REGULAR PAPER

Japanese Journal of Applied Physics 54, 07HF05 (2015)
http://dx.doi.org/10.7567/JJAP.54.07HF05

High-range-resolution imaging using frequency domain interferometry
with stabilization techniques for real-time vascular ultrasound
Hirofumi Taki1*, Kousuke Taki2, Makoto Yamakawa3, Tsuyoshi Shiina4, Motoi Kudo2, and Toru Sato5
1

Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Department of Anatomy, Shiga University of Medical Science, Otsu 520-2192, Japan
3
Advanced Biomedical Engineering Research Unit, Kyoto University, Kyoto 606-8501, Japan
4
Graduate School of Medicine, Kyoto University, Kyoto 606-8501, Japan
5
Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
E-mail: taki@ecei.tohoku.ac.jp
2

Received December 7, 2014; accepted February 9, 2015; published online June 10, 2015
In the present study, we employed two techniques to acquire high-range-resolution images of human carotid arteries in vivo using frequency
domain interferometry and the Capon method. One technique ensures the robust depiction of artery interfaces; the other suppresses thedeterioration of the imaging performance due to variation of the echo waveform. We applied the proposed method to raw data obtained using acommercial ultrasonographic device with a 7.5 MHz linear array probe. Our method succeeded to depict a horizontal 0.15-mm-thick agar
membrane stably, and the standard deviation of the estimated depth was suppressed to 26.7% of that obtained using the conventional method.
Our method also succeeded in acquiring high-range-resolution images of six human carotid arteries in vivo. Requiring 0.06 s on a desktop PC witha single CPU for a 1 ' 2 cm region of interest, our method is suitable for real-time imaging. © 2015 The Japan Society of Applied Physics

1.

Introduction

Cardiovascular disease remains a substantial cause of
mortality.1) The assessment of cardiac function is one of
the main clinical issues.2–5) Another clinical issue is arterial
plaques whose rupture or erosion leads to abrupt thrombosis,
and the urgent demand is how to establish a marker ofvulnerable plaques.6) Transcutaneous ultrasound B-mode
imaging is widely used to detect plaques in carotid arteries.7)
Thus, improving the spatial resolution of imaging would
bring a major advancement in identiﬁcation of high-risk
plaques.8) Other trials focus on the measurement of carotid
arterial stiﬀness.9–11) Carotid artery wall thickness, known as
the carotid intima-media thickness (CIMT), determined byultrasonography (US), is also a measure of early atherosclerosis.9,12,13) Because these measures of arterial stiﬀness
lack suﬃcient reliability for clinical routine applications,14)
improvement in the range resolution of US is needed toestablish more reliable markers of cardiovascular risk.
Using a higher transmit frequency improves the spatial
and contrast resolutions because narrower beam and pulse
widths can be used; however, a high-frequency pulse is
rapidly attenuated, limiting its practicality.15) Alternatively,
tissue harmonic imaging and spatial compound imaging
suppress speckle noise and consequently improve the contrast
and spatial resolution. However, it is diﬃcult to acquirea range resolution higher than one-half the pulse length
because each of these modes generally uses a data-independent delay-and-sum beamformer with a set of predetermined weights.15)
In the ﬁeld of radio imaging, since the 1960s, adaptive
beamforming algorithms have been proposed to improve
spatial resolution without using high transmit frequencies.
One common technique is the use of a Capon beamformer,
which uses a set of weights calculated by minimizing theoutput power, subject to the constraint that a desired signal
gives a constant response.16) In US, signals from diﬀerent
targets strongly correlate. Therefore, strategies involving
output-power minimization do not work because theinterference signals cancel the desired signal.17,18) Spatial-

