Seminar Report_Noise reduction in ECHO_part 2_v2.0.pdf

Noise Reduction In Echocardiography Images Using Contourlet Transform

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Dept. of Electronics & Communication Engineering, MBCET

CHAPTER 1

INTRODUCTION

One of the common methods for medical imaging is ultrasonic waves. Ultrasonic

imaging has gained much popularity through medical sciences recently and some of the main

reasons of its prominence are due to the fact that it is has a high speed of imaging and high

degree of time resolution, requires small instruments and low cost. Also, it is non-invasive,

displays the image immediately (very short processing time), harmless for human body and is

portable in all places. These facts encourage physicians prefer this kind of imaging as the first

step to recognize the disease. Ultrasonic imaging of heart is called echocardiography.

One of the main drawbacks of this ultrasonic imaging is its high noise, especially

speckle noise. Speckle noise is different in imaging of different organs, but always appears as

small grains depending on structure and composition of the organs. As a result, it would be

very difficult for even the best specialists to interpret echocardiography images as it requires

some long instructive courses and depends much on the specialist’s experience. Hence, the

need for automatic analysis methods is preferred widely. It can make recognition quantitative,

scientific, accurate, quick and independent of individual’s opinion. Speckle reduction is one

of the pre-processing stages for automated procedures. In other words, the omission of

speckle noise from ultrasonic images is the first step for better implementation of automated

procedures. Currently available techniques for omission of speckle noise like “wavelet”

despite of several advantages, suffer from drawbacks which encourage researchers to find

new techniques. One of the recently developed processing methods for images is called

Contourlet Transform technique which has several significant and effective applications such

as noise reduction, compression and classification of images based on the inherent

characteristics of images.


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CHAPTER 2

CONTOURLET TRANSFORM

Efficient representation of visual information lies at the heart of many image

processing tasks, including compression, denoising, feature extraction, and inverse problems.

Efficiency of a representation refers to the ability to capture significant information about an

object of interest using a small description. For image compression or content-based image

retrieval, the use of an efficient representation implies the compactness of the compressed file

or the index entry for each image in the database. For practical applications, such an efficient

representation has to be obtained by structured transforms and fast algorithms. For one-

dimensional piecewise smooth signals, like scanlines of an image, wavelets have been

established as the right tool, because they provide an optimal representation for these signals

in a certain sense. However, natural images are not simply stacks of 1-D piecewise smooth

scan-lines; discontinuity points (i.e. edges) are typically located along smooth curves (i.e.

contours) owing to smooth boundaries of physical objects. For echocardiography images in

specific, all the useful information in the image is along the edges of the same, which contain

intrinsic geometrical structures. As a result of a separable extension from 1-D bases,

wavelets in 2-D are good at isolating the discontinuities at edge points, but will not “see” the

smoothness along the contours. In addition, separable wavelets can capture only limited

directional information – an important and unique feature of multidimensional signals. These

disappointing behaviors indicate that more powerful representations are needed in higher

dimensions.

Any technique for denoising and enhancing natural images with smooth contours such

as echocardiography images should have the following as the desiderata.

1) Multiresolution. The representation should allow image to be successively

…………approximated, from coarse to fine resolutions.

2) Localization. The basis elements in the representation should be localized

…………..in both the spatial and the frequency domains.

3) Critical sampling. For some applications (e.g., compression), the

…………...representation should form a basis, or a frame with small redundancy.


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4) Directionality. The representation should contain basis elements oriented at

…………a variety of directions, much more than the few directions that are offered

…………by separable wavelets.

5) Anisotropy. To capture smooth contours in images, the representation

….should …contain basis elements using a variety of elongated shapes with

.....different aspect ratios.

2.1 Concept

Fig. 2.1 depicts the advantage of Contourlet transform over Wavelet transform.

The improvement of the Contourlet transform can be attributed to the grouping of nearby

wavelet coefficients, since they are locally correlated due to the smoothness of the contours.

