Reprinted from

REGULAR PAPER

Increasing Bandwidth of Ultrasound Radio Frequency Echoes Using Wiener Filter
for Improvement of Accuracy in Measurement of Intima–Media Thickness
Sho Kageyama, Hideyuki Hasegawa, and Hiroshi Kanai

Jpn. J. Appl. Phys. 52 (2013) 07HF04# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

REGULAR PAPER

Japanese Journal of Applied Physics 52 (2013) 07HF04
http://dx.doi.org/10.7567/JJAP.52.07HF04

Increasing Bandwidth of Ultrasound Radio Frequency Echoes Using Wiener Filter
for Improvement of Accuracy in Measurement of Intima–Media Thickness
Sho Kageyama1 , Hideyuki Hasegawa1;2 , and Hiroshi Kanai1;2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
E-mail: kanai@ecei.tohoku.ac.jp
2

Received November 21, 2012; revised December 27, 2012; accepted February 26, 2013; published online June 20, 2013
It is very important to make early diagnoses of atherosclerosis for the prevention of lifestyle-related diseases. The intima–media thickness (IMT) is
used as a diagnostic index of cerebrovascular diseases and atherosclerosis throughout the body including the coronary artery. In the field of the
medical diagnostics, ultrasonic equipment using a pulse–echo method is widely used. In conventional ultrasonic diagnostic equipment, ultrasonicimages are obtained by receiving ultrasonic echoes and converting their amplitudes into brightness. In general, ultrasonic B-mode images aredegraded by the narrow-band characteristics of the ultrasonic transducer. In the present study, a method was proposed for shortening the lengthsof the received ultrasonic pulses from an object of interest using a Wiener filter. As a result, the lengths of ultrasonic pulses were shortened andthe visibility of interfaces of the intima–media complex of the carotid arterial wall was improved by the proposed method, which realizes accurate
measurement of the IMT. # 2013 The Japan Society of Applied Physics

1. Introduction

In recent years, cardiovascular diseases such as myocardial
infarction have been increasing in Japan with the westernization of the diet, the aging of society, and a chronic lackof exercise due to modern lifestyles, which are the maincauses of lifestyle-related diseases. It is very important tomake early diagnoses of atherosclerosis for the preventionof these diseases. Ultrasonic diagnostic equipment has been
widely used in clinical situations for various reasons
including less physical and mental hardship to patients andnon-invasiveness making it suitable for repetitive diagnosis
in the early stages of diseases.
In the very early stages of atherosclerosis, it is known thatthe surface of the intima in the arterial wall becomes roughowing to insults to endothelial cells and the internal elastic
lamina.1) Thus, the spatial resolution in the direction of
the ultrasound beam should be comparable to the thicknessof the endothelial cell in order to diagnose the surface
roughness.2) In addition, the intima–media thickness (IMT)
is used as a diagnostic index of atherosclerosis andcerebrovascular diseases throughout the body including thecoronary artery.3,4)
In the ﬁeld of medical diagnostics, ultrasonic diagnostic
equipment using a pulse–echo method is widely used. In
conventional ultrasonic diagnostic equipment, ultrasoundimages are obtained by receiving ultrasonic echoes andconverting their amplitudes into brightness. There is aproblem in the reconstructed images that aﬀects clinicaldiagnosis. Ultrasonic images are degraded by a speciﬁc
pattern called speckle noise. The speckle noise exhibits apattern that occurs as a result of the random interference ofultrasonic echoes scattered in the living tissue, and thepattern might be misrecognized as nonuniformity of theliving tissue due to its appearance. In general, an ultrasonictransducer used in ultrasonic diagnostic equipment has
narrow-band characteristics. Therefore, the emitted ultrasonic pulses exhibit reverberation5) and, thus, the boundariesof the obtained images are blurred. For this reason, it isdiﬃcult to measure the IMT of the carotid arterial wall
accurately, and it is diﬃcult to diagnose atherosclerosis at an
early stage. The accuracy of IMT measurement would be