averaging techniques suppress the cross-correlation between
the signals from diﬀerent targets.19,20) Thus, several groups
have used the Capon method with spatial averaging to
improve the lateral resolution in US.21–23) Another approachis the use of eigenvalue adaptive beamforming algorithms.24,25) Because these methods introduced the assumption that the targets are modeled as points, the grid size
should be small enough to achieve suﬃcient spatial
resolution and robustness. However, this incurs highcomputational cost, indicating the diﬃculty of using thesemethods with real-time signal processing. They also require
high signal-to-noise ratio (SNR) conditions.
Frequency domain interferometry (FDI) imaging has been
proposed to improve the range resolution in atmosphericradar 26) and optical coherence tomography;27) however, thesemethods involve the use of narrow-band signals, and thus
blind application of these methods to US is unlikely to
succeed. In a previous study, we proposed a high range
resolution method based on FDI with an adaptive beamforming algorithm.28,29) This method employed several techniques
to deal with the broadband signals and succeeded inacquiring an image of a swine femoral artery with highrange resolution. However, optimization of the parametersettings received little attention.
Our goal is to realize the practical use of the high-rangeresolution imaging for screening early signs of atherosclerosis and for detecting the position and shape of a plaquecorrectly. The presence of coherent interference reduces theperformance of conventional FDI imaging to a great extent interms of estimating echo intensity than in terms of spatial
resolution.23) Conventional FDI imaging has insuﬃcientaccuracy in estimating echo intensity, resulting in a lower
continuity for images in the lateral direction than in thecase of conventional B-mode imaging. We previously foundthe necessity of employing frequency averaging to suppress
coherent interference in a simple simulation study without
noise.29) However, FDI imaging employing the conventionalfrequency averaging technique requires two conditions; theﬁrst is a high SNR and the second is that the echo waveform
returned from each target is almost the same as the waveform

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H. Taki et al.

of the reference signal.30) We have investigated the eﬀects
of the bandwidths used for frequency averaging and for
imaging on the performance of FDI imaging in terms of
estimating echo intensity, and proposed the frequency
averaging stabilization technique that ensure the robust
depiction of artery interfaces when there is a thin layer close
to the arterial wall.31) We also proposed the referencecompound technique that suppresses the deterioration of FDI
imaging performance due to variation of the echo waveform.32) In this study, we apply FDI imaging with the two
proposed techniques to an agar membrane, a swine femoral
artery in vitro, and six living human carotid arteries in vivo.
We explain the methods, present experimental results
obtained using a commercial US device, and form conclusions related to our ﬁndings.
2.

Fig. 1. Schema of the frequency averaging technique. Colored diagonal
elements of the covariance matrix RH are distributed among the diagonal
elements of the covariance matrix after frequency averaging RA.

Materials and methods

The method presented is based on FDI with the Capon
method, which is an adaptive beamforming algorithm. To
improve the range resolution in US, we apply this method toeach individual scan line of the radio frequency (RF) data
reconstructed from the in-phase and quadrature (IQ) data.29)
In this section, we brieﬂy describe FDI and the Capon
method, and subsequently propose a technique that suppresses the deterioration in FDI imaging performance due tothe echo waveform variation. Finally, we explain a robust
imaging technique that we call the reference compoundtechnique.
2.1

FDI imaging with the Capon method
FDI imaging is used to estimate the intensity of an echo that
returned from a desired depth. This method transforms thereceived signal that returned from a region of interest (ROI)
to that in the frequency domain and sums the frequency
components of the signal after phase compensation. The
phase of each component of the echo that returned from agiven depth depends on the product of the frequency of thecomponent and the depth. Therefore, FDI imaging employs
phase compensation to integrate the frequency components ofthe echo that returned from the desired depth coherently.29)
The application of the Capon method requires that all thefrequency components of the echo from a single target havethe same intensity. To fulﬁll the requirements for ultrasoundimaging, we apply the whitening technique, which assumes
that the echo that returned from a single target resembles thereference signal in waveform, and normalizes the frequency
components of the received signal with the reference signal:

XHk ¼ XPk XRk =ðjXRk j2 þ Þ;

ð1Þ

where η is a term for stabilization, and XHk, XPk, and XRk
are the k-th frequency components of the received RF data
after whitening, the received RF data before whitening, and areference signal of the RF data without whitening, respectively. In this study, we use the RF data of 1 cm width in eachscan line after a common delay and sum process, where we
employ a rectangular window function in the time domain, as
we did in our previous work.29)
The Capon method suppresses the contribution of theechoes that returned from targets at undesired depths, subject
to a constant response at the desired depth. This problem isexpressed asminimize P ¼ WT RH W subject to CT W ¼ 1;

ð2ÞRH ¼ XH XT
H ;

ð3Þ



T

XH ¼ XH1 XH2    XHN ;
TC ¼ e jk1 r e jk2 r    e jkN r ;