Therefore, a sparse expansion for natural images can be obtained by first applying a

multiscale transform, followed by a local directional transform to gather the nearby basis

functions at the same scale into linear structures.

Figure 2.1. Wavelet versus new scheme: illustrating the successive refinement by

the two systems near a smooth contour, which is shown as a thick curve separating

two smooth regions.

Wavelet Contourlet


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In essence, wavelet-like transform for is used edge detection, and then a local

directional transform for contour segment detection .With this insight, a double filter bank

structure (Figure 2.4) is developed for obtaining sparse expansions for typical images having

smooth contours. In this double filter bank, the Laplacian pyramid is first used to capture the

point discontinuities, and then followed by a directional filter bank to link point

discontinuities into linear structures. The overall result is an image expansion using basic

elements like contour segments, and thus is named Contourlet. In particular, Contourlet has

elongated supports at various scales, directions, and aspect ratios. This allows Contourlet to

efficiently approximate a smooth contour at multiple resolutions. In the frequency domain,

the Contourlet transform provides a multiscale and directional decomposition.

2.2 Laplacian Pyramid

One way to obtain a multiscale decomposition is to use the Laplacian pyramid (LP)

introduced by Burt and Adelson. The LP decomposition at each level generates a

downsampled lowpass version of the original and the difference between the original and the

prediction, resulting in a bandpass image. Figure 2.2(a) depicts this decomposition process,

where H and G are called (lowpass) analysis and synthesis filters, respectively, and M is the

sampling matrix. The process can be iterated on the coarse (downsampled lowpass) signal. In

filter banks, sampling is represented by sampling matrices; for instance, downsampling x[n]

by M yields xd[n] = x[Mn], where M is an integer matrix .

Fig. 2.2 Laplacian pyramid (a) One level of decomposition. The outputs are a coarse approximation a[n] and a

difference b[n] between the original signal and the prediction. (b) Structure

(a) (b)


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A drawback of the LP is the implicit oversampling. However, in contrast to the

critically sampled wavelet scheme, the LP has the distinguishing feature that each pyramid

level generates only one bandpass image and this image does not have “scrambled”

frequencies. This frequency scrambling happens in the wavelet filter bank when a highpass

channel, after downsampling, is folded back into the low frequency band, and thus its

spectrum is reflected. In the LP, this effect is avoided by downsampling the lowpass channel

only. The LP with orthogonal filters (that is, the analysis and synthesis filters are time

reversal, h[n] = g[−n], and g[n] is orthogonal to its translates with respect to the sampling

lattice by M) provides a tight frame.

2.3 Directional Filter Bank

Bamberger and Smith constructed a 2-D directional filter bank (DFB) that can be

maximally decimated while achieving perfect reconstruction. The DFB is efficiently

implemented via an l-level binary tree decomposition that leads to 2l subbands with wedge-

shaped frequency partitioning as shown in Figure 2.3.1(a).

The original construction of the DFB involves modulating the input image and using

quincunx filter banks with diamond-shaped filters. To obtain the desired frequency partition,

a complicated tree expanding rule has to be followed for finer directional subbands.

An alternative simplified DFB is intuitively constructed from two building blocks.

Fig. 2.3.1. Directional filter bank. (a) Frequency partitioning where l = 3 and there are 23 = 8 real wedge-

shaped frequency bands. Subbands 0–3 correspond to the mostly horizontal directions, while subbands 4–7

correspond to the mostly vertical directions. (b) The multichannel view of an l-level tree-structured directional

filter bank.


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The first building block is a two-channel quincunx filter bank with fan filters (Figure

2.3.2) that divides a 2-D spectrum into two directions: horizontal and vertical. The second

building block of the DFB is a shearing operator, which amounts to just reordering of image

samples.