improved if the lengths of received ultrasonic pulses could
be shortened, which means that the bandwidth of thereceived ultrasonic echo signal is broadened.
Methods have been developed for broadening thefrequency characteristics of the received ultrasonic echoes
to shorten the pulse length. These methods use spatial
compounding6–8) and frequency compounding,8–16) resulting
in improved spatial resolution. The spatial-compounding
method is an image-synthesizing method that uses diﬀerent
images obtained by emitting ultrasound beams from
diﬀerent directions to the same region. The frequencycompounding method also synthesizes diﬀerent images,
which have diﬀerent speckle patterns because ultrasonicsignals with diﬀerent center frequencies are used. However,
the time resolution is degraded in the spatial-compounding
method and the spatial resolution is degraded in thefrequency-compounding method because images are compounded at diﬀerent spatial resolutions.8) Moreover, inconventional ultrasonic transducers, it is known that speckle
reduction using these compounding methods is not eﬀective
because they have narrow-band frequency characteristics.17)
In the present study, we focus on a ﬁltering method using
a Wiener ﬁlter18–22) as a method for shortening the lengthsof the received ultrasonic pulses. Ideally, the received
ultrasonic echoes are expressed as a convolution between the
distribution of the scattering coeﬃcients of objects, whichhave a wide-band characteristic, and the impulse response of
the ultrasonic transducer (narrow band). The Wiener ﬁlter isdesigned as an inverse ﬁlter using the transfer characteristicsof the transducer, which has narrow-band characteristics,
and is weighted using the signal-to-noise ratio (SNR) to
broaden the frequency characteristics of the transducer inthe frequency range with a good SNR and also attenuate thepower of the received echo signal in the frequency range
with a low SNR. A received ultrasonic pulse is shortenedby broadening its frequency characteristics using the Wiener
ﬁlter.
2. Principles
2.1 Principle of Wiener filter M j ð!Þ

Figure 1 shows a block diagram illustrating how to estimate
the spatial distribution of the reﬂectivity of an object f^i;j ðtÞ,07HF04-1# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 52 (2013) 07HF04

S. Kageyama et al.

(a)noise Ni,j (ω)
true reflectivity

Gi,j (ω)

Hj (ω)
transfer function

M j (ω)^Fi,j (ω)−50

Wiener filter

Fig. 1. Block diagram of the system for obtaining estimate F^i; j ð!Þ using

Wiener ﬁlter M j ð!Þ.

(b)

where F^i;j ð!Þ is its frequency spectrum. In Fig. 1, Gi;j ð!Þ,H j ð!Þ, Ni;j ð!Þ, and M j ð!Þ are the frequency spectra of theecho from an object, the transfer function of the transducer,
noise, and the impulse response of the Wiener ﬁlter,
respectively. In addition, i and j are the beam number andframe number, respectively. In the case of the measurementof an object with movement such as a carotid artery, thereceived echo varies frame by frame. Therefore, in thepresent study, the transfer function H j ð!Þ and the Wiener
ﬁlter M j ð!Þ are estimated for each frame.
Wiener ﬁlter M j ð!Þ is determined so as to minimize themean squared diﬀerence between the spectrum of the true
reﬂectivity Fi;j ð!Þ and its model F^i;j ð!Þ. The estimate F^i;j ð!Þ
is given byF^i;j ð!Þ ¼ Gi;j ð!Þ  M j ð!Þ
Gi;j ð!Þ  H j ð!Þ
;ð1Þ
¼
jH j ð!Þj2 þ PN ð!Þ=PF ð!Þ
where PN ð!Þ and PF ð!Þ are the averaged power spectraof the noise and the true reﬂectivity Fi;j ð!Þ, respectively.18–22) However, the power spectrum PF ð!Þ of thetrue signal Fi;j ð!Þ cannot be obtained, because the true
reﬂectivity Fi;j ð!Þ is not obtained before applying the
Wiener ﬁlter M j ð!Þ to the received signal Gi;j ð!Þ; thus,
there is an inconsistency in the expression of the Wiener
ﬁlter M j ð!Þ. Traditionally, for this problem, the power
spectrum obtained by averaging the power spectra [Gi;j ð!Þ]is assumed as the power spectrum PF ð!Þ of the true
reﬂectivity.4) However, Gi;j ð!Þ includes the transfer characteristics H j ð!Þ. Therefore, it is not appropriate to obtain
the weighting function PN ð!Þ=PF ð!Þ using the received
ultrasonic echo Gi;j ð!Þ. Therefore, we evaluated the SNR
using the magnitude-squared coherence function (MSCF)23)
because PN ð!Þ=PF ð!Þ is the inverse of the SNR. The MSCFj i ð!Þj2 is given byj i ð!Þj2 ¼

jE j ½Gi;j ð!Þ  Gi;jþ1 ð!Þj2
E j ½jGi;j ð!Þj2   E j ½jGi;jþ1 ð!Þj2 ;