ð4Þ
ð5Þ

where kl is the l-th wavenumber of the frequency components
used by FDI imaging, r=2 is the desired depth, and [·]+ and[·]T denote the complex conjugate and the transpose,respectively. Because P = WT+RHW = ∣WT+XH∣2, P is theecho intensity of the frequency components that are summed
coherently using the weighting vector W. The constraint in
Eq. (2) guarantees a constant contribution from the echothat returned from a target located at the desired depth of
r=2. The minimization problem of Eq. (2) can be solved by
the application of Lagrange multiplier methods without thecalculation of the optimum weighting vector. The solution of
Eq. (2) is given by
PCap ðrÞ ¼

1
;
C R1
H C
T

ð6Þ

26)
where R1
H denotes the inverse matrix of RH.

2.2

Frequency averaging for a stabilized beam pattern
Frequency averaging has been used to suppress thecorrelation between the echoes that returned from diﬀerent
depths,26,29) similar to the spatial averaging employed byspatial domain interferometry imaging.20) We have theoretically investigated the eﬀect of the bandwidths used for
frequency averaging and for imaging on the performance of
FDI imaging in estimating echo intensity, and propose atechnique that ensure the robust depiction of artery interfaces
when there is a thin layer close to the arterial wall.31) Whenthe bandwidth for frequency averaging is wider than that for
imaging, the frequency components, which have frequencies
close to the center frequency, are distributed among thecovariance matrix uniformly, as shown in Fig. 1. Thissmoothes out the excessive suppression of the echo intensity
estimated by the Capon method. We call this techniquefrequency averaging stabilization (FAS).31) In this section,
we ﬁrst describe the process of frequency averaging, andsubsequently explain the eﬀect of FAS.
This technique averages the submatrices of the covariancematrix of the received signal along the diagonal direction.
The covariance matrix after frequency averaging is given
by

07HF05-2© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HF05 (2015)RA ¼

H. Taki et al.

M
1X
Rm ;
M m¼1

ð7Þ

Rmij ¼ XHðiþm1Þ XHð jþm1Þ ;ð8Þ

where Rmij is the ði; jÞ element of the m-th submatrix Rm, andM is the number of submatrices.
After applying whitening and frequency averaging to thereceived signal, the intensity estimated by FDI imaging with
the Capon method expressed in Eq. (2) is modiﬁed asTminimize P0 ðrÞ ¼ WT
ð9Þ
A RA WA subject to CA WA ¼ 1;
T
CA ¼ expð jk1 rÞ expð jk2 rÞ    expð jkNMþ1 rÞ ; ð10Þ
where WA is a modiﬁed weighting vector of size L =N − M + 1. The intensity estimated by FDI imaging, using anappropriate weighting vector WA acquired by the Capon
method, is

P0Cap ðrÞ ¼

1

;
1
0
CT
A ðRA þ  EÞ CA

ð11Þ

where ηAE is a diagonal loading matrix used to avoid
instability in the calculation of the inverse matrix.29)
In a previous study, frequency averaging is used tosuppress the correlation between echoes from diﬀerent
targets.29) Frequency averaging assumes that the frequency
component of the received RF data after whitening is
expressed byX
XHi ¼
o expðjki ro Þ;
ð12Þ
oki ¼ k1 þ ði  1Þk;ð13Þ

where αo is the amplitude of the echo that returned from theo-th target, ro=2 is the target depth of the o-th target, and Δkis the wavenumber of the sampling frequency interval. In thiscase, an element of the covariance matrix after frequency
averaging is given byM
X1XHðiþm1Þ XHð jþm1Þ
M m¼1
X
¼
jo j2 expfjði  jÞkro g þ gij ;RAij ¼

Equation (15) shows that the cross-correlation term gij issuppressed in proportion to a sinc function:

ð14Þ

gij /

X
o1 ;o2¼

X

o1 ;o2

 o1  o 2

BA  BI
IAve  FS IAve ;ð18Þ
BA
where IAve is the average intensity of frequency components
after whitening. We call FS the stabilization factor. We
rewrite the covariance matrix after frequency averaging usinga Toeplitz matrix RT:
ﬃ