Figure 2.3.3 shows an application of a shearing operator where a −45◦ direction edge

becomes a vertical edge. By adding a pair of shearing operator and its inverse (“unshearing”)

to before and after, respectively, a two channel filter bank in Figure 2.3.2, a different

directional frequency partition is obtained while maintaining perfect reconstruction. Thus, the

key in the DFB is to use an appropriate combination of shearing operators together with two-

directionpartition of quincunx filter banks at each node in a binary tree-structuredfilter bank,

to obtain the desired 2-D spectrum division as shown in Figure 2.3.1 (a). Using multirate

identities, it is instructive to view an llevel tree-structured DFB equivalently as a 2l parallel

channel filter bank with equivalent filters and overall sampling matrices as shown in Figure

2.3.1 (b). Denote these equivalent (directional) synthesis filters as D(l) k , 0 ≤ k < 2l, which

correspond to the subbands indexed as in Figure 3(a).

Fig. 2.3.2 Two-dimensional spectrum partition using quincunx filter banks with fan filters. The black

regions represent the ideal frequency supports of each filter. Q is quincunx sampling matrix.

Fig. 2.3.3 . Example of shearing operation that is used like a rotation operation for DFB decomposition.

(a) The “cameraman” image. (b) The “cameraman” image after a shearing operation.


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The corresponding overall sampling matrices have the following diagonal forms

1 1

( )

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(2 ,2) for 0 2

for 2 2(2,2 )

l l

l

k l ll

diag kS

kdiag

− −

−−

≤ <=

≤ ≤…………………..2.3.1

which means sampling is separable. The two sets correspond to the mostly horizontal and

mostly vertical set of directions, respectively. From the equivalent parallel view of the DFB,

the family

{ } l 2

( ) ( )

0 k<2 ,[ ] l l

k km

d n S m≤ ∈

−ℤ

……………………...2.3.2

obtained by translating the impulse responses of the equivalent synthesis filters ( )l

kD over the

sampling lattices by ( )l

kS provides a basis for discrete signals in 2 2( )l ℤ . This basis exhibits

both directional and localization properties. Figure 2.3.4 demonstrates this fact by showing

the impulse responses of equivalent filters from an example DFB. These basis functions have

quasi-linear supports in space and span all directions. In other words, the basis 2.3.2

resembles a local Radon transform and are called Radonlets. Furthermore if the building

block filter bank in Figure 2.3.2 uses orthogonal filters, then the resulting DFB is orthogonal

and 2.3.2 becomes an orthogonal basis.

Fig. 2.3.4 Impulse responses of 32 equivalent filters for the first half channels, corresponding to the mostly horizontal

directions, of a 6-levels DFB that uses the Haar filters. Black and gray squares correspond to +1 and −1, respectively.

Because the basis functions resemble “local lines”, they are called “Radonlets.”


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2.4 Discrete Contourlet Transform

As noted earlier, directional filter bank is designed to target high frequencies of the

input image which contains some information about directions, so it receives a little

information about lower frequencies. But regarding the frequency segments shown in fig.3, it

would be possible that lower frequencies enter some directional sub-bands. That is why the

directional filter bank alone cannot present a sparse display for images. The fact will cause

the directional filter bank to be mixed with a multi-scale composition which can consequently

omit low frequencies of the input image before directional filter bank. Fig.2.3 shows a

multiscale and directional composition using the Laplacian Pyramid and the directional filter

bank. Images are firstly transmitted through the Laplacian Pyramid then it arrives at the

directional filter bank, so the directional data can been extracted. This behavior is exactly

practiced for the low pass segment of the image.

Figure2.3. The original Contourlet transform. (a) Block diagram. (b) Resulting frequency division.

As a result of this mixture, the repeated structure is a binary filter bank called

Contourlet bank filter which analyses the images into directional sub-bands in several scales.

Since the steps of multi-rate and directional analysis are discrete and separate from each

other, we can have different numbers relating to various directions so a multi-scale and

directional extension is presented. In addition to this, the analysis of all-binary tree of

directional filter bank in the Contourlet transform can be expanded to an arbitrary tree

structure. This is very similar to the expansion of wavelet transform to wavelet packets. The

result would be a group of multi-scale directional expansions called Contourlet packets.

