DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 20 |NUMBER: 1 |2022 |MARCH
BEMD Based C oss Bila e al Fil e ing Technique
o Speckle Reduc ion in Ul asound Images
Bhawna GUPTA , Vinee KHANDELWAL
Depa men o Elec onics and Communica ion Enginee ing, Jaypee Ins i u e o In o ma ion Technology,
Sec o -62, 201309 Noida, U a P adesh, India
bha[email p o ec ed], inee .khandelw[email p o ec ed]
DOI: 10.15598/aeee. 20i1.4265
A icle his o y: Recei ed Jun 22, 2021; Re ised No 22, 2021; Accep ed Dec 28, 2021; Published Ma 31, 2022.
This is an open access a icle unde he BY-CC license.
Abs ac . In his pape , Bidimensional Empi ical
Mode Decomposi ion (BEMD) based C oss Bila e al
Fil e (CBF) echnique o speckle educ ion in ul a-
sound images has been p oposed. The e e ence image
is ob ained by denoising he noisy image using pixel-
wise Wiene il e ing. Then, bo h he noisy image and
he e e ence image a e decomposed in o a se o In-
insic Mode Func ions (IMFs) and he esidue im-
age using BEMD echnique. CBF is applied be ween
noisy image IMFs and he co esponding e e ence im-
age IMFs. The image is econs uc ed back wi h hese
modi ied IMFs and he esidue. The p oposed me hod
exploi s he edge in o ma ion in he e e ence image o
imp o ing he quali y o he denoised image. The pe -
o mance o he p oposed me hod has been es ed o
eal ul asound images and simula ed images ha ing
noise o di e en a iance. The expe imen al esul s
show ha he p oposed algo i hm pe o ms be e han
o he s a e-o -a me hods in e ms o Edge Keeping
Index (EKI), Co ela ion Coe icien (CC), Figu e o
Me i (FOM), S uc u al Simila i y (SSIM), Peak Sig-
nal o Noise Ra io (PSNR) and Signal o Noise Ra io
(SNR) o syn he ic images. The algo i hm gi es be -
e pe o mance o eal ul asound images in e ms o
Mean o Va iance Ra io (MVR) and Equi alen Num-
be o Looks (ENL).
Keywo ds
BEMD, CBF, noise educ ion, speckle.
1. In oduc ion
Wi h he ad ancemen o a ious image acqui ing ha d-
wa e in applica ions like medical diagnosis, syn he ic
ape u e ada s, o a ia ion, la ge numbe o images
a e being acqui ed and u ilized. These digi al images
a ailable in la ge magni ude a e a ec ed by noise due
o a ious ex e nal as well as in e nal ac o s. One such
widely used applica ion o diagnos ic pu poses is ul-
asound image, whose pe cei ed quali y is deg aded
by he exis ence o speckle noise which is imminen
owing o he p esence o physical phenomenon such as
sca e ing a he ime o image acquisi ion [1]. Due
o he high equency cha ac e is ic o speckle noise,
denoising algo i hms u ilized o imp o e he quali y o
hese images ace he challenge o p ese ing he edge
in o ma ion. Speckle educ ion in ul asound images is
an essen ial s ep and a ge s imp o emen in he qual-
i y o he image in e ms o PSNR, CC, SNR, FOM,
SSIM, EKI, MVR and ENL [2], [3] and [4].
The s a e-o - he-a speckle educ ion algo i hms
wo k in spa ial domain. The spa ial domain ech-
niques mainly use local s a is ics o in o ma ion edun-
dancy be ween simila pa ches and eplace he pixel
alue by p ocessing he nea by pixel alues. Mos suc-
cess ul amongs his ca ego y a e di usion-based il e s
like Speckle Reducing Aniso opic Di usion (SRAD),
De ail p ese ing aniso opic di usion (DPAD),
Pe ona-Malik’s Aniso opic Di usion (PMAD) [5], [6],
[7] and [8], Bila e al il e s [9] and [10], and pa ch-
based me hods like Non Local Mean Fil e (NLM) [11],
[12], [13] and [14] and Op imized Bayesian Nonlocal
Mean il e (OBNLM) [15] and [16]. The pa ch selec-
ion in pa ch-based me hods is icky so ha he noise
emo al does no lose he edge in o ma ion while de-
noising. The e o e, ecen wo ks [17], [18] and [19] use
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modi ied NLM and Block Ma ching and 3D il e ing
(BM3D) algo i hms o educe speckle while ying o
p ese e he edge in o ma ion.