ð2Þwhere  is the complex conjugate. The MSCF j i ð!Þj2 isa function evaluating the phase coherency of echoes in
diﬀerent frames. Assuming that the noise is random, it isconsidered that the signal component has phase coherency
and that the noise component is not coherent. Therefore,
using the MSCF j i ð!Þj2 , the SNR WSNR ð!Þ is given by
WSNR ð!Þ ¼

0

1

Nbeam
X1

Nbeam

i¼0

j i ð!Þj2;
1  j i ð!Þj2

ð3Þ

where Nbeam is the number of beam positions.23,24)
Figure 2(a) shows an example of the MSCF and Fig. 2(b)shows the SNR, each of which was obtained by Eq. (3). We
measured a silicone plate in water using a 10-MHz linear| γ i (ω)|2

amplitude [dB]Fi,j (ω)

received signal

estimate

1 − | γ i (ω)|

2

50

0

signal−to−noise ratio
0

5

10

15

20

frequency [MHz]Fig. 2. (Color online) (a) Magnitude-squared coherence function j i ð!Þj2

and 1  j i ð!Þj2 (i ¼ 150), (b) average signal-to-noise ratio WSNR ð!Þ
obtained using magnitude-squared coherence function j i ð!Þj2 in themeasurement of a silicone plate at 13.5 mm depth in a water tank.

array probe (the sampling frequency of ultrasonic RF echoes
was 40 MHz and the frame rate was 30 Hz). As shown in
Fig. 2, ideally it is desirable for a transducer to have a wide
bandwidth. However, the transducer used in measurement
has narrow-band characteristics. As a result, the measured
SNR also shows narrow-band characteristics. The Wiener
ﬁlter, which applies weights to the frequency characteristicsof the ﬁlter by considering the inverse of the SNR, operates
as an inverse ﬁlter in the frequency range with a good SNR
whereas the ﬁlter is suppressed in the frequency range witha low SNR. Therefore, the ﬁlter works in a very limited
frequency band when the ﬁlter is directly weighted by the
SNR.
2.2 Identification of transfer function H j ð!Þ
2.2.1 Estimation of power of transfer function H j ð!Þ

The important issue in designing the Wiener ﬁlter is how to
identify the transfer function H j ð!Þ. When image processing
is carried out using the Wiener ﬁlter, H j ð!Þ is commonly
obtained from the point spread function (PSF).25–27) The PSF
can be obtained by measuring an echo from a point scatterer.
This can be done by measuring a ﬁne wire placed in a watertank. However, biological tissues exhibit frequency-dependent attenuation, which changes the waveform of an
ultrasonic echo. Therefore, it is desirable to obtain the PSF
from echoes from an object of interest. However, when an
object has many point scatterers, there are many dips in the
power spectrum of an echo signal due to interference, andsuch frequency characteristics cannot be used as the PSF.
In the transfer system shown in Fig. 1, Gi;j ð!Þ is thefrequency spectrum of the echo signal obtained byultrasound equipment. Assuming that fi;j ðtÞ is the group of
impulses, it is considered that Gi;j ð!Þ is the sum of H j ð!Þ
with diﬀerent phase characteristics due to time delays of theimpulses. The frequencies at which dips occur in the power
spectrum jGi;j ð!Þj2 depend on the time delays of echoes.
From this fact, frequencies with dips should be random frombeam by beam due to the random distribution of scatterers in

07HF04-2# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 52 (2013) 07HF04

S. Kageyama et al.

tissue. Therefore, the power spectrum of the transfer
function with noise jH j0 ð!Þj2 is obtained by smoothing out
the dips in jGi;j ð!Þj2 by averaging fjGi;j ð!Þj2 g obtained at
diﬀerent beam positions as follows:X1
1 NbeamjH j0 ð!Þj2 ¼
jGi;j ð!Þj2
Nbeam i¼0
¼


