versatile medical image denoising algorithm

8/9/2019 versatile medical image denoising algorithm

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Indian Streams Research JournalVol -3 , ISSUE 4, May.2013

ISSN:-2230-7850 Available online at www.isrj.net

1

AN EFFICIENT MEDICAL IMAGE DENOISING ALGORITHM

SRINIVASAKIRAN GOTTAPU AND M.VENUGOPAL RAO

Dept Of ECE , K.L University ,Andhra Pradesh , India.

Professor ,Dept Of ECE ,K.L University Andhra Pradesh , India.

ABSTRACT

Noise suppression in medical images is a particularly delicate and difficult task. A trade-off

between noise reduction and the preservation of actual image features has to be made in a way that

enhances the diagnostically relevant image content. Image processing specialists usually lack the

biomedical expertise to judge the diagnostic relevance of the De-noising results. For example, in

ultrasound images, speckle noise may contain information useful to medical experts the use of speckled

texture for a diagnosis was discussed in. Also biomedical images show extreme variability and it is

necessary to operate on a case by case basis. This motivates the construction of robust and Efficient

denoising methods that are applicable to various circumstances, rather than being optimal under very

specific conditions. In this paper, we propose one robust method that adapts itself to various types of image

noise as well as to the preference of the medical expert: a single parameter can be used to balance the

preservation of relevant details against the degree of noise reduction. The proposed algorithm is simple to

implement and fast. We demonstrate its usefulness for denoising and enhancement of the CT, Ultrasound

and Magnetic Resonance images.

ORIGINAL ARTICLE


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Index Terms

Medical Image denoising, Efficient Noise Filtering, Noise Suppression.

I. INTRODUCTION

Fourier and related representations are classical methods that have been widely used in image

processing applications. The noise removal has been done using the Wiener filter, which is derived by

assuming a signal model of uncorrelated Gaussian distributed coefficients in the Fourier domain and

utilizes second-order statistics of the Fourier coefficients. Statistical modelling of image features at

multiple resolution scales is a topic of tremendous interest for numerous disciplines including image

restoration, image analysis and segmentation, data fusion, etc.

Noise suppression in medical images is a particularly delicate and difficult task. A trade-off

between noise reduction and the preservation of actual image features has to be made in a way that

enhances the diagnostically relevant image content. Image processing specialists usually lack the

biomedical expertise to judge the diagnostic relevance of the De-noising results. For example, in ultrasound

images, speckle noise may contain information useful to medical experts; the use of speckled texture for a

diagnosis was discussed in. Also biomedical images show extreme variability and it is necessary to operate

on a case by case basis. This motivates the construction of robust and Efficient De-noising methods that are

applicable to various circumstances, rather than being optimal under very specific conditions.

The notion of robustness in multi-scale denoising was addressed in. In this Paper, we propose one

robust method that adapts itself to various types of image noise as well as to the preference of the medical

expert: a single parameter can be used to balance the preservation of relevant details against the degree of

noise reduction. Lee proposed digital image enhancement and noise filtering by use of local statistics.

Recently Pizurica and co-authors [9] proposed a low-complexity joint detection and estimation method. In

particular, the method applies the minimum mean squared error criterion assuming that each wavelet

coefficient [10][11]represents a signal of interest with a probability leading to the generalized likelihood


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3

ratio formulation in the wavelet domain. They proposed an analytical model for the probability of signal

presence, which is adapted to the global coefficient histogram and to a local indicator of spatial

activity(e.g., the locally averaged magnitude of the wavelet coefficients).

In this paper, we propose a related, but more flexible method, which is applicable to various and

unknown types of image noise. We employ a preliminary detection of the wavelet coefficients that

represent the features of interest in order to empirically estimate the conditional pdfs of the coefficients

given the useful features and given background noise. At the same time, the preliminary coefficient

classification is also exploited to empirically estimate the corresponding conditional pdfs of the local

spatial activity indicator (LSAI). The preliminary classification step in the proposed method relies on the

persistence of useful wavelet coefficients across the scales, and is related to the one in, but avoids its

iterative procedure.