Amongs hese a ious me hods, he bila e al il e
p oposed by Tomasi and Manduchi in 1998 [9] aims
o denoise he image while p ese ing edge de ails by
weigh a e aging he neighbo ing pixels based on hei
spa ial dis ance and simila i y. I has been applied o
a ious ields like image denoising [9] and [20], pho o-
g aph enhancemen [21], o ange comp ession [22], as
i is non-i e a i e, simple and deli e s a s able pe o -
mance compa able o many o he il e s. The disad-
an age o long unning ime o his me hod has been
wo ked upon by a ious me hods [22], [23] and [24].
Bila e al il e ing has also been applied in wa ele do-
main o denoising in [20], which ep esen s in e es ing
esul s bu does no pe o m well o eal image denois-
ing. In se e e noise cases, he pe o mance o non-local
me hods is be e bu ha is a he cos o compu a-
ion complexi y and limi a ion o o e smoo hening he
image. High quali y denoised image by local p ocessing
can be ob ained by join bila e al il e [21] and [25],
which calcula es weigh s using ano he e e ence image.
Ge ing high quali y p e-es ima ed e e ence image is
a c ucial s ep in his me hod as he esul depends on
he chosen e e ence image.
Empi ical Mode Decomposi ion (EMD) in oduced
in 1998 [26] is a e y powe ul algo i hm decomposing
he signal in i s IMFs [27]. This decomposi ion is done
based on hei oscilla ion in he spa ial domain. The
basis unc ions calcula ed in his me hod a e signal-
dependen and a se ies o IMFs a e es ima ed ia an i -
e a i e p ocedu e known as si ing [28]. The EMD was
in oduced in images in 2003 in [29] and he BEMD o
images was in oduced in 2005 in [30]. The BEMD is
also a signal-dependen adap i e echnique, decompos-
ing he image in o a se ies o IMFs and a esidue. The
low-o de IMFs a e he high- equency componen s and
he high o de IMFs a e he low- equency componen s.
The speckle noise has high equency cha ac e is ic,
he e o e he low o de IMFs a e ha ing mo e noise
componen s as compa ed o he high o de IMFs. Ac-
co dingly, some BEMD based denoising algo i hms u i-
lizes his ac o disca d he noise exis ing in he low
o de IMFs [31], [32] and [33]. Bu his may no always
be ue and a signi ican noise componen may also be
p esen in u he IMFs as well.
The CBF was in oduced in 2004 o denoise low-ligh
image [21] and o enhance he ambien image ha ely
on lash pho og aph in o ma ion [25]. These me hods
a e based on Bila e al il e equa ion and exploi s he
ac ha he Signal o-Noise Ra io (SNR) o he lash
image is highe han ha o he no- lash image. Denois-
ing algo i hms can exploi his echnique o images,
whe e e e ence image is he one wi h highe SNR. As
in mos o he cases, he o iginal noiseless image is no
a ailable so choosing he co ec e e ence image is a
challenge. Laplacian py amid has been u ilized o de-
noising image using CBF in [34], whe e he e e ence
image has been aken as he Wiene il e ed e sion
o he noisy image. Some o he CBF based image de-
noising algo i hms combine Non-local Means [35] and
mul i-sized 2D ha d h esholding [36] o signi ican e-
sul s. Mos o he high- equency componen s o he
image con ain de ail in o ma ion such as edges. Mos
o he noise is also in high equency, he e o e, hese
algo i hms hough gi ing good denoising pe o mance,
loose impo an edge de ails. These de ails a e o im-
po ance o diagnos ic pu poses when dealing wi h ul-
asound images.
This pape in oduces a hyb id echnique whe ein
he high SNR e e ence image is calcula ed using
Wiene il e ing he noisy image. The IMF’s a e com-
pu ed o bo h noisy image and e e ence image. The
edge in o ma ion in he e e ence image IMFs is a c u-
cial in o ma ion ha is impo an om he poin o
iew o diagnosis. The p oposed echnique u ilizes his
edge in o ma ion in e e ence image o ob aining a be -
e quali y denoised image in e ms o edge de ails. To
achie e his, a CBF is applied be ween he noisy image
IMFs and he co esponding e e ence image IMFs o
ge despeckled image. This helps in p ese ing he edge
in o ma ion while denoising he ul asound image.