¼

Nbeam
X1

Nbeam

i¼0

1

Nbeam
X1

Nbeam

i¼0

amplitude [dB]150jG0i;j ð!Þ þ Ni;j ð!Þj2

0−50

ðjG0i;j ð!Þj2 þ jNi;j ð!Þj2 Þ

1

Nbeam
X1

Nbeam

i¼0

0
B

Nbeam
X1

@

0

5

1
2

jNi;j ð!Þj C
C
C;
C
X
A
jG0i;j ð!Þj2

B
i¼0
jG0i;j ð!Þj2 B
B1 þ Nbeam 1

reference beam of received echonoise
10
frequency [MHz]15

20

Fig. 3. (Color online) Power spectrum of the reference beam of thereceived echo jGi;j ð!Þj2 and that of noise jN^ j ð!Þj2 obtained from the signal
measured with no object in a water tank.

i¼0

jH j ð!Þj2 ¼
¼

1

Nbeam
X1

Nbeam

i¼0

1

Nbeam
X1

Nbeam

i¼0

0

beam No. 1
beam No. 2
beam No. 3

−50

0

5

10
frequency [MHz]15

20

Fig. 4. (Color online) Generation of dips of the power spectra fjGi;j ð!Þj2 g

in in vivo measurement at 5.0, 15.0, and 25.0 mm in the lateral direction(i ¼ 50, 150, and 250, respectively).

2.2.2 Estimation of phase of transfer function H j ð!Þ

jG0i;j ð!Þj2
ðjGi;j ð!Þj2  jN^ j ð!Þj2 Þ:50amplitude [dB]

ð4Þwhere G0i;j ð!Þ is the frequency spectrum of the received echo
without noise Ni;j ð!Þ. In Eq. (4), the terms G0
i;j ð!Þ  Ni;j ð!Þ
and G0i;j ð!Þ  Ni;j
ð!Þ are assumed to become zero upon
averaging because Gi;j ð!Þ and Ni;j ð!Þ are uncorrelated. To
obtain jH j ð!Þj2 correctly, jNi;j ð!Þj2 must be removed from
Eq. (4). In the present study, the power spectrum of noise
jNi;j ð!Þj2 was estimated from the signal obtained during themeasurement with no target in a water tank so that there
was no echo (only noise is contained in the measured
signal). The estimate of the power spectrum of noisejN^ j ð!Þj2 was obtained by averaging the power spectra of
the signal with no target measured at all beam positions.
The power spectrum jH j ð!Þj2 of the transfer function isestimated by removing the estimated power spectrum ofnoise jN^ j ð!Þj2 from that of the received echo jGi;j ð!Þj2 asfollows:

ð5Þ

The power spectrum of noise jN^ j ð!Þj2 is shown in Fig. 3
with an example of the power spectrum of a received echo
jGi;j ð!Þj2 measured in vivo. Ultrasonic echoes from theposterior wall of a carotid artery were measured in vivo andthe reference power spectra at 5.0, 15.0, and 25.0 mm in thelateral direction (i ¼ 50, 150, and 250, respectively) are
shown in Fig. 4.
As shown in Fig. 4, some dips in the power spectra
occurred at diﬀerent frequencies owing to the interference of
echoes from a large number of point scatterers. As a result,the phase of the ultrasonic RF echoes was diﬀerent at
diﬀerent ultrasonic beam positions. The magnitude of thetransfer function jH j ð!Þj estimated from the power spectraof the received echoes jGi;j ð!Þj2 using Eq. (5) is shown in
Fig. 5, and jGi;j ð!Þj2 at 15.0 mm (i ¼ 150; j ¼ 0) in thelateral direction is also shown in the same ﬁgure. As shownin Fig. 5, some dips that occurred in jGi;j ð!Þj2 were
suppressed by beam averaging, and the spectrum envelope
was obtained. This spectrum envelope was used as themagnitude of the transfer function jH j ð!Þj.