RA ¼ FS IAve RT þ R0 ;P0CAP ðrÞ ¼ minimize WTA R A WA1expðjkiþm1 ro1 þ jkjþm1 ro2 Þ
M m¼1

 minimize FS IAve WTA R T WA0
þ minimize WTA R WAo1 o2 expfjði  jÞkro1 g

M
1Xexpð jkjþm1 rÞ
M m¼1
X
ﬃ
o1 o2 expfjði  jÞkro1 g

0
ﬃ FS ITrue þ minimize WTA R WA ;ð15Þ

o1 ;o2

 expfjðkj þ Mk=2Þrg
r ¼ ro2  ro1 ;sinðMkr=2Þ
;Mkr=2
ð16Þ

where RAij is the ði; jÞ element of the covariance matrix after
frequency averaging RA, gij is the cross-correlation term, andΔr=2 is the target interval between o1 and o2. The proposed
method assumes that multiple ﬂat interfaces exist in a ROI,
and in this case, the proposed method depicts sharp peaks
at the target depths. Therefore, in arterial wall imaging thetarget interval denotes the interval between two interfaces.

ð19Þ

where all the diagonal elements of RA have positive values.
When the covariance matrix becomes a Toeplitz matrix, FDI
imaging can estimate the true echo intensity.20,34) Therefore,
the intensity estimated by FDI imaging given by Eq. (11) isalso rewritten as

M
X



ð17Þ

where BA = MΔk is the bandwidth for frequency averaging,and c is the speed of sound. The bandwidth for imaging BI isgiven by LΔk. We use the whole bandwidth B for frequency
averaging and imaging, i.e., B = BA + BI. The conventional
FDI imaging allocates one-half of the whole bandwidth forfrequency averaging.
FAS allocates a wide bandwidth for frequency averaging
to improve the performance of FDI imaging in estimatingecho intensity, and predicts the underestimation of echo
intensity in FDI imaging at its worst. When the bandwidth forfrequency averaging is wider than that for imaging, i.e., when
the size of the submatrix L is smaller than the number ofsubmatrices M, the diagonal elements of the covariancematrix RH, which has frequencies close to the center
frequency, are distributed along the diagonal elements ofthe covariance matrix after frequency averaging RA, as
shown in Fig. 1. The additive value to each diagonal elementof the covariance matrix RA is expressed by
M
1X
MLþ1
IAve
XHl XHi ﬃ
M l¼L
M

o

gij ¼

sinðMkr=2Þ sinðBA r=cÞ¼;
Mkr=2
BA r=cð20Þ

where ITrue is the true echo intensity. Equation (20) indicatesthat the estimated intensity in the proposed FDI imaging is
supposed to be larger than FSITrue. These frequency
components smooth out the excessive suppression of theecho intensity estimated by the Capon method at the cost of
a little range resolution. When FS = 1=3, the estimatedintensity is supposed to be larger than −4.77 dB relative tothe true echo intensity.
2.3 Reference compound applied to FDI imaging with theCapon method

As US uses broadband signals, the target shape causes large
variations in the intensity and phase of each frequency
component of a received signal, resulting in a large variationin the echo waveform. FDI imaging with the Capon method
assumes that the echo waveform that returned from a single

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H. Taki et al.

target resembles the waveform of the reference signal. Whenthe echo waveform that returned from a target is diﬀerent
from the reference waveform, the estimated intensity at thetarget depth decreases and the target image blurs. Therefore,
we used multiple reference signals to satisfy the condition
that the echo waveform of each target in a ROI resembled
at least one of the reference waveforms. We estimate theintensity of a measurement plane using each reference signal
separately, and then average the estimated intensities.
Q
1X
PCapRC ðrÞ ¼
PCapR ðr; qÞ;
ð21Þ
Q q¼1
where PCapR ðr; qÞ is the intensity estimated by FDI imaging
using the q-th reference signal, and Q is the number ofreference signals used. We call this technique the referencecompound (RC) technique. When the reference signal
resembles the target echo waveform, the intensity proﬁleestimated using the reference signal is supposed to have a
sharp and large peak at the target depth. This means thatthe average of the intensities estimated using the multiplereference signals has the potential to depict target images
stably. In addition, the appearance of false images depends
on the reference signal used. This implies that RC can havethe same eﬀect as the frequency compound in suppressing
speckle noise.32)
In ultrasound imaging of the human carotid artery in alongitudinal section, the vessel wall interfaces are supposed
to be ﬂat in the incident region of the ultrasound beam. We
thus used multiple ﬂat interfaces with various slope angles asreference targets for vessel wall imaging in the experimental
study. This setting neglects the waveform change caused by
the measurement depth variation, because this waveformchange causes a slight deterioration of image quality.33)
2.4