(a) (b)


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The Contourlet transform has specific characteristics, for example it is defined based

on rectangular shaped networks, and thus a thorough description and interpretation is

proposed for the discrete world whose pixels are settled on a rectangular network. Because of

being defined based on a rectangular network, the Contourlet have more two-dimensional

frequency segments on central squares rather than central circles of curvelet and other

systems defined on polar coordinates.

2.5 Denoising using Contourlet Transform

The improvement in approximation by Contourlets based on keeping the most

significant coefficients will directly lead to improvements in applications, including

compression, denoising, and feature extraction. As an example, for image denoising, random

noise will generate significant wavelet coefficients just like true edges, but is less likely to

generate significant contourlet coefficients. Consequently, a simple thresholding scheme

applied on the Contourlet transform is more effective in removing the noise than it is for the

wavelet transform.

Figure 2.4 displays a “zoom-in”

comparison of denoising when

applying wavelet and contourlet hard-

thresholding on the ‘Lena’ image.

The contourlet transform is

shown to be more effective in

recovering smooth contours, both

visually as well as in PSNR. A more

sophisticated denoising scheme that

takes into account the dependencies

across scales, directions and locations

in the contourlet domain using

statistical modeling of contourlet

coefficients is presented and shows

further improvements.

Fig 2.4. Denoising experiments. From left to right, top to

bottom are: original image, noisy image (PSNR = 24.42

dB), denoising using wavelets (PSNR = 29.41 dB), and

denoising using contourlets (PSNR = 30.47 dB).


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CHAPTER 3

ECHOCARDIOGRAPHY

An echocardiogram often referred to in the medical community as a cardiac ECHO or

simply an ECHO, is a sonogram of the heart, also known as a cardiac ultrasound, it uses

standard ultrasound techniques to image two-dimensional slices of the heart. The latest

ultrasound systems now employ 3D real-time imaging.

In addition to creating two-dimensional pictures of the cardiovascular system, an

echocardiogram can also produce accurate assessment of the velocity of blood and cardiac

tissue at any arbitrary point using pulsed or continuous wave Doppler ultrasound. This allows

assessment of cardiac valve areas and function, any abnormal communications between the

left and right side of the heart, any leaking of blood through the valves (valvular

regurgitation), and calculation of the cardiac output as well as the ejection fraction. Other

parameters measured include cardiac dimensions (luminal diameters and septal thicknesses)

and E/A ratio.

Echocardiography was an early medical application of ultrasound. Echocardiography

was also the first application of intravenous contrast-enhanced ultrasound. This technique

injects gas-filled micro bubbles into the venous system to improve tissue and blood

delineation. Contrast is also currently being evaluated for its effectiveness in evaluating

myocardial perfusion. It can also be used with Doppler ultrasound to improve flow-related

measurements (see Doppler echocardiography).

Echocardiography is either performed by cardiac sonographers, cardiac physiologists

or doctors trained in cardiology.

3.1 Purpose

Echocardiography is used to diagnose cardiovascular diseases. In fact, it is one of the

most widely used diagnostic tests for heart disease. It can provide a wealth of helpful

information, including the size and shape of the heart, its pumping capacity and the location

and extent of any damage to its tissues. It is especially useful for assessing diseases of the

heart valves. It not only allows doctors to evaluate the heart valves, but it can detect

abnormalities in the pattern of blood flow, such as the backward flow of blood through partly

closed heart valves, known as regurgitation. By assessing the motion of the heart wall,


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echocardiography can help detect the presence and assess the severity of any wall ischemia

that may be associated with coronary artery disease. Echocardiography also helps determine

whether any chest pain or associated symptoms are related to heart disease.

Echocardiography can also help detect any cardiomyopathy, such as hypertrophic

cardiomyopathy, as well as others. The biggest advantage to echocardiography is that it is

noninvasive (doesn't involve breaking the skin or entering body cavities) and has no known

risks or side effects.