Section 2.2.1 proposed a method for estimating the magnitude jH j ð!Þj of a transfer function. However, as shown in
Eq. (1), it is necessary to obtain the phase term of thetransfer function. Therefore, this section describes amethod for estimating the phase term of the transfer
function.
In the present study, the magnitude jH j ð!Þj of the transfer
function was estimated using ultrasonic echoes from an
object of interest because jH j ð!Þj is inﬂuenced by thefrequency-dependent attenuation of tissue. However, the= H j ð!Þ should not be inﬂuenced by the attenuation ofphase = H j ð!Þ is obtained
tissue. Therefore, in the present study, using the emitted ultrasonic pulse received by a hydrophone
in a water tank. The signal sðtÞ [whose frequency spectrum isdenoted by Sð!Þ] received by the hydrophone is composedof the frequency characteristics of the driving signal Xð!Þand the transfer function of the ultrasonic transducer Yt ð!Þ.
By assuming that the driving signal is an impulse, the phase= H j ð!Þ of the transfer function is obtained as 
= H j ð!Þ ¼

=2 Sð!Þ because H j ð!Þ is composed of the frequency
characteristics Yt ð!Þ and Yr ð!Þ of transmitting and receiving
transducers, respectively. In the present study, the sametransducer was used for transmitting and receiving [Yt ð!Þ ¼
Yr ð!Þ ¼ Yð!Þ].

07HF04-3# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 52 (2013) 07HF04

S. Kageyama et al.

removed by estimating the regression line of the phase
spectra using the least-squares method. Twice the residual= H j ð!Þ of the transfer function.
phase was used as the phase amplitude [dB]50

2.3 Control parameter  used for weighting function
0

received echo |Gi,j (ω) |spectrum envelope |Hj (ω) |2
2

−50
0

5

10
frequency [MHz]15

20

Fig. 5. (Color online) Spectrum envelope (corresponding to jH j ð!Þj)obtained by averaging the power spectra of the received echoes fjGi; j ð!Þjg
from a silicone plate with respect to beam position and the power spectrumof the received RF echo jGi; j ð!Þj at the lateral position of 15.0 mm(i ¼ 150).

1
normalized amplitude(a)sampling frequency 1 GHz
sampling frequency 40 MHz

0.5
0
−0.5
depth [mm]0.1 mm(b)0phase [rad]

−50

−100
original
unwrapped
least−square line
time delay deleted

−150

−200

0

5

10
frequency [MHz]15

Section 2.1 described a method which estimates the SNR,
PF ð!Þ=PN ð!Þ, using the MSCF. In addition, the relative
magnitude of the weighting function PN ð!Þ=PF ð!Þ to thetransfer function H j ð!Þ needs to be determined. The Wiener
ﬁlter M j ð!Þ behaves as an inverse ﬁlter 1=H j ð!Þ when the
SNR is much larger than the magnitude of the transfer
function jH j ð!Þj. On the other hand, if the SNR is small, theWiener ﬁlter M j ð!Þ behaves as a matched ﬁlter. Methods
using a real constant to control the contribution of theweighting function have been developed,27,28) and methods
in which the weighting function PN ð!Þ=PF ð!Þ is controlled
by multiplying by a control parameter , which is called
pseudo inverse ﬁltering, have also been developed.29–31)
The former limits the eﬀect of the Wiener ﬁlter M j ð!Þ byassuming that the SNR is constant at every frequency. The
latter realizes a wider bandwidth of the ﬁlter by controllingthe eﬀect of the weighting function PN ð!Þ=PF ð!Þ. A smaller
control parameter  ( 0) is usually preferred in order toimprove the spatial resolution at the expense of increased
noise. In a conventional Wiener ﬁlter,  ¼ 1:0. On the other
hand, the ﬁlter works as an inverse ﬁlter at every frequency
when  is low, corresponding to the assumption of a high
SNR at all frequencies. In such a case, the noise in thefrequency band away from the resonant frequency of atransducer tends to be ampliﬁed even though better spatial
resolution is realized. Thus, the improvement of the spatial
resolution was evaluated using the received echoes from a
ﬁne wire (13 m in diameter), which corresponds to a point
scatterer. A 10-MHz linear array probe was used, thesampling frequency of the ultrasonic RF echo was 40 MHz,and the frame rate was 30 Hz. The magnitudes of the transfer
function H j ð!Þ and weighting function PN ð!Þ=PF ð!Þ wereboth normalized to limit control parameter  to between 0
and 1 as follows:1
H j ð!Þjnormalized ¼ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ  H j ð!Þ;!n
X
jH j ð!Þj2

20

!¼0

Fig. 6. (Color online) (a) Emitted ultrasonic pulse sampled at 1 GHz andsame pulse downsampled to 40 MHz. (b) Phase spectra of the signal in (a).