The emainde o he pape is o ganized as ollows.
Sec ion 2. , p o ides a b ie o e iew o BEMD al-
go i hm along wi h CBF algo i hm. In Sec. 3. , he
p oposed denoising me hod is desc ibed. The pe o -
mance e alua ion o he p oposed me hod is illus a ed
in Sec. 4. , and Sec. 5. p esen s he conclusions.
2. Backg ound
2.1. Bidimensional Empi ical Mode
Decomposi ion
BEMD is an adap i e echnique which can be applied
o images o decompose hem in o a se o a ious IMFs
and a esidue. The s eps o calcula ion o he IMFs
and he esidue a e as illus a ed he e.
Le he obse ed image be deno ed by o(x, y). This
being an i e a i e p ocess, le he esidue o he m h
IMF be ep esen ed by m(x, y), which is aken as he
inpu o he calcula ion o he nex IMF. Le he inpu
image aken o he gene a ion o m h numbe IMF,
m= 1, . . . , M a he k h i e a ion o he si ing p ocess,
k= 0, . . . , K −1in wo spa ial dimensions (x, y), be
deno ed by im,k(x, y).
1. Ini ializing he si ing p ocess o he calcula ion
o he i s IMF wi h m= 1 and k= 0,im,k(x, y)
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is aken o be he obse ed image. i.e i1,0(x, y) =
o(x, y).
2. Local maxima and minima o im,k(x, y)a e ex-
ac ed.
3. Using he applica ion speci ic spline in e pola ion
o all local maxima, calcula e he uppe en elope
ue(x, y). Also, using he in e pola ion o all local
minima, calcula e he lowe en elope le(x, y).
4. The mean en elope en m,k(x, y)is calcula ed om
he uppe and lowe en elopes ob ained in s ep 3.
en m,k(x, y) = ue(x, y) + lu(x, y)
2.(1)
5. The mean en elope en m,k(x, y)is sub ac ed
om he inpu signal o calcula ing he upda ed
signal o he nex i e a ion.
im,k(x, y) = im,k−1−(x, y)en m,k(x, y),
k→k+ 1.(2)
6. Calcula e he s anda d de ia ion ε, om he esul
ob ained in s ep 5.
ε=
M−1
X
x=0
N−1
X
y=0
|im,k(x, y)−im,k−1(x, y)|2
i2
m,k−1(x, y).(3)
7. I he s anda d de ia ion εcalcula ed in s ep 6
is less han a p ede ined alue (usually 0.2–0.3),
hen he esul o s ep 5 is he equi ed m h IMF
om(x, y), else epea s eps 2–6.
om(x, y) = im,k(x, y).(4)
8. The esidue o he m h IMF is de ined as:
m(x, y) = im,0(x, y)−om(x, y).(5)
9. Fo he calcula ion o he nex IMF his esidue
calcula ed in s ep 8 is aken as he inpu signal
and going back o s ep 2 again.
im+1,0(x, y) = m(x, y).(6)
S eps 2–9 a e epea ed un il esidue calcula ed has
no mo e ex ema poin s. Thus, o o al o ‘M’ IMFs
and he las esidue M, he o iginal signal can be ep-
esen ed as:
o(x, y) =
M
X
m=1
=im(x, y) + M(x, y).(7)
The high o de IMFs a e co esponding o he low
equency while low o de IMFs, a e co esponding o
he high equency.
2.2. C oss Bila e al Fil e
CBF algo i hm is explained he e in b e i y o he sake
o illus a ion. Le Inand I deno e he noisy image
and he e e ence image, espec i ely. The unc ion gd
a enua es he il e ke nel weigh s in spa ial domain on
he basis o he dis ance be ween he pixels. Also, he
edge s opping unc ion gese s weigh s on he basis o
in ensi y di e ence be ween he pixels. Then he alue
o he pixel a loca ion qusing CBF can be calcula ed
as:
ICBF
q=1
n(q)X
q′∈Ω
gd(∥q−q′∥)qe(I q −I q′)Inq′,
(8)
whe e n(q)is he no maliza ion ac o gi en by:
nq=X
q′∈Ω
gd(∥q−q′∥)qe(I q −I q′),(9)
and Ωis he window size. The dis ance scaling unc-
ion gdis Gaussian unc ion as gi en in Eq. (10), whe e
s anda d de ia ion σdcon ols i s wid h and he a i-
able xin equa ion is Euclidean dis ance be ween qand
q′∈Ω.
g(x) = exp −x2
2σ2
d.(10)
The edge s opping unc ion geis also Gaussian unc-
ion as gi en in Eq. (11) below whe e s anda d de ia-
ion σeis con olling i s wid h.
ge(I q −I q′) = exp −1
2I (q)−I (q′)
σe2!.
