Synopsis

The main objective of our project is de-noising of MR brain images.

The MR images have poor quality and low signal to noise ratio, major

concern of our project is to improvise and make it easier for analysis. The

project deals with implementation, testing and evaluation of de-noising

algorithm for MR brain image.

The project focuses on denoising of the MR image using thresholding

and filters. Here an attempt is also done to compare performance of three

filters using matlab. This comparison is done by statistical analysis

considering entropy, mean and contrast value and most effective filter is

found.

CHAPTER: 1

INTRODUCTION

1. INTRODUCTION

Basic idea behind denoising algorithm is to help the medical analysts with

easy detection of unwanted growth in brain like tumours. Our project also

involves performance evaluation of three different filters. Based on the

results of this evaluation we identify the best of the three.

The ultimate challenge of the project is to develop matlab code to

combine imaging technology with a workable diagnostic system that is

capable of detecting tumours in its early stages. The presence of noise in a

digital image increases the complexity in image analysis. An unwanted film

artifact which obstructs the view of the image as well as the noise present is

eliminated by pre processing techniques.

1.1 BRAIN TUMOUR

In the evolution of healthcare services, there is an increasing need for

greater effective use of imaging data in medical diagnosis and individual risk

assessment, treatment selection, and disease prevention. Brain tumour is the

second leading cause of cancer death. The incidence of brain tumour is

increasing rapidly, particularly in older population as compared to younger

ones[1]. A brain tumour is an abnormal growth of cells within the brain or

inside the skull, which can be cancerous or non-cancerous. Tumours can

directly destroy all the healthy brain cells. It can also indirectly damage the

healthy cells by crowding other parts and causing inflammation, brain

swelling and pressure in the skull. Brain tumour cells differ from normal

cells in a number of ways, which helps in its detection.

1.2 Magnetic Resonance Imaging (MRI):

Magnetic resonance is a complex interaction between hydrogen

protons in biologic tissues, a static magnetic field i.e the magnet, and energy

in the form of radiofrequency (RF) waves of a specific frequency introduced

by coils placed next to the body part of interest. Field strength of the magnet

is directly related to signal-to-noise ratio. While 1.5 Telsa magnets have

become the standard high-field MRI units, 3T–8T magnets are now available

and have distinct advantages in the brain and musculoskeletal systems.

Spatial localization is achieved by magnetic gradients surrounding the main

magnet, which impart slight changes in magnetic field throughout the

imaging volume. The energy state of the hydrogen protons is transiently

excited by Rf, which is administered at a frequency specific for the field

strength of the magnet. The subsequent return to equilibrium energy state i.e.

relaxation of the protons results in a release of Rf energy, which is detected

by the coils that delivered the Rf pulses. The echo is transformed by Fourier

analysis into the information used to form an MR image. The MR image thus

consists of a map of the distribution of hydrogen protons, with signal

intensity imparted by both densities of hydrogen protons as well as

differences in the relaxation times of hydrogen protons on different

molecules.

1.3 NEED FOR MRI

MRI is the acronym of MAGENTIC RESONANT IMAGING.MRI

provides non-invasive, high quality images of neuro-anatomy and disease

processes. Through its ability to detect contrast in the density of soft tissues,

MRI is well suited to monitor and evaluate cerebral tumours as they develop

and respond or, as the case may be, fail to respond to therapy. There are

many sequences that can be used on MRI and the different sequences often

provide different contrast between tissues so the most appropriate sequence

should be chosen according to disease and what the clinicians want to detect.

Early detections and corrections based on accurate diagnosis are important

steps to improve the disease outcome.