An ultrasonic pulse received by a hydrophone (FORCE
Technology MHA9-150) placed in a water tank is shown in
Fig. 6(a). In the present study, modiﬁed ultrasonic diagnostic
equipment (ALOKA SSD-6500 with a 10-MHz linear arrayprobe) was used for transmitting and receiving ultrasonicpulses. The signal received by the hydrophone was sampled
at 1 GHz using an oscilloscope (Tektronix TDS-2014). The
signal acquired by the oscilloscope was downsampled to
40 MHz because the ultrasonic echo signal obtained by the
SSD-6500 diagnostic equipment was sampled at 40 MHz.
= Sð!Þ of the signal
Figure 6(b) shows the phase spectrum 
received by the hydrophone. There is a constant slope in theentire phase spectrum owing to the time delay of ultrasonicpropagation from the linear array to the hydrophone. The
phase change due to the ultrasonic propagation is proportional to the frequency. Therefore, the constant slope wasð6ÞPN ð!Þ 1
PN ð!Þ
;¼ !n PF ð!Þ normalized X
PF ð!Þ
PN ð!Þ
!¼0

ð7Þ

PF ð!Þ

where !n is the Nyquist angular frequency. The spatial
resolution (deﬁned by the full width at half maximum) was
evaluated by applying the Wiener ﬁlter M j ð!Þ at diﬀerent
values of  to the echo from the ﬁne wire, as shown in
Fig. 7(a). The optimal control parameter opt was 0.01706
as shown in Fig. 7(a). As shown in Fig. 7(b), the durationof the received echo from a ﬁne wire was shortened (thefull width at half maximum was improved from 0.20 to0.12 mm). Using this optimal control parameter opt , theproposed Wiener ﬁlter is deﬁned as follows:
H j ð!Þjnormalized
M j ð!Þ ¼: ð8Þ
PN ð!Þ jH j ð!Þjnormalized j2 þ opt P ð!Þ 07HF04-4F

normalized# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

S. Kageyama et al.

beam No. 1
1.0 mm0.125

0.11650.01706

0.11640.115

0.11630.1162
0.010

0

0.015

0.020

0.025

0.030

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
control parameter β

1Conventional

Proposed1

received echo g i,j ( t )^estimated fi,j ( t )10.0 mm0
normalized amplitude

beam No. 3

0.11660.110(b)beam No. 2

0.120

depth [mm](a)full width at half maximum [mm]Jpn. J. Appl. Phys. 52 (2013) 07HF04

lateral distance [mm]Fig. 8. (Color online) (a) Conventional B-mode image of a carotid arteryof a posterior wall and (b) B-mode image obtained by applying proposed
Wiener ﬁlter M j ð!Þ with optimal control parameter opt ¼ 0:01706.

−1
1

received echo g i,j ( t )^estimated fi,j ( t )0.5

00.1 mmdepth [mm]Fig. 7. (Color online) (a) Evaluation of the spatial resolution using thereceived RF echo from a ﬁne wire (13 m in diameter) for determining
control parameter  of the weighting function PN ð!Þ=PF ð!Þ. (b) Received
RF echo gi;j ðtÞ from a ﬁne wire (13 m in diameter), the estimate f^i;j ðtÞ, andtheir envelopes obtained using the proposed Wiener ﬁlter M j ð!Þ controlled
by the optimal control parameter opt .

3. Experimental Results and Discussion

Figure 8 shows a conventional B-mode image of a carotid
artery of a 25-year-old healthy male and the B-mode image
obtained by the proposed Wiener ﬁlter with the optimal
control parameter opt , which was determined in themeasurement of a ﬁne wire as described in Sect. 2.3. As
shown in Fig. 8, the noise in the intravascular lumen was
reduced by the proposed Wiener ﬁlter M j ð!Þ. In addition, thebrightnesses of the adventitia and intima in the posterior wall
became distinct.
The power spectra of the original echo gi;j ðtÞ and theestimate f^i;j ðtÞ at 5.0, 15.0, and 25.0 mm in the lateral
direction (i ¼ 50, 150, and 250, corresponding to beamNos. 1, 2, and 3 in Fig. 8, respectively), and the power
spectra of the transfer function H j ð!Þ, weighting function
PN ð!Þ=PF ð!Þ, and Wiener ﬁlter M j ð!Þ ( j ¼ 0) are shown in
Fig. 9. The power spectra of the estimates were broadenedby the proposed Wiener ﬁlter as shown in Fig. 9. However,in the power spectrum of the weighting function in Fig. 9,
the peak frequency of 3 MHz was lower than that of thenominal center frequency of 10 MHz. It is considered thatthe movement of the carotid artery degraded the coherency