(11)
The s anda d de ia ion σdis ob ained as in con en-
ional Bila e al il e ing. Also, as he e e ence image
has less noise, σeis no se e y la ge. E en when he
alue o σeis aken small and ixed alue o σeis aken
o all images, he edge s opping unc ion geensu es
ha p ope weigh s a e chosen wi hou o e -blu ing
o unde -blu ing he images.
3. BEMD Based
C oss-Bila e al Fil e ing
This sec ion in oduces he p oposed BEMD based
c oss bila e al il e o speckle educ ion in Ul asound
images. The o iginal image has speckle noise as well as
he i al edge in o ma ion in he high equency compo-
nen s and his is e lec ed in he low o de IMFs o he
image. Re e ence image is ob ained a e p ocessing
he o iginal image wi h Wiene il e . This e e ence
image is being decomposed using BEMD algo i hm o
ge a se o IMFs. Ob ained low o de IMFs e ain
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Residue
IMF1 IMF2 IMF M Residue
IMF1 IMF2 IMF M
Residue
IMF1 IMF2 IMF M
O iginal Image Re e ence Image
Bidimensional Empi ical Mode Decomposi�on
C oss Bila e al Fil e ing
Wiene Fil e ing
Denoised Image
Fig. 1: Block Diag am o he p oposed scheme.
dominan edge in o ma ion as noise componen has
been educed p io ly. Also, he high o de IMFs will
ha e he smoo h egion in o ma ion a e he educ ion
o noise.
Hence, he p oposed echnique u ilizes he dominan
edge in o ma ion in he low o de IMFs o il e ed image
and he noise ee non-edge in o ma ion in he high o -
de IMFs o his e e ence image. The algo i hm applies
he CBF be ween he same le el IMFs o he o iginal
image and he il e ed image e e ed o as e e ence
image. This helps in p ese ing he edge de ails while
emo ing he speckle noise om he ul asound im-
age as well as educes he blu ing in he smoo h e-
gions. The block diag am o he p oposed algo i hm is
as shown in Fig. 1.
The s eps in he p oposed algo i hm a e as ollows:
1. Calcula e he BEMD o he o iginal ul asound
image o(x, y)which has speckle noise.
2. Denoise he o iginal noisy image wi h pixel-wise
Wiene il e [37] o calcula e he e e ence im-
age. The noise componen has o be addi-
i e while applying his il e , so he mul iplica-
i e speckle noise is con e ed o addi i e noise
η(n1, n2)applying log ans o ma ion. Assuming
ha η(n1, n2)is ha ing ze o mean and a iance σ2
η,
Wiene il e es ima es he local mean and a i-
ance a ound each pixel o he chosen IMF.
µe=1
NK X
x,yϵw
o(x, y),(12)
σ2
e=1
NK X
x,yϵw
o2(x, y)−µ2
e,(13)
whe e wis he window co esponding o he
N×K neighbo hood o each pixel in he IMF.
This il e hen c ea es a pixel-wise es ima e gi en
as:
oe(x, y) = µe+σ2
e−σ2
η
σ2
e
(o(x, y)−µe).(14)
3. Calcula e he BEMD o he e e ence image calcu-
la ed in s ep 2.
4. Apply CBF on all he IMFs o he o iginal image
aking he co esponding il e ed image IMFs as
he e e ence componen .
5. Recons uc he image om he ou pu IMFs ob-
ained in s ep 4 o ge he inal denoised image.
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IMF 1 IMF 2 IMF 3 IMF 4
IMF 5 IMF 6 IMF 7 IMF 8
IMF 9 Noisy Image
(a)
IMF 1 IMF 2 IMF 3 IMF 4
IMF 5 IMF 6 IMF 7 IMF 8
IMF 9 Fil e ed Image
(b)
Fig. 2: (a) Noisy e us image and i s BEMD IMFs and (b) Fil e ed e us image and i s BEMD IMFs.