CHAPTER 2

BLOCK DIAGRAM AND NEED

FOR DENOISING

2.1NOISE IN MR IMAGES

Noise is like interferences which present as a irregular granular

pattern. This random variation in signal intensity degrades image

information. The main source of noise in the image is the patient's body i.e

RF emission due to thermal motion. The whole measurement chain of the

MR scanner such as coils and electronics equipments also contributes to the

noise. This noise corrupts the signal coming from the transverse

magnetization variations of the intentionally excited spins on the selected

slice plane. The signal to noise ratio (SNR) is equal to the ratio of the

average signal intensity over the standard deviation.

Artifacts often corrupt MRI images. These artifacts have many

causes and consequences on image appearance. Salt and pepper noise is most

common type of noise present in MR images. This type of noise can be

caused by dead pixels, analog to digital converters errors, bit errors in

transmission, etc. Salt and pepper noise is a form of noise typically seen on

images. It represents itself as randomly occurring white and black pixels.

Salt and pepper noise creeps into images in situations where quick transients,

such as faulty switching, take place. In salt and pepper noise such as sparse

light and dark disturbances, pixels in the image are very different in color or

intensity from their surrounding pixels; the defining characteristic is that the

value of a noisy pixel bears no relation to the color of surrounding pixels.

Generally this type of noise will only affect a small number of image pixels.

When viewed, the image contains dark and white dots, hence the term salt

and pepper noise.

The original image is as shown below

Fig 2.1:Original image

2.1 NEED FOR DE-NOISING

Noise in images hinders the correct analysis of the images by affecting

the quality of the image. Noise reduction is the process of removing noise

from a signal. When a device captures an image, the device sometimes adds

extraneous noise to the image. This noise must be removed from the image

for other image processing operations to return valuable results . Some noise

can simply be removed by smoothing an image or masking it within the

frequency domain, but most noise requires more involved filtering, such as

windowing or adaptive filters .Noise appears in an image due to a number of

reasons. The formation of an MRI mage is done in steps. In each step, there

may be a fluctuation from the normal working conditions. This fluctuation

adds a random value to the captured signals. When these signals are Fourier

transformed and the image is formed, the fluctuation contributes to the noise.

2.2 BLOCK DIAGRAM

The block diagram represents the different steps involved in our project.

Initially image is acquired from MATLAB. This acquired image is pre

processed in order to remove film artifacts. The unwanted film artifacts are

removed in order to improve the image appearance. This is followed by the

enhancement of the image where we apply non linear filters on the image.

The output obtained by applying each of these filters is studied separately.

Thus the performance evaluation of these filters is done by applying

statistical analysis to the images obtained after filtering. The best

performance filter can hence be concluded from this stage and finally a de-

noised MR brain image is obtained as output.

MR brain image

IMAGE ACQUISITION

Pre processing

Denoised MR Brain Images

Median Filter Adaptive Filter

Performance evaluation

Of the filters

Image Acquisition

Weighted Median

Filter

Removal of film artifacts

CHAPTER 3

THEORETICAL BACKGROUND

3.1 Image Acquisition

Image of a patient obtained by MRI scan is displayed as an array of

pixels and stored in Matlab7.1.In image processing, it’s necessary to

smoothen an image while preserving its edge. The assumption is that noise is

captured by the high frequency coefficients, thus by filtering these

coefficients, the unwanted noise is removed. But the edges are also high

frequency components hence its necessary to preserve these while removal

of noise. A grayscale image can be specified by giving a large matrix whose

entries are between 0 to 255, 0 corresponds to black while white corresponds

to white pixels.

3.2 Pre-processing

Pre-processing is a processes that inputs the data to produce output

that is used as an input to another program. The pre-processing is used for

loading the input MRI images to the MATLAB environment and also it

removes any kind of noise present in the input images. Pre-processing

involves the operations that are required prior to the main data analysis and

extraction of information. This involves removal of film artifacts and

removal of unwanted skull portions from MRI.

3.21 Film artifacts:

Artifacts often corrupt MR images. We need to to prevent their

appearance and recognize the diagnostic pitfalls they can mimic. These

artifacts have many causes and consequences on image appearance. The

better we understand how MR images are built, the better we will be able to

deal with artifacts. The knowledge of film artifacts and noise producing

factors is important for continuing maintenance of high image quality.