The classification step of the proposed method involves an adjustable parameter that is related to the

notion of the expert-defined relevant image features. In certain applications the optimal value of this

parameter can be selected as the one that maximizes the signal-to-noise ratio (SNR) and the algorithm can

operate as fully automatic. However, we believe that in most medical applications[10] the tuning of this

parameter leading to gradual noise suppression[11] may be advantageous. The proposed algorithm is

simple to implement and fast. We demonstrate its usefulness for denoising and[12] enhancement of the CT,

Ultrasound and Magnetic Resonance images.

This paper is organized as follows. Section-II describes the basic theory of the proposed algorithm.

Section-III illustrate the versatile Noise filtration technique. Section IV elaborate the Summary of

proposed algorithm. Section V and VI shows the Implementation of proposed algorithm to Ultra sound

images and magnetic resonance images respectively, Results are discussed and conclusion is given in

section VII.


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4

II. BASIC THEORY OF PROPOSED ALGORITHM

In this setion !e !i"" st#dy the theoretia" onept $ehind the proposed %ethod, and then the ne!

pratia" a"&orith% is desri$ed. 'e start fro% a &enera" noise %ode"k k ky w n= , !here kw is the

#n(no!n noise)free !ave"et oeffiient, a point)!ise %athe%atia" operation *addition in the ase of

additive noise and %#"tip"iation in the ase of spe("e noise+ and kn an ar$itrary noise ontri$#tion. O#r

!ave"et do%ain esti%ation approah re"ies on the oint detetion and esti%ation theory and is re"ated to

the pro$"e% of the spetra" a%p"it#de esti%ation. -he a"&orith% is i%p"e%ented #sin& the #adrati

sp"ine !ave"ets

Let kX denote a rando% varia$"e, !hih ta(es va"#es kx fro% the $inary "a$e" set{ }0,1 . -he

hypothesis /the !ave"et oeffiient ky represents a si&na" of interest0 is e#iva"ent to the event 1kX = ,

and the opposite hypothesis is e#iva"ent to 0k

X = . -he !ave"et oeffiients representin& the si&na" of

interest in a &iven s#$ $and are identia""y distri$#ted rando% varia$"es !ith the pro$a$i"ity density

f#ntion | ( |1)k kY X kp w . i%i"ar"y, the oeffiients in the sa%e s#$ $and, orrespondin& to the a$sene of

the si&na" of interest, are rando% varia$"es !ith the pdf| ( | 0)k kY X k

p w .

Under the %ode" ass#%ptions, the %ini%#% %ean s#ared error esti%ate *the onditiona" %ean+ of kw

is ( | , 1) ( 1 | ) ( | , 0)k k k k k k k k w E w y X P X y E w y X k = = = + = ( 0 | )k kP X y= !here .( )E stands for the epeted

va"#e. If the si&na" of interest is s#re"y a$sent in a &iven !ave"et oeffiient, then Wk0and

E(wk|yk,Xk=0)0. In the ase !here the si&na" of interest is s#re"y present, !e approi%ate

E(wk|yk,Xk=1)yk,!hih ao#nts for the fat that vast %aority of the oeffiient %a&nit#des representin&


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the si&na" of interest are hi&h"y a$ove the noise "eve". App"yin& aye5s r#"e, one an epress ( 1 | )k kP X y= as

a &enera"i6ed "i(e"ihood ratio, and o#r esti%ate $eo%es

1

k k

k k

k k

w y

=

+

'here ( )

( )

( | 1) 1 ||,

( | 0) 0 ||

kk

k

k k

k kk

k k

p y P XY X

p y P XY X

=

= =

=

P

P *2+

And P sy%$o"ia""y denotes the prior (no!"ed&e that is #sed to esti%ate the pro$a$i"ity of si&na"

presene.