Simulation and experimental setup
In the simulation study, we investigate the performance of the
proposed method when there are two horizontal interfaces ina ROI, where the waveform that returned from each interface
is the same as that of the reference signal. When the received
signal includes no noise, the echo that returned from twointerfaces is given bysðIT ; tÞ ¼ sR ðtÞ þ sR ðt  2IT =cÞ;ð22Þwhere IT is the target interval and sR(t) is the reference signal.
We can construct the received signal from sloped interfacesby employing the echo from a sloped interface as thereference signal sR(t). To investigate the eﬀects of noisein the proposed method, we added white noise to theconstructed received signal given by Eq. (22). The signal
intensity is the average echo intensity in the −3 dB temporal
width of a reference signal, and the noise intensity is theaverage echo intensity of the received signal in a 2 cm rangethat includes no echo signal.
Experiments were conducted using a Hitachi EUB-8500
US device with a 7.5 MHz linear array to acquire raw IQ data.
The IQ data were converted to RF data, where the sampling
frequency of the converted RF data was 30 MHz.29) The
transmit focal depth was 15 mm, and the scan line and range
intervals of the US device were about 0.27 and 0.05 mm,
respectively. Figure 2 shows the echo waveforms of threeinterfaces between 20% gelatin and 4% agar at a depth ofFig. 2. Echo waveform of an interface between 20% gelatin and 4% agar,
where 10 echoes of diﬀerent scan lines were coherently averaged after arrival
time adjustment to suppress noise. The slope angles of the interface are 0, 4,
and 10°.

15 mm, which we use as the reference signals. In thedetermination of each reference signal, we averaged 10
echoes of diﬀerent scan lines coherently to suppress noise. In
the FDI imaging, we used a single-frame US data to depict
each image. The −6 dB bandwidth of the echo from thehorizontal interface was 2.6 MHz. The half-power width of
the ultrasound beam of the US device in the lateral direction
was about 0.5 mm at a depth of 1.5 cm. We supposed that thesound velocity was 1500 m=s, and thus the range interval of
the RF data was 0.025 mm. We used a rectangular windowfunction of 1 cm width to cut out the received signal in the
ROI from the whole signal. Because each signal of a scanline, at depths from 1 to 2 cm, consisted of 400 range
samples, the sampling interval in the frequency domain was
75 kHz. In this study, we used bandwidths of 4, 5, and6 MHz. The corresponding bands were from 5.3 to 9.3 MHz,
from 4.8 to 9.8 MHz, and from 4.1 to 10.1 MHz, where thenumbers of frequency components N were 54, 68, and 81,
respectively. As FDI imaging with the Capon method has
a spatial resolution of about 0.05 mm, a range interval of
0.01 mm is adequate for this method.29) Therefore, we used arange sampling interval of 0.01 mm. The sampling frequencyof 30 MHz determines the range sampling interval for theconventional B-mode method of 0.025 mm. We had adjusted
the range interval of the B-mode images to 0.01 mm byinterpolation.
The optimum stabilization term η in Eq. (1) is proportional
to the noise intensity of the k-th frequency component of thereceived signal when the received signal intensity is equal to
the reference signal intensity; however, it is diﬃcult tomeasure noise intensity because it commonly varies. Therefore, we introduced the assumption we made in our previous
work that the expectation of the noise intensity was uniform
in all frequency components.29) In this study, for the valueof η, we used the average intensity of the received signal in
the band from 11 to 14 MHz, adjusting the average signal
intensity of the received signal to that of the reference signal:
 ¼ IRS IPN =IPS ;ð23Þ

where IRS is the average intensity of the reference signal in
the band used in the proposed method, and IPN and IPS are the07HF05-4© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 07HF05 (2015)