IMF 1 IMF 2 IMF 3 IMF 4
IMF 5 IMF 6 IMF 7 IMF 8
IMF 9 Noisy Image
(a)
IMF 1 IMF 2 IMF 3 IMF 4
IMF 5 IMF 6 IMF 7 IMF 8
IMF 9 Fil e ed Image
(b)
Fig. 3: (a) Noisy kidney image and i s BEMD IMFs and (b) Fil e ed kidney image and i s BEMD IMFs.
The pseudo code o he algo i hm is as shown below:
•Read he noisy image Inand esize i o a s anda d
size as pe he da ase : Hsize = 256;
•Calcula e he IMFs o noisy image In:
[im , Res] = emd(In);
•Wiene Fil e he noisy image o ob ain il e ed
image I :
I = wiene 2(In);
•Calcula e he IMFs o il e ed image:
[im 2, Res2] = emd(I );
•Modi y IMFs using CBF aking dis ance sigma
(sigmad), edge s opping sigma (sigmae), ke nel
size (ksize):
Fo i e a ion i = 1 : size (im ,2);
–Compu e x(i) = im (:,i);
Fo i e a ion i = 1 : size (im 2,2);
–Compu e y(i) = im 2 (:,i);
Fo i e a ion i = 1 : size (x,2);
–Calcula e cb _ou 1(i) = c oss_bila e al_ il
(x(i), y(i), sigmad, sigmae, ksize);
and de ail1(i) = x(i) - cb _ou 1(i);
•Recons uc he image:
Reco e = 0;
Reco e 1 = 0;
Fo i e a ion i = 1 : size (cb _ou 1,2);
–Calcula e Reco e 1 = Reco e 1 +
cb _ou 1(:,i) + de ail1(:,i);
Reco e = Reco e 1 + Res;
4. Expe imen al Resul s
The kidney and e us syn he ic images ob ained us-
ing Field II simula ion p og am [38] ha e been used
in ou expe imen s ha we e pe o med on MATLAB.
The speckle noise has been added o he image wi h
σ2= 0.1,0.2, and 0.3.
BEMD algo i hm is applied on he noisy syn he ic
e us image o ob ain he IMFs and he esidue.
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O iginal Image Noisy Image
Fil e ed Image
(a) O iginal Image
O iginal Image Noisy Image
Fil e ed Image
(b) Noisy image
O iginal Image Noisy Image
Fil e ed Image
(c) Fil e ed Image
Denoised Image
(d) Denoised Image
Fig. 4: Syn he ic e us image o σ2= 0.1.
Figu e 2(a) shows he BEMD IMFs o noisy syn-
he ic e us image, ha a e ob ained o noise a iance
σ2= 0.1. The spline in e pola ion ha is used in ou
case is a cubic spline. The low o de IMFs can be
seen o ha e high equency componen s co espond-
ing o noise and edges o he image. As he Wiene
il e gi es op imal pe o mance o addi i e noise, he
mul iplica i e speckle was con e ed o addi i e noise
using log- ans o ma ion be o e adding o he syn he ic
image.
Pixel-wise Wiene il e ing u ilizing 8-neighbo hood
o local egion calcula ion was applied o he noisy
image. The BEMD algo i hm was hen applied on
his il e ed image o ge he IMFs which a e shown
in Fig. 2(b) along wi h esidual image. I can be no ed
ha he low o de IMFs o he il e ed image a e now
ep esen ing he dominan edge de ails.
As he Wiene il e has denoised he image, so IMFs
o his il e ed image a e aken as he e e ence. CBF
on all he IMFs o he noisy image and he co espond-
ing IMFs o he il e ed image has been applied o ge
he modi ied IMFs. Based on ex ensi e expe imen s
pe o med on di e en images, he alue o dis ance
sigma σd, edge s opping sigma σeand ke nel size a e
unde aken as 1.8, 2.5, and 5, espec i ely o bes e-
sul s. These modi ied IMFs along wi h he esidue o
he inpu image a e u ilized o econs uc he denoised
image in which he edge in o ma ion has been e ained.