Pi6#ria718738798 proposed a %ethod to esti%ate this pro$a$i"ity for eah !ave"et oeffiient fro%

its "oa" s#rro#ndin&, #sin& a hosen indiator ke of the "oa" spatia" ativity. In parti#"ar, sine o#r

esti%ate of the pro$a$i"ity of si&na" presene is a f#ntion of ke , !e !rite

( ) ( )1 | 1 |k k kP X P X e= = =P , and rep"ae k $y( )( )

( | 1)1 | |

( | 0)0 | |

kk k k k

kk kk k

p eP X e Y Xrk

p eP X e Y X

=

= =

=

*3+

'hereris the ratio of #nonditiona" prior pro$a$i"ities

( )

( )

1

0k

k

P Xr

P X

=

==

*4+

:or a &iven type of noise, one an derive the o%p"ete esti%ator ana"ytia""y. In s#h approahes

!here the re#ired onditiona" densities need to $e epressed ana"ytia""y, the hoie of the "oa" spatia"

ativity indiator is #s#a""y restrited to si%p"e for%s; even !hen ke is defined si%p"y as the "oa""y

avera&ed oeffiient %a&nit#de, ertain si%p"ifyin& ass#%ptions a$o#t the statistia" properties of the


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transfor%, as ( )( )2, 2LH HLj k lk lS g h= and ( ) ( )2 2( 1)

2 2j

HHk lj k lS g h

= 7?8. -o initia"i6e the "assifiation, !e

start fro% D DJ J=W Y , !here @isthe oarsest reso"#tion "eve" in the !ave"et deo%position.

o! !e address the esti%ation of the !ave"et oeffiients DJY #sin& the esti%ated %as( Djx . -he

esti%ator re#ires the onditiona" densities ( | )| k kk kp y xY X and ( | )| k kk k

p e xE X . ine ( | )| k kk kp y xY X is #s#a""y

hi&h"y sy%%etria" aro#nd 0 , in pratie !e sha"" rather esti%ate the onditiona" pdfBs ( | )| k kk kp m xM X of

the oeffiient manit!des | |k km y= . As the "oa" spatia" ativity indiator ke , !e #se the avera&ed ener&y

of the nei&h$orin& oeffiients of ky !here the nei&h$ors are the s#rro#ndin& oeffiients in a s#are

!indo! at the sa%e sa"e and the /parent0 *i.e., the oeffiient at the sa%e spatia" position at the first

oarser sa"e+. avin& the esti%ated %as( 1 x { .. }Nx x= , Let 0 { : kS k x= 0}= , and 1 { : 1}kS k x= = . -he e%piria"

esti%ates | 0| ( )mM X kk kp and | 0| ( )eE X kk

p are o%p#ted fro% the histo&ra%s of 0{ : }km k S and 0{ : }ke k S

respetive"y *$y nor%a"i6in& the area #nder the histo&ra%+. i%i"ar"y, ( | 1)| kk kp yM X and ( | 1)| kk k

p eE X are

o%p#ted fro% the orrespondin& histo&ra%s for 1k S .

O#r esti%ation approah sti"" re#ires the pro$a$i"ity ratio. easonin& that ( 1)kP X = an $e

esti%ated as the frationa" n#%$er of "a$e"s for !hih 1kx = , !e esti%ate the para%eter rfro% previo#s

e#ation as

1

1

Nkk

Nkk

xr

N x

=

=

=

-hen the fina" esti%ation is defined as


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?