among signals, particularly in the high-frequency range,
because the motion (corresponding to the time shift of theecho signal) leads to a larger phase shift at higher
frequencies. Therefore, the SNR at low frequencies became
larger than that at high frequencies. In future work,
correction of the inﬂuence of the movement of a target inin vivo measurement needs to be investigated.
The received ultrasonic RF echoes fgi;j ðtÞg at 5.0, 15.0,
and 25.0 mm in the lateral direction (i ¼ 50, 150, and 250,
respectively) and the estimates f f^i;j ðtÞg obtained using the
proposed Wiener ﬁlter M j ð!Þ are shown in Fig. 10(a), andthe envelopes are shown in Fig. 10(b). In addition, as shownin Fig. 10(b), the lumen–intima boundary (LIB) and media–
adventitia boundary (MAB) became distinct, and thus, it
became easier to measure the IMT, especially in beams
No. 2 and 3.
In the present study, the magnitude of the transfer function(corresponding to the PSF), jH j ð!Þj, was determined using
echoes in the whole measured region. Therefore, theperformance of the proposed Wiener ﬁlter would be
degraded if the frequency characteristics of echoes werechanged by undesirable phenomena, such as frequencydependent attenuation of the propagation medium. For
measurement of the carotid artery, the above-mentioned
method of designing the ﬁlter is eﬀective because echoesfrom the media–adventitia interface of the arterial wall,
which is the object of interest, are dominant in the region
measured in the present study. However, in future work, theperformance of the proposed ﬁlter should be improved bydesigning the ﬁlter region by region.
4. Conclusions

In this study, we proposed a method for improving the
spatial resolution of an ultrasonic image, that is, broadening
the frequency characteristics of the received echoes ofan echo signal, using a Wiener ﬁlter. To determine an

07HF04-5# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 52 (2013) 07HF04

S. Kageyama et al.

amplitude [dB]

50
50
0
0
beam No. 1
beam No. 2
beam No. 3

−50
0

5

original
10frequency [MHz]

−50
20

0

5

estimated10
frequency [MHz]

15

20

−50

0
amplitude [dB]15

beam No. 1
beam No. 2
beam No. 3

50
−50
−100

0

transfer function−100

0weighting function

510
15
frequency [MHz]200wiener filter

51015
frequency [MHz]

20

0

5
10
15
frequency [MHz]20

Fig. 9. (Color online) Power spectra of original echoes fgi; j ðtÞg and estimates f f^i; j ðtÞg at 5.0, 15.0, and 25.0 mm in the lateral direction (i ¼ 50, 150, and250, respectively), and the power spectra of the transfer function H j ð!Þ, weighting function PN ð!Þ=PF ð!Þ, and Wiener ﬁlter M j ð!Þ ( j ¼ 0).

(a)

1

(b)

original
proposed1
original
proposed
0.5

0beam No. 1
01

1

normalized amplitude

normalized amplitude

beam No. 1−10beam No. 2

0.5
beam No. 2

−1

0

1

1

0

0.5
beam No. 3
beam No. 3−10
1.0 mmdepth [mm]depth [mm]1.0 mmFig. 10. (Color online) Received ultrasonic RF echoes fgi;j ðtÞg at 5.0, 15.0, and 25.0 mm in the lateral direction (i ¼ 50, 150, and 250, respectively) and theestimates f f^i; j ðtÞg, and their envelopes obtained using the proposed Wiener ﬁlter M j ð!Þ ( j ¼ 0).

appropriate weighting function for the Wiener ﬁlter, theSNR was estimated using the magnitude-squared coherencefunction. In the proposed Wiener ﬁlter, the power of thetransfer characteristic was obtained by averaging the power
spectra of received echoes from an object of interest, each ofwhich has many dips. The phase of the transfer characteristic
was obtained from the phase of the ultrasonic pulse emitted
from diagnostic equipment. Also, the optimal parameter
controlling the eﬀect of the weighting function wasdetermined by evaluating the spatial resolution using thereceived echo from a ﬁne wire. The proposed method was
also applied to echoes from the carotid artery. The spatial
resolution of the B-mode image was improved and theintima–media thickness of the posterior wall could be
identiﬁed more easily.

