an algorithm in image preparing for image denoising. Not at all like local

mean filter, which take mean estimation of a gathering of pixels surrounding an

objective pixel for smoothning of the image, non-local referred to filtering

takes a mean of pixels in the image, weighted by how comparative these pixels

are to the objective pixel. This outcomes in substantially has high post

filtering display, and lesser loss of detail from the image contrasted and from

local mean algorithm.

Chapter – 2 Literature

2

The Literature Survey passes on clarity and focus to

the research issue, upgrades the technique to be proposed and extends the basic

data about issue close by. It gives a structure to setting up the criticalness

of the examination. Inside the setting of a quantitative research approach, the

literature survey has a critical measure of time and effort. Distinctive

critical journals, research papers and other related papers are used for

increasing start to finish learning. These papers are referenced underneath

with a short introduction :

Perona and Malik

(1990)1

developed a iterative approach of edge detection and multiscale

smoothing which is known as Anisotropic diffusion filter. This filter relies

upon second order partial differential equation (PDE) in anisotropic medium. It

does intra-region smoothing instead of between zone smoothing Advantage of this

method is that it upgrades picture quality by protecting article limits, edge

sharpening. It beats the drawbacks of spatial filters and its obstruction is

that it produces stair case affect.

Tomasi and

Manduchi (1998)2 shown Bilateral filter, This filter is the

mix of range filtering and domain filtering. It is non-iterative and

fundamental filter. The advantage of bilateral filter is that it jam edges and

gives best results over center filter yet it prompts all the all the more

smoothing or blurring of a photo.

J.Wang et al

(2006)3 proposed fast non-local means algorithm.

As the non-local means denoising algorithm proposed by Buades et al., is

computationally over the top thusly, another algorithm that abatements the cost

of computation for calculating the similarity of neighboring window is

proposed. Regardless introducing a deduced measure about the resemblance of

neighborhood windows, by then a profitable Summed square Image (SSI) plan and

Fast Fourier Transform (FFT) to revive all the calculation of this measure.

This algorithm is around fifty times faster than the original non-local

Algorithm both theoretically and experimentally, yet conveys equivalent results

of the extent which mean-squared error (MSE) and perceptual image quality.

G.C. Gavrincea

(2007)4 shown wavelet

based denoising In this paper for image denoising four decomposition using haar

wavelet provoking arrangement of coefficients called wavelet coefficients and to

get rid of noisy bit of banner, detail coefficients from each level are

thresholded and this is a substantially more compelling strategy for managing

noisy banners as opposed to filtering.

A. Dauwe et al.

(2008)5

proposed several progressions to the original non-local means algorithm

introduced by Buades et al. As a result of the colossal measure of weight

calculations, the original algorithm has a high computational cost. A

difference in image quality towards the original algorithm is to dismiss the responsibilities

from one of a kind windows. This shocking effect of dissimilar windows can be

wiped out by setting their contrasting weights with zero. This stimulated

approach is additionally streamlined by misusing the symmetry in the weights,

which generally halves the calculation time. Appeared differently in relation

to the original algorithm, this method produces images with extended psnr and

better visual execution in less calculation time. The proposed upgrades can

also be associated in other image Processing assignments which use the

possibility of repetitive structures, for instance, intra-frame Super

resolution or detection of digital image impersonation.

V. Kamati er al

(2009)6 shown changes to non-local means (NLM)

image denoising method to reduce the computational multifaceted nature. The

proposed strategy replaces the window similarity by a changed multi-resolution

based approach with numerous less relationships rather than all pixels

examination. This approach also uses filtering out non-similar neighborhood

pixels in light of settled estimated window diminish mean regards. The proposed

approach is around 80 times speedier than interesting Baudes NLM algorithm with

close subjective and to target quality estimations.

k Bartusek et al

(2011)7

presented wavelet develop denoising frameworks focusing as for the

wavelet thresholding systems and the point of confinement estimation.

soft, Hard, semi-soft and non-negative garrote thresholding

techniques are delineated and associated with test images with two various

point of confinement estimators; one uses the general edge and the second is

gotten from the Bayesian risk minimization. The results are stood out

concurring from three parameters: SNR, control contrast and power slant.

D. Peter and

Ramya et al. (2012)8 proposed a novel adaptive non-local means for

image denoising. In this adaptive non local means filtering, immediately the

image is smoothed using Gaussian filter and after that the noisy image is to be

segmented in light of power level using k means amass which is especially

effective in denoising significantly noisy level images. In light of test comes

to fruition adaptive non-local means filter is had all the earmarks of being

astoundingly effective in visual quality and gives extraordinary result as

stand out from regular non-local means algorithm.

B. vijilin and

V.K. Govindan (2013)9 displayed perfect edge decision for wavelet

change in light of visual quality. With perfect utmost regard, most outrageous

dreary information is ousted from input image realizing better weight and

besides high visual quality revamped image.

Chapter – 3 Problem Defination

3

The quality of a image is affected by noise. Noise

plays an important role in the degradation of a image. The noise which is

present in a image is removed or degraded by the image denoising process. Noise

in a image is mostly occurred due to the data transmission media, sources of

radiation which are discreate, capturing of the instruments and quantization of

a image. All these factors are responsible for the degradation of a image. The noise

in a image can be removed by various denoising techniques. In this a image

noise is investigated for terms of its causes and how an image noise can be

removed better or which denoising algo gives better results in removing noise

from a image. A better denoising algorithm will provide a better deblurring of

an image. In a MRI various denoising algorithms provide different values of the

noise removal values.

Chapter – 4 Objective

4

The main objective of this MRI image are as follows:

1. In

this various algorithms are used to give different values of a single image.

2. To

apply a denoising algorithm on an image, so as to improve the quality of a

image

3. The

information of a image should not be lost.

4. To

calculate the values of various algorithms like wiener, total variation, bilateral,NL-means,

wavelet denoising and anisotropic diffusion which will show the change in the image.

5. To

compare the values of each denoising algorithm used on a MRI image.

Chapter – 5 Proposed work

5

The method of removing an nose from the image

is a challenging task. Various approaches are there for the removal of a noise

in a image, and these approaches provides a different results in the denoising

of an image. The main focus of these entire denoising algorithms is to remove

the noise in an image. In this various denoising algorithms are used on a

single type of image. The various algorithms used in this are as follows:

1. Wiener

algorithm

2. Total

Variation algorithm

3. Bilateral

algorithm

4. NL-means

algorithm

5. SureShrink

algorithm

6. VisuShrink

algorithm

7. BayesShrink

algorithm

8. Anisotropic

diffusion

All these various

denoising algorithms provides there different results. And the result of all

these algorithms is compared with each other. At the end the algorithm which

removes the noise in a image in large quantity is chosen as a best algorithm. All

these different algorithms will have different values for each different image.

Here we will perform these algorithms of different MRI images.