versatile medical image denoising algorithm
TRANSCRIPT
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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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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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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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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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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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