Artifacts may be very noticeable or just a few pixels out of balance but can

give confusing artifactual appearances with pathology that may be

misdiagnosed.

3.22 Removal of film artifacts:

The MRI brain image consists of film artifacts or label such as patient

name, age and marks. Film artifacts are removed using tracking algorithm by

thresholding. The film artifacts are higher in intensity than the surrounding

pixels. Thus a threshold value for these film artifacts can be found. Then,

starting from the first row and first column of the image, intensity value of

the pixels are analyzed. The pixels with intensity greater than that of the pre

determined threshold value are removed from MRI. Hence, high intensity

film artifacts are removed from MRI brain image. Usually film artifacts are

found at the four corners of the image and hence it is possible to write a

general code for removing film artifacts from MR brain images.

Fig 3.1:Image without film artifacts

3.3 Image Enhancement:

Image enhancement is the improvement of digital image quality,

without any knowledge about the source of degradation. We have considered

mean filter initially but due to many disadvantages of this filter we have

considered other filters.

Image enhancement improves the virtual appearance of an MRI. The

role of enhancement technique is removal of high frequency components

from the images. Enhancement techniques such as median filter, weighted

median filter and adaptive filter reduces the edge blurring effects. In this

project we use these three filters and denoise the image using them .

3.31 Mean filter or Average filter:

Mean filtering is a simple, intuitive and easy to implement method of 

smoothing images, i.e reducing the amount of intensity variation between

one pixel and the next. It is often used to reduce noise in images. The idea of

mean filtering is simply to replace each pixel value in an image with the

mean or average value of its neighbors, including itself. This has the effect

of eliminating pixel values which are unrepresentative of their surroundings.

It is based around a kernel, which represents the shape and size of the

neighborhood to be sampled when calculating the mean. Often a 3×3 square

kernel is used, although larger kernels 5×5 square can be used for more

severe smoothing. When the neighborhood considered is too large, blurring

and other unwanted effects can appear .

 Two main problems with mean filtering are:

A single pixel with a very unrepresentative value can significantly

affect the mean value of all the pixels in its neighbourhood.

When the filter neighbourhood straddles an edge, the filter will

interpolate new values for pixels on the edge and so will blur that

edge. This will cause problem as we require sharp edges in the output.

In general the mean filter acts as low pass filter and, therefore, reduces the

spatial intensity derivatives present in the image

3.32 Denoising using Median filter:

The median filter is a nonlinear digital filtering technique, often used

to remove noise by applying a smoothening technique. Such noise reduction

acts as a typical pre-processing step to improve the results of later

processing. Median filtering is very widely used in digital image processing

because, under certain conditions, it preserves edges while removing noise.

Edges are of critical importance to the visual appearance of images, for

example. for small to moderate levels of (Gaussian) noise. An effective noise

reduction method for salt and pepper noise involves the usage of certain

filters like median filter.

Although other types of noise e.g., ., impulse or Poisson noise have also been

studied in the literature of image processing, the term “image de-noising” is

usually devoted to the problem associated with additive white Gaussian

noise. Mathematically, if we use Y=X+W to denote the degradation process

where X represents clean image, and Y represents noisy image, then the

image de-noising algorithm attempts to obtain the best estimate of X from Y.

The optimization criterion can be mean squared error based or perceptual

quality driven though image quality assessment itself is a difficult problem,

especially in the absence of an original reference.

A median filter is an example of a non-linear filter and, if properly designed,

is very good at preserving image detail. A median filter is a rank-selection

(RS) filter, a particularly harsh member of the family of rank-conditioned

rank-selection (RCRS) filter . A median filter is a rank-selection (RS) filter, a

particularly harsh member of the family of rank-conditioned rank-selection

(RCRS) filter .A much milder member of that family, one that selects the

closest of the neighboring values when a pixel's value is external in its

neighborhood, and leaves it unchanged otherwise, is sometimes preferred,

especially in photographic applications. Median and other RCRS filters are

good at removing salt and pepper noise from an image, and also cause

relatively little blurring of edges, and hence are often used in computer

vision applications.