O iginal Image Noisy Image
Fil e ed Image
(a) O iginal Image
O iginal Image Noisy Image
Fil e ed Image
(b) Noisy image
O iginal Image Noisy Image
Fil e ed Image
(c) Fil e ed Image
O iginal Image Noisy Image
Denoised Image
(d) Denoised Image
Fig. 5: Syn he ic kidney image o σ2= 0.1.
Figu e 4 shows he syn he ic e us image, i s noisy e -
sion o σ2= 0.1, il e ed e e ence image and he i-
nal econs uc ed denoised image. As can be seen, he
denoised image is pe cep ually o he same quali y as
ha o he o iginal image. Following he simila p oce-
du e esul s o he syn he ic kidney image a e ob ained
which a e shown in Fig. 3 and Fig. 5, espec i ely. I is
wo h no ing ha he esul s p o ided by he p oposed
echnique a e pe cep ually e y pleasing.
Table 2, Tab. 3,Tab. 4, Tab. 5, Tab. 6 and Tab. 7
shows he compa ison o a ious pa ame e s ob ained
o a ying alues o σ o he wo Field II syn he ic
images, e us and kidney. As can be no iced, he p o-
posed algo i hm pe o ms be e han he exis ing ech-
niques in e ms o EKI and PSNR, o noise a iance
σ2= 0.1,0.2and 0.3. The alues ob ained o EKI pa-
ame e gi es be e esul s e en a highe noise a i-
ances, clea ly showing be e edge keeping capabili y
o he p oposed algo i hm.
Also, as seen in he esul ables, p oposed echnique
gi es compa able esul s wi h he exis ing echniques
in e ms o SNR, CC, SSIM and FOM o σ2= 0.1.
A he same ime, as can be analyzed om he alues
ob ained by expe imen a ion ha he scheme is gi ing
compa able esul s in e ms o hese pa ame e s o
highe alues o σ2= 0.2and σ2= 0.3also. Thus, we
can summa ize ha he echnique pe o ms accep ably
well e en a highe noise le els.
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O iginal Image Noisy Image P oposed EMD BEMD BEMD Th esholding
CBF Th esholding Enhanced BEMD Laplacian CBF NLM CBF Con en ional EMD
Bila e al SRAD NLM OBNLM PMAD
(a) (b) (c) (d) (e)
( ) (g) (h) (i) (j)
(k) (l) (m) (n) (o)
Fig. 6: Syn he ic kidney: (a) O iginal image, (b) Noisy image o σ2= 0.1, Denoised images using he me hods, (c) P oposed
EMD echnique, (d) BEMD [31], (e) BEMD Th esholding [32], ( ) CBF Th esholding [36], (g) Enhanced BEMD [33],
(h) Laplacian CBF [34], (i) NLM CBF [35], (j) Con en ional EMD [30], (k) Bila e al [9], (l) SRAD [5], (m) NLM [11],
(n) OBNLM [16] and (o) PMAD [7].
Tab. 1: S uc u al Simila i y (SSIM) o a ious echniques.
Technique MVR ENL
P oposed echnique 18.81 ±2.63 5.41 ±2.37
BEMD [31] 18.51 ±3.76 5.25 ±2.79
BEMD h esholding [32] 18.13 ±4.02 5.18 ±2.82
CBF h esholding [36] 17.89 ±4.54 5.23 ±2.33
Enhanced BEMD [33] 18.02 ±4.93 5.14 ±2.64
Laplacian CBF [34] 17.95 ±4.82 5.11 ±2.18
NLM CBF [35] 17.63 ±4.22 5.01 ±2.13
Con en ional EMD [30] 17.91 ±5.32 5.01 ±2.54
Bila e al [9] 15.42 ±5.16 3.96 ±2.32
SRAD [5] 17.66 ±4.52 4.87 ±2.35
NLM [11] 17.01 ±4.14 4.91 ±2.15
OBNLM [16] 17.81 ±4.71 4.95 ±2.61
PMAD [7] 16.39 ±6.21 4.33 ±2.79
Figu e 6 shows he isual esul s ob ained by a ious
denoising algo i hms applied on he kidney image co -
up ed by a speckle o a iance 0.1. I is clea ly isible
ha he p oposed echnique is able o con ol he o e
smoo hness sho coming o some algo i hms and also
has be e pe cep ual quali y in e ms o he edges in
he image.