3.2 Transthoracic Echocardiogram

A standard echocardiogram is also known as a transthoracic echocardiogram (TTE),

or cardiac ultrasound. In this case, the echocardiography transducer (or probe) is placed on

the chest wall (or thorax) of the subject, and images are taken through the chest wall. This is a

non-invasive, highly accurate and quick assessment of the overall health of the heart. A

cardiologist can quickly assess a patient's heart valves and degree of heart muscle contraction

(an indicator of the ejection fraction). The images are displayed on a monitor, and are

recorded either by videotape (analog) or by digital techniques.

An echocardiogram can be used to evaluate all four chambers of the heart. It can

determine strength of the heart, the condition of the heart valves, the lining of the heart (the

pericardium), and the aorta. It can be used to detect a heart attack, enlargement or

hypertrophy of the heart, infiltration of the heart with an abnormal substance. Weakness of

the heart, cardiac tumors, and a variety of other findings can be diagnosed with an

echocardiogram. With advanced measurements of the movement of the tissue with time

(tissue doppler), it can measure diastolic function, fluid status and dys-synchrony.

Fig. 3.1 Normal Heart (TTE View)


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The TTE is highly accurate for identifying vegetations (masses consisting of a

mixture of bacteria and blood clots), but the accuracy can be reduced in up to 20% of adults

because of obesity, chronic obstructive pulmonary disease, chest-wall deformities, or

otherwise technically difficult patients. TTE in adults is also of limited use for the structures

at the back of the heart, such as the left atrial appendage. Transesophageal

echocardiography may be more accurate than TTE because it excludes the variables

previously mentioned and allows closer visualization of common sites for vegetations and

other abnormalities. Transesophageal echocardiography also affords better visualization

of prosthetic heart valves.

"Bubble contrast TTE" involves the injection of agitated saline into a vein, followed

by an echocardiographic study. The bubbles are initially detected in the right atrium and

right ventricle. If bubbles appear in the left heart, this may indicate a shunt, such as a patent

foramen ovale, atrial septal defect, ventricular septal defect or arteriovenous malformations in

the lungs

3.3 Transesophageal Echocardiogram

A transesophageal echocardiogram, or TEE is an alternative way to perform

an echocardiogram. A specialized probe containing an ultrasound transducer at its tip is

passed into the patient's esophagus. This allows image and Doppler evaluation which can be

recorded.

It has several advantages and some disadvantages compared to a transthoracic

echocardiogram (TTE).

3.3.1 Advantages

The advantage of TEE over TTE is usually clearer images, especially of structures

that are difficult to view transthoracicly (through the chest wall). The explanation for this is

that the heart rests directly upon the esophagus leaving only millimeters that the ultrasound

beam has to travel. This reduces the attenuation (weakening) of the ultrasound signal,

generating a stronger return signal, ultimately enhancing image and Doppler quality.

Comparatively, transthoracic ultrasound must first traverse skin, fat, ribs and lungs before


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reflecting off the heart and back to the probe before an image can be created. All these

structures, along with the increased distance the beam must travel, weaken the ultrasound

signal thus degrading the image and Doppler quality.

In adults, several structures can be evaluated and imaged better with the TEE,

including the aorta, pulmonary artery, valves of the heart, both atria, atrial septum, left atrial

appendage, and coronary arteries. TEE has a very high sensitivity for locating a blood clot

inside the left atrium.

3.3.2 Disadvantages

� TEE requires a fasting patient, (the patient must follow the ASA NPO guidelines(i.e.

usually not eat or drink anything for eight hours prior to the procedure)

� Requires a team of medical personnel

� takes longer to perform

� May be uncomfortable for the patient

� May require sedation or general anesthesia

� has some risks associated with the procedure (esophageal perforation-- 1 in 10,000,

and adverse reactions to the medication).