It is used to reduce ‘salt and pepper’ noise. This technique calculates the

median of the surrounding pixels to determine the new value of the pixel. A

window of size 3*3 is taken. The nine elements in this window are stored in

an array and then these elements are sorted in ascending order of their pixel

values. The median is calculated from these sorted pixels and then the centre

element of the 3*3 matrix is replaced by this median value i.e. .the intensity

value of the centre pixel is replaced with the median value. This procedure is

done for all the pixels in the image to smoothen the edges of MRI. The

window size to be selected depends on the amount of smoothening required

for the concerned case.

Calculating the median value of a pixel neighborhood: Here the central pixel

value of 14 is replaced with the median value: 13. This is an example for 3×3

window; larger neighborhoods will produce more severe smoothing.

Algorithm for Median filter:

1. Read MR image and store it in a 2-D matrix.

2. Consider a n*n window. Starting from the first row and first column, store

the elements in an array (n should be an odd number).

3. Sort the elements in an array in ascending order.

4. Select the median value from the (centre most elements) from sorted

array.

5. Replace the centre pixel of the window by the median value.

6. Repeat the above steps by moving the window and hence applying it for

all the pixels in the image.

Fig 3.2a:3*3 median filtered image.

Fig 3.2b:5*5 median filtered image.

NO

YES

READ AN MR IMAGE TO MATLAB

STORE IN A 2D MATRIX

SELECT A r*c WINDOW

r=1 c=1

STORE THE ELEMENTS OF THE WINDOW IN AN

ARRAY a[i] i=1 count=1

j=j+1

IS a[i]>a[j]?

temp=a[i] a[i]=a[j] a[j]=temp

i=i+1 count++

START

YES

NO

IS count<n?

GET THE MEDIAN VALUE

REPLACE CENTRE PIXEL WITH MEDIAN

r=r+1 c=c+1

IS r<p && c<q?

OBSERVE THE OUTPUT

A BC

3.33 Denoising using Weighted Median filter:

Weighted Median (WM) filters have the robustness and edge

preserving capability of the classical median filter and resemble linear FIR

filters in certain properties. Furthermore, WM filters belong to the broad

class of nonlinear filters called stack filters. This enables the use of the tools

developed for the latter class in characterizing and analyzing the behavior

and properties of WM filters, e.g. noise attenuation capability. Pixels

intensity values are examined and depending on the range of intensity,

particular weights are multiplied. Applications of it include: idempotent

weighted median filters for speech processing, adaptive weighted median

and optimal weighted median filters for image and image sequence

restoration, weighted medians as robust predictors in DPCM coding and

Quincunx coding, and weighted median filters in scan rate conversion in

normal TV and HDTV systems.

To calculate the weighted median of a set of numbers you need to find

the median and if this number does not exist in the record set take the

average of the values above and below the median instead.

Algorithm for Weighted Median filters:

1. Read MR image and store in a 2-D matrix.

2. According to the pixel intensities ,multiply them by their corresponding

weights.

3. Consider a n*n window. Starting from the first row and first column,store

the elements in an array (n is an odd number).

4. Sort the elements in an array in ascending order.

5. Select the median value from the (centre most elements) from sorted

array.

6. Replace the centre pixel of the window by the median value.

7. Repeat the above steps by moving the window and hence applying it for

all the pixels in the image.

Fig 3.3a:5*5 weighted median filtered image

Fig 3.3b:3*3 weighted median filtered image.