Fo he sake o comple eness, he e icacy o p oposed
echnique is also e alua ed by pe o ming expe imen s
on he eal ul asound image da abase aken om [39].
The eal images ha e h ee se s o da a namely kid-
ney, li e , and gall bladde images, each ha ing a ound
85 images. Th ee egions we e selec ed andomly o
all h ee se s and he MVR and ENL ha e been calcu-
la ed. The Fig. 7(a) shows he eal li e ul asound im-
age, whe e h ee andomly selec ed egions a e ma ked
which a e used o he calcula ion o MVR and ENL
alues. The Fig. 7(b) and Fig. 7(c) depic s he MVR
and ENL plo s ob ained o selec ed egions in he eal
li e image da abase o compa ing he pe o mance o
ou p oposed me hod wi h ha o exis ing one. I is
wo h no ing ha ou p oposed me hod wo ks ai ly
well compa ed o he o he s.
Table 1 shows he MVR and ENL mean alues along
wi h he s anda d de ia ion o he eal li e ul a-
sound image da abase. Two di e en egions we e se-
lec ed in each US image o MVR and ENL calcula-
ion. These egions we e andomly selec ed mainly in
homogeneous and edge egions o a pa icula US im-
age. Recons uc ed US images we e ob ained o all
he il e s and MVR and ENL alues we e calcula ed
in hese egions. I is o be no ed ha he bes MVR
and ENL alues a e ob ained o he p oposed il e .
Based on he esul s, he nex candida e in e ms o
he pe o mance was Laplacian CBF compa ed o he
exis ing me hods in e ms o MVR and ENL alues.
Simila expe imen s we e pe o med on kidney and
gall bladde eal ul asound image da a se s also, how-
e e , due o pauci y o space we ha e shown MVR and
ENL plo s o li e da abase only. The esul s ob ained
o he o he se s a e also in conjunc ion wi h he e-
sul s shown he e.
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(a)
MVR1 MVR2 MVR3
0
5
10
15
20
25
P oposed echnique
BEMD
BEMD h esholding
CBF h esholding
Enhanced BEMD
Laplacian CBF
NLM CBF
Con en io
nal BEMD
Bila e al
SRAD
NLM
OBNLM
PMAD
(b)
P oposed echnique
0
1
2
3
4
5
6
7
8
ENL1 ENL2 ENL3
BEMD
BEMD h esholding
CBF h esholding
Enhanced BEMD
Laplacian CBF
NLM CBF
Con en io
nal BEMD
Bila e al
SRAD
NLM
OBNLM
PMAD
(c)
Fig. 7: (a) Real li e image wi h selec ed egions, (b) MVR plo and (c) ENL plo .
Tab. 2: Co ela ion Coe icien (CC) o a ious echniques.
Technique
CC
Noise a iance σ2
Syn he ic e us image Syn he ic kidney image
0.1 0.2 0.3 0.1 0.2 0.3
P oposed echnique 0.95342 0.93070 0.92330 0.93840 0.92590 0.88210
BEMD [31] 0.95834 0.93007 0.92193 0.94284 0.90968 0.87969
BEMD h esholding [32] 0.95038 0.92852 0.91310 0.92435 0.88928 0.82736
CBF h esholding [36] 0.94911 0.90321 0.88398 0.91329 0.82987 0.77120
Enhanced BEMD [33] 0.95201 0.92654 0.87511 0.92643 0.88321 0.82101
Laplacian CBF [34] 0.93750 0.90440 0.89230 0.90760 0.85880 0.77830
NLM CBF [35] 0.94880 0.89530 0.87020 0.91020 0.83980 0.76430
Con en ional EMD [30] 0.95102 0.92555 0.87480 0.92645 0.87332 0.81060
Bila e al [9] 0.91368 0.84291 0.78464 0.84947 0.74776 0.67000
SRAD [5] 0.94191 0.87916 0.81739 0.91540 0.82920 0.75551
NLM [11] 0.93126 0.87093 0.82044 0.87618 0.78484 0.71328
OBNLM [16] 0.95155 0.90697 0.86630 0.90923 0.83734 0.77571
PMAD [7] 0.94638 0.88481 0.82668 0.90595 0.80801 0.72333
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Tab. 3: Signal o Noise Ra io (SNR) o a ious echniques.