3.4 Stress Echocardiography

A stress echocardiogram, also known as a stress echo or SE, utilizes ultrasound

imaging of the heart to assess the wall motion in response to physical stress. First, images of

the heart are taken "at rest" to acquire a baseline of the patient's wall motion at a resting heart

rate. The patient then walks on a treadmill or utilizes another exercise modality to increase

the heart rate to 80% of the target heart rate (target heart rate = 220 - your age). Finally,

images of the heart are taken "at stress" to assess wall motion at the peak heart rate. A stress

echo assesses wall motion of the heart; it does not, however, image the coronary arteries

directly. Ischemia of one or more coronary arteries could cause a wall motion abnormality

which could indicate coronary artery disease (CAD). The gold standard test to directly image

the coronary arteries and directly asses for stenosis or occlusion is a cardiac catheterization.

A stress echo is a non-invasive test and is performed in the presence of a licensed medical

professional, such as a cardiologist, and an ultrasound technician.


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CHAPTER 4

EXPERIMENTAL VALIDATION & RESULTS

To discuss the quality of images obtained, some complete cycles of echocardiography

images related to healthy individuals from Shahid Rajayi (Tehran,Iran) Hospital and

converted a complete cycle of echocardiography from 5 healthy individuals to 70 continuous

frames, then processed each frame with 4 different methods of median filter, Wiener filter,

wavelet and Contourlet by denoising per frame to an extent which does not omit significant

information from the image, finally converted this set of 70 reconstructed images into one

complete cycle again. The obtained results are divided into two categories: quantitative and

qualitative.

4.1 Quantitative Result

In this section different techniques of denoising such as median filter, Wiener filter,

wavelet and Contourlet techniques are studied and their efficiencies are compared. To do this,

we omit the noise of heart echocardiography images using 4 abovementioned techniques to

the extent that no information is lost from the images. Now we have to use proper

quantitative criteria to know about the denoising procedure.

Here, some common criteria are used to compare the results quantitatively.

• Mean Square Error (MSE): The MSE is the second moment (about the origin) of the

error, and thus incorporates both the variance of the estimator and its bias. For an

unbiased estimator, the MSE is the variance. Like the variance, MSE has the same

units of measurement as the square of the quantity being estimated. In an analogy

to standard deviation, taking the square root of MSE yields the root mean square

error or root mean square deviation (RMSE or RMSD), which has the same units as

the quantity being estimated; for an unbiased estimator, the RMSE is the square root

of the variance, known as the standard error.

This criterion studies the amount of difference between the filtered qi image and the

original pi image, in which N and M are numbers of rows and columns of the image,

respectively.

2

1

1( )

N

i i

i

MSE p qMN =

= −∑


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• Peak Signal-to- noise Ratio (PSNR): PSNR is the term for the ratio between the

maximum possible power of a signal and the power of corrupting noisethat affects the

fidelity of its representation. Because many signals have a very wide dynamic range,

PSNR is usually expressed in terms of the logarithmic decibel scale.

The PSNR is most commonly used as a measure of quality of reconstruction

of a noisy image. The signal in this case is the original image. It is used as

an approximation to human perception of reconstruction quality, therefore in some

cases one reconstruction may appear to be closer to the original than another, even

though it has a lower PSNR. PSNR is given by the relation

in which n would be equal to 8 for the gray scale images

• Signal to MSE: Since the rate of signal-to-noise is not adequate for evaluating noise

in the ultrasonic images, a more proper criterion called SMSE is rather used .

• Contrast Speckle Ratio (CSR): In which that 1µ and 2µ indicate mean and variance of

the foreground object, and 1σ and 2σ indicate the background, respectively. These

indexes are either edge improvement or noise of image.

The common filters used for denoising are usually low pass filters like mean filters

which of course are not appropriate for speckle noise omission, since they clear the high

frequencies and omit the edges of image. Median and other similar filters can eliminate the

speckle noise efficiently along with many useful and significant details of the image, which

unacceptable for the physicians. Another filter used for denoising is the Weiner filter. This

filter benefits from 2nd degree statistical characteristics of Fourier; but since it is designed to

prevent cumulative noise, it would not be appropriate for speckle elimination which is

2 120 log

n

PSNRM SE

−=

101

2

1

2

10log

( )

N

i

N

i i

i

piSMSE

p q

=

=

= −

∑

∑

2 2

|

|CSR 2 1

2 1

| µ −µ=

|σ −σ


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multiplying. Wavelet technique operates better than median and Weiner filters in denoising.