3.34 Denoising using Adaptive Median filter:

An adaptive filter is a filter that self adjusts its transfer function

according to an optimizing algorithm. Because of the complexity of the

optimizing algorithms, most adaptive filters are digital filters that perform

digital signal processing and adapt their performance based on the input

signal. It is used for impulsive noise reduction of an image without the

degradation of an original image.

The shape of the filter basis is adapted to follow the high contrasted

edges of the image.In this way,the artifacts introduced by a circularly

symmetric filter at the border of high contrasted areas are reduced.

Fig 3.4a:3*3 adaptive filtered image.

Fig 3.4b:5*5 adaptive filtered image.

Algorithm for Adaptive Median filter:

1. Read MR image and store in a 2-D matrix.

2. Select the required maximum and minimum intensity values.

3. The median value is selected by sorting the elements of the matrix.

4. If the pixel intensity values lie outside the pre determined range, then

it is considered as a noise pixel and is replaced by the calculated median

value.

5. If the pixel intensity value lies within the pre determined range, then

no change is made to the pixel values.

YES

NO

STORE IN A 2D MATRIX

READ AN MR

IMAGE TO

MATLAB

SELECT REQUIRED Smin

AND Smax

START

IS Smin< PIXEL <Smax?

REPLACE THE PIXEL BY MEDIAN

OUTPUT IMAGE

CHAPTER 4

PERFORMANCE EVALUATION

AND CONCLUSION

4.1 Performance Evaluation

If the enhanced image can help the observer perceive the region of interest

Better than original image the it can be said that original image has been

improved. Statistical measurement such as variance ,entropy are used to

measure local enhancement.

4.11 MEAN:

For vectors, MEAN(X) is the mean value of the elements in X. For Matrices,

MEAN(X) is a row vector containing the mean value of each column. For

N-D arrays, MEAN(X) is the mean value of the elements along the first non-

singleton dimension of X. MEAN(X,DIM) takes the mean along the

dimension DIM of X.

Example: If X = [0 1 2 3 4 5] then mean(X,1) is [1.5 2.5 3.5] and mean(X,2)

is [1 4].

4.12 Standard Deviation:

The definition for standard deviation of a data vector X is given by:

S=[1/(n-1){ (xi-xbar)^2}]^(1/2)

xbar=(1/n) xi

where i varies from 1 to n and n is the number of elements in the sample. s =

std(X), where X is a vector, returns the standard deviation using the above

equation. The result is the square root of an unbiased estimator of the

variance of the population from which X is drawn, as long as X consists of

independent, identically distributed samples.

If X is a matrix, std(X) returns a row vector containing the standard

deviation of the elements of each column of X. If X is a multidimensional

array, std(X) is the standard deviation of the elements along the first

nonsingleton dimension of X.

s = std(X,flag) for flag = 0, is the same as std(X). For flag = 1,

std(X,1) returns the standard deviation using (2) above, producing the second

moment of the set of values about their mean. s = std(X,flag,dim) computes

the standard deviations along the dimension of X specified by scalar dim. Set

flag to 0 to normalize Y by n-1; set flag to 1 to normalize by n. Standard

deviation also represents the contrast value of an image.

ENTROPY

One of the quantitative measures in digital image processing is Entropy.

Claude Shannon introduced the entropy concept in quantification of information

content of messages. Although he used entropy in communication, it can be used

as a measure and quantify the information content of digital images. A digital

image consists of pixels arranged in rows and columns. Each pixel is defined by its

position and by its gray scale level. For an image consisting of of L gray levels, the

entropy is defined as:

where P(i) is the probability of each gray scale level. As an example a digital

image of type unsigned integer 8 has 256 different levels from 0(black) to

255(white). It must be noticed that in combined images the number of levels is

very large and grey level intensity of each pixel is a decimal, double number. For

images with high information content the entropy is large. The larger alternations

and changes in an image give larger entropy and the sharp and focused images

have more changes than blurred and misfocused images. Hence, the entropy is a

measure to assess the quality of different aligned images from the same scene.