Technique
SNR
Noise a iance σ2
Syn he ic e us image Syn he ic kidney image
0.1 0.2 0.3 0.1 0.2 0.3
P oposed echnique 14.0920 12.8840 11.4910 15.5620 13.9340 12.4030
BEMD [31] 14.0620 12.6740 11.4590 15.6020 13.6940 12.4430
BEMD h esholding [32] 13.7653 12.1382 11.2891 15.1528 12.9726 12.0628
CBF h esholding [36] 12.7261 9.9268 8.2108 12.6753 11.4367 8.9624
Enhanced BEMD [33] 13.9211 11.2167 10.3427 14.4563 12.2731 10.3821
Laplacian CBF [34] 13.7400 12.9200 11.3230 14.5660 13.8250 12.3670
NLM CBF [35] 12.6540 9.8660 8.0320 12.4530 11.3450 8.0630
Con en ional EMD [30] 13.9140 11.0110 10.2900 14.2440 12.0820 10.2030
Bila e al [9] 10.7200 7.9790 6.4897 10.7320 8.0182 6.5425
SRAD [5] 12.6000 9.2820 7.3429 13.7580 10.2860 8.4398
NLM [11] 11.7240 8.8585 7.3089 11.7650 8.9261 7.3852
OBNLM [16] 13.3050 10.3730 8.6871 13.3320 10.4920 8.8753
PMAD [7] 12.9410 9.4890 7.5779 13.2020 9.6131 7.6633
Tab. 4: Figu e o Me i (FOM) o a ious echniques.
Technique
FOM
Noise a iance σ2
Syn he ic e us image Syn he ic kidney image
0.1 0.2 0.3 0.1 0.2 0.3
P oposed echnique 0.88195 0.85261 0.81317 0.88341 0.85238 0.83860
BEMD [31] 0.82919 0.85146 0.81217 0.86334 0.86088 0.82560
BEMD h esholding [32] 0.81092 0.84838 0.80283 0.85392 0.84294 0.82934
CBF h esholding [36] 0.88392 0.82019 0.78291 0.85281 0.83827 0.77385
Enhanced BEMD [33] 0.83182 0.82791 0.79201 0.86389 0.83982 0.82739
Laplacian CBF [34] 0.88102 0.81890 0.77839 0.85930 0.83029 0.76321
NLM CBF [35] 0.88021 0.81820 0.77352 0.84920 0.82940 0.76429
Con en ional EMD [30] 0.82761 0.84320 0.78133 0.86112 0.83281 0.81143
Bila e al [9] 0.81285 0.74764 0.70383 0.77549 0.72620 0.69278
SRAD [5] 0.86349 0.78487 0.73090 0.83815 0.75237 0.73401
NLM [11] 0.87531 0.79219 0.75194 0.83151 0.78397 0.74317
OBNLM [16] 0.89364 0.84390 0.80875 0.88295 0.78922 0.76806
PMAD [7] 0.86438 0.79341 0.73724 0.85802 0.76742 0.71880
Tab. 5: Peak Signal o Noise Ra io (PSNR) o a ious echniques.
Technique
PSNR
Noise a iance σ2
Syn he ic e us image Syn he ic kidney image
0.1 0.2 0.3 0.1 0.2 0.3
P oposed Technique 24.983 23.117 22.748 24.821 22.281 21.842
BEMD [31] 24.946 23.077 22.383 24.322 22.188 21.158
BEMD h esholding [32] 24.126 22.764 21.853 23.019 21.934 21.021
CBF h esholding [36] 24.421 21.839 22.210 23.583 21.021 21.012
Enhanced BEMD [33] 22.593 21.294 21.256 22.593 21.245 20.183
Laplacian CBF [34] 23.453 20.987 20.837 24.839 20.548 20.634
NLM CBF [35] 24.332 21.712 22.590 23.383 20.628 21.522
Con en ional EMD [30] 22.398 20.671 20.330 22.317 20.672 19.821
Bila e al [9] 21.056 18.009 16.260 19.025 15.992 14.254
SRAD [5] 23.058 19.463 17.260 22.192 18.459 16.398
NLM [11] 22.336 19.310 17.594 20.288 17.239 15.518
OBNLM [16] 24.002 21.030 19.306 21.971 19.054 17.350
PMAD [7] 23.539 19.837 17.690 21.730 17.878 15.686
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