1

k k

k k

k k

rw y

r

=

+

'here

( | 1)|

( | 0)|

kk k

k

kk k

p mM X

p mM X

= And ( | 1)|

( | 0)|

kk k

k

kk k

p eE X

p eE X

=

In :i&. 1, !e sho! an ea%p"e of the e%piria" densities ( | )| k kk kp m xM X

and ( | )| k kk kp e xE X

. -he

diret o%p#tation of the ratios k and k fro% the nor%a"i6ed histo&ra%s sho!n in :i&. is not appropriate

d#e to errors in the tai"s. One so"#tion is to first fit a ertain distri$#tion to the histo&ra%. ere !e app"y a

si%p"er approah, o$servin& that $oth ( )log k and ( )log k an $e approi%ated !e"" $y fittin& a piee)

!ise "inear #rve as i""#strated in :i&. 1. :or%a""y, !e approi%ate

, 11 1log( )

, 12 2

k kk

k k

a b m

a b m

+

Fig .1(. Vi#ua "%pari#"! *"r a Pei MR I%age& 2i!d" )B)& K3( a!d 30 = +a, Origi!a I%age +-,

N"i#$ I%age +, Spatia$ Adaptie 2ie!er *iter +d, Pr"p"#ed *iter.

Fig 1). Vi#ua "%pari#"! *"r a ?rai! MR I%age "* #i5e 481B)41& 2i!d" )B)& K3(a!d 30 = . +a,

Origi!a I%age +-, N"i#$ I%age +, Spatia$ Adaptie 2ie!er *iter +d, Pr"p"#ed *iter.


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1?

Fig 14. Vi#ua "%pari#"! *"r a Spi!e MR I%age "* #i5e 4>@B4;9& 2i!d" )B)& K3(a!d 30 = . +a,

Origi!a I%age +-, N"i#$ I%age +, Spatia$ Adaptie 2ie!er *iter +d, Pr"p"#ed *iter.

VII. CONCLUSIONS

In this paper, !e have deve"oped a "o!)o%p"eity De)noisin& a"&orith% #sin& the oint statistis of

the !ave"et oeffiients and onsider the dependenies $et!een the oeffiients. !e have addressed the

deve"op%ent of ne! a"&orith%s for i%prove%ent in i%a&e reonstr#tion $y s#ppressin& artifats s#h as

$"#rrin&, noise, rin& and other a"iasin& artifats fro% sparse proetions, o%%on"y arise in C-, #sin&

advaned !ave"ets s#h as #adrati sp"ine !ave"et transfor%. and de%onstrated to $e effetive"y

preservin& the "oa" feat#res s#h as ed&es, orners and "oa" orientations. -hese tehni#es are

i%portant in %edia" dia&nosis app"iations.

:#rther !or( fo#ses on the etension of %#"ti reso"#tion $ased denoisin& she%es to 3D)voe" data.

Additiona""y, a detai"ed o%parison of the denoisin& she%es $efore and after a C-)reonstr#tion is

needed Con"#sion.


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Table .1:Signal to Noise Comparisons for the three Test Images.

Re"!#truti"!

Met'"d

Te#ti%age1&6B6&K3) Te#ti%age(&6B6&K3) Te#ti%age)&6B6&K38

SNR+d?, PSNR

+d?,

C"%p.

Ti%e +Se,

SNR

+d?,

PSNR

+d?,

C"%p.

Ti%e

+Se,

SNR

+d?,

PSNR+d?

,

C"%p.

Ti%e+Se,

N"i#$ i%age 1>.> 2.=< ) ) ) 1>.>1 2>.31 ) ) ) 23.?9 32.


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2=

Table.2: Signal to Noise Ratio comparison for three images. Pelvic MR Image,

Brain MR Image and Spine MR Image, window size 3X3, K=2

Re"!#truti"!

Met'"d

Pei MR I%age Si5e 944B9(9

3)@

?rai! MR I%age Si5e 481B)41

3)@

Spi!e MR I%age Si5e 4>@B4;9

3)@

SNR+d

?,

PSNR+d?

,

C"%p.

Ti%e +Se,

SNR+d

?,

PSNR+d?

,

C"%p.

Ti%e

+Se,

SNR+d

?,

PSNR+d?

,

C"%p.

Ti%e

+Se,

N"i#$ i%age 11..


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21

Ta-e.) I%p"rta!t *eature# Ver#atie de!"i#i!g ag"rit'%# *"r 61( B 61( Pei i%age it' 20 = .

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versatile medical image denoising algorithm

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