Nevertheless, when compared with Contourlet technique it should be noted that although the

Contourlet can reproduce edges, it cannot provide coefficients of image contours. Hence, a

simple threshold method to denoise in the Contourlet transform would work more effectively

than wavelet transform.

Table1. Comparison of Different Evaluation Criteria

CRTIERIA DIFFERENT METHODS

Median filter Wiener filter Wavelett Contourlet

PSNR

10.1735

4.2383

4.8102E-004

2.8073E-004

SMSE

38.0561

41.8589

81.3092

83.6479

CSR

4.3605

4.3904

4.6318

4.8102


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4.2 Qualitative Result

To assure the qualitative improvement of the results, the complete cycles obtained

after the speckle denoising by the 4 methods mentioned before were shown to an expert

cardiologist along with the original cycle. Specialists also approved the obtained results,

without knowing which cycle is the proposed one, They automatically chose the cycle

obtained from Contourlet technique as the most distinct cycle. After comparing the cycle with

the original one, they remarked that despite the improvements in quality, no information has

been lost.

Figure 4.2. Compare of different methods of noise reduction. (a) The original noisy image. (b) denoised and

reconstructed image by Wiener filtering . (c) denoised and reconstructed image by Median- filtering .(d)

denoised and reconstructed image by Wavelet Transform . (e) denoised and Reconstructed image by the

proposed Contourlet method .


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CHAPTER 5

CONCLUSION

As the speckle noise prominent in ultrasonic images severely damage the image

quality, the procedure of speckle reduction is one of the preprocessing stages in order to

extract characteristics and to analyze images. In this report speckle noise reduction with the

aid of the new multi-scale and directional method for denoising: Contourlet transform

technique was performed on echocardiography images. Improvements in quantitative results

such as mean square error (MSE), peak signal-to-noise ratio (PSNR) and signal to mean

square error (SMSE) symbolizes the efficiency of this approach when compared to other

common denoising techniques.

Qualitative results (specialist recognition) also proved the fact the least dimming and

the best resolution in comparison with other common techniques for noise reduction was

achieved using this technique. In fact, vital information was conserved even after denoising

which wouldn’t have happened if other denoising techniques such as wiener filtering

technique are used.


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REFERENCES

1. Laleh Panjeh Shahi, Ahmad Shalbaf, RDCS, Richard Zahra Alizadeh sani, Hamid

Behnam, “Noise Reduction In Echocardigraphy Images Using Contourlet

Transform”, Biomedical Engineering (MECBME), 2011 1st Middle East Conference

21-24 Feb. 2011

2. Minh N Do and Martin Vetterli, Fellow, IEEE, “The Contourlet Transform: An

Efficient Directional Multi resolution Image Representation”, IEEE Trans. Image

Processing, vol.14, 2091- 2106 Dec 2005.

3. Sang Keun Oh, Joon Jae Lee, Chul Hyun Park, Bum Soo Kim,KilHoum Park, “New

Fingerprint Image Enhancement Using Directional Filter Bank” IEEE Int.Conf.

Signal Processing and Communications, 24-27 Nov. 2007.

4. Yue Lu and Minh N.Do” A New Contourlet Transform with Sharp Frequency

Localization” IEEE Int.Conf. Image Processing, 8-11 Oct. 2006.

5. Shao-Weidal1, Yan-Kuisun, Xiao -Lin Tian, Ze-Sheng Tang,” Image Desnoising

Based On Complex Contourlet Transform,” IEEE Int. Conf. Wavelet Analysis and

Pattern Recognition, 2 -4 Nov.2007.

Seminar Report_Noise reduction in ECHO_part 2_v2.0.pdf

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