1) E. Sho, M. Sho, T. M. Singh, H. Nanjo, M. Komatsu, C. Xu, H. Masuda,

and C. K. Zarins: Exp. Mol. Pathol. 73 (2002) 142.

2) K. Kitamura, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 51 (2012)

07GF08.
3) N. Ibrahim, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 51 (2012)

07GF07.
4) C. Arihara, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 45 (2006)

4727.
5) T. Kimura, H. Kanai, and N. Chubachi: IEICE Trans. Fundam. Electron.

Commun. Comput. Sci. E78-A (1995) 1677.
6) S. Huber, M. Wagner, M. Medl, and H. Czembirek: Ultrasound Med. Biol.

28 (2002) 155.
7) M. Pernot, M. Tanter, J. Bercoﬀ, K. R. Waters, and M. Fink: IEEE Trans.

Ultrason. Ferroelectr. Freq. Control 51 (2004) 606.
8) J. R. Sanchez and M. L. Oelze: IEEE Trans. Ultrason. Ferroelectr. Freq.

Control 56 (2009) 1327.

9) P. A. Magnin, O. T. von Ramm, and F. L. Thurstone: Ultrason. Imaging 4(1982) 267.
10) G. E. Trahey, J. W. Allison, S. W. Smith, and O. T. von Ramm: Ultrason.

07HF04-6# 2013 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 52 (2013) 07HF04

S. Kageyama et al.

Imaging 8 (1986) 151.

22) J. Jan: Medical Image Processing, Reconstruction and Restoration:

Concepts and Methods (CRC Press, Boca Raton, FL, 2005).

11) I. Akiyama, N. Yoshizumi, and K. Nakamura: Proc. IEEE Ultrasonics
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)

Symp., 2009, p. 2712.
J. G. Abbott and F. L. Thurstone: Ultrason. Imaging 1 (1979) 303.
S. M. Gehlbach and F. G. Sommer: Ultrason. Imaging 9 (1987) 92.
H. E. Melton, Jr. and P. A. Magnin: Ultrason. Imaging 6 (1984) 159.
V. L. Newhouse, N. M. Bilgutay, J. Saniie, and E. S. Furgason: Ultrason.
Imaging 20 (1982) 59.
F. L. Lizzi, M. E. Elbaum, and E. Feleppa: U.S. Patent 4561019 (1985).
N. Yoshizumi, S. Saito, D. Koyama, K. Nakamura, A. Ohya, and I.
Akiyama: J. Med. Ultrason. 36 (2009) 53.
A. Rosenfeld and A. C. Kak: Dijitaru Gazo Shori (Digital Image
Processing) (Kindai Kagaku, Tokyo, 1978) [in Japanese].
W. K. Pratt: Digital Image Processing (Wiley, New York, 1978).
H. C. Andrew and B. R. Hunt: Digital Image Restoration (Prentice Hall,
Upper Saddle River, NJ, 1997).
M. Saito: Dijitaru Gazo Shori (Digital Image Processing) (Tokai
University Press, Hiratsuka, 1986).

23) H. Kanai: Oto to Shindo no Supekutoru Kaiseki (Spectrum Analysis ofSound and Vibration) (Corona, Tokyo, 2008) [in Japanese].
24) T. Fukushima, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 50 (2011)

07HF02.
25) T. Taxt and R. Jiřı́k: IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51(2004) 163.
26) D. Iracà, L. Landini, and L. Verrazzani: IEEE Trans. Ultrason. Ferroelectr.

Freq. Control 36 (1989) 216.

27) W. Yeoh and C. Zhang: IEEE Trans. Biomed. Eng. 53 (2006) 2001.
28) S. Sin and C. Chen: IEEE Trans. Image Process. 1 (1992) 3.
29) S. Masy, T. F. Johansen, and B. Angelsen: J. Acoust. Soc. Am. 113(2003) 2009.
30) S. Hantscher, A. Reisenzahn, and C. G. Diskus: IET Rader Sonar Navig. 2(2008) 315.
31) J. R. Fienup, D. K. Griﬃth, L. Harrington, A. M. Kowalczyk, J. J. Miller,

07HF04-7

and J. A. Mooney: Proc. SPIE 4792 (2002) 1.

# 2013 The Japan Society of Applied Physics