H. Taki et al.

respective average intensities of the received signal in theband from 11 to 14 MHz and in the band used by the
proposed method. IRS=IPS adjusts the average intensity of thereceived signal to that of the reference signal. Using ηAEstabilizes R1
A at the cost of a decrease in SNR. As thisdecrease reduces the image quality of the proposed method,
we should use small ηA values. In the present study, we used
−40 dB of the average value of the diagonal terms of RA as
the value for ηA.29)
We investigated the accuracy of FDI imaging in measuring
the thickness of a vessel wall using a ﬁxed swine femoral
arteries embedded in a gelatin block. First, adventitial layers
were removed completely from a fresh femoral artery. We
followed the methods of our previous work29) to prepare theﬁxed gelatin block with the artery and to measure the vesselwall thickness. First, we measured a longitudinal sectionof the ﬁxed artery using a commercial US device. Aftercompletion of the US measurement, an anatomist immediately cut the gelatin block with a blade inserted into the pairof slits in the cutting case, where the pair of slits was used toadjust the cut section in the imaging plane. This process
guaranteed that the cut site was very close to the ultrasoundimaging site. The anatomist traced the vessel wall interfaces
microscopically. We subsequently applied the proposed FDI
imaging to the received IQ data of six human carotid arteriesof three living normal subjects to examine the performance ofthe proposed method in a clinical situation.
The RC works when multiple reference signals are used, incases where the echo waveform of each target in a ROI
resembles at least one of the reference waveforms. To handle
waveform variation due to the varying slope angle of thearterial wall interfaces, we employed six reference signalsthat returned from ﬂat interfaces between 20% gelatin and 4%
agar, with slope angles of 0 to 10 deg in 2-degree steps, as
shown in Fig. 2. The center of each interface was located at a
depth of 15 mm.
3.
3.1

Results and discussion

Range resolution of FDI imaging in a simulation study
We evaluated the performance of FAS, which smoothes out
the excessive suppression of the echo intensity estimated by
FDI imaging with the Capon method.31) Figure 3 shows theintensity estimated by conventional B-mode imaging, conventional FDI imaging and FDI imaging with FAS, where the
SNR is from 0 to 30 dB, there are two horizontal interfaces ina ROI, and the target interval is 0.2 mm. In this evaluation,
we employ FDI imaging without RC. Because the −6 dB
bandwidth of the signal used in this simulation study is
2.6 MHz, the conventional B-mode imaging has a range
resolution of about 0.3 mm. The conventional FDI imaging
allocates one-half of the whole bandwidth for frequency
averaging.29) The conventional FDI imaging has a higher
range resolution than the B-mode imaging; however, its
performance is unstable at low SNR. FDI imaging with FAS
showed the interfaces reliably. FDI images were acquiredwith a suﬃcient range resolution using a 2 MHz bandwidth;
this result is consistent with those of a previous study.29)
We also employed FDI imaging with FAS, allocating a
bandwidth of 3 MHz for frequency averaging from a total
bandwidth of 5 MHz. Because the bandwidth for imaging is
2 MHz, the remainder BA–BI is 1 MHz for this setting. FDI

(a)

(b)

(c)

(d)

(e)
Fig. 3. Estimated intensity as a function of the SNR from 0 to 30 dB when
there are two interfaces at depths of 15.0 and 15.2 mm. The intensity proﬁles
are estimated by (a) conventional B-mode imaging, (b) and (c) conventional
FDI imaging, and (d) and (e) FDI imaging with FAS. The bandwidth forfrequency averaging (BA) and that for imaging (BI) are respectively (b) 2 and2 MHz, (c) 3 and 3 MHz, (d) 3 and 1 MHz, and (e) 3 and 2 MHz.

imaging with FAS is supposed to have high range resolution
and greater robustness.
Figure 4 shows the estimated echo intensity of the target
interfaces calculated by the conventional FDI imaging andby FDI imaging with FAS, where there are two interfaces at
depths of 15.0 and 15.2 mm and the true echo intensity is
0 dB.31) Our previous study shows that the cross-correlation
term is proportional to a sinc function given by Eq. (17). The
sinc function is less than 0.25 when πBAΔr=c is larger than
2.48. Therefore, the suppression of the cross-correlation termby more than 6 dB requires a constraint on the bandwidth forfrequency averaging given byBA  c=2:53ITmin ;ð24Þ

where ITmin is the minimum target interval. When the target
interval is 0.2 mm, the bandwidth of 3 MHz for frequency
averaging is suﬃcient for the suppression of the crosscorrelation term. However, using a wide bandwidth means

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H. Taki et al.

(a)Fig. 4. Estimated echo intensity of target interfaces calculated using theconventional FDI imaging and the FDI imaging with FAS, where there are
two target interfaces at depths of 15.0 and 15.2 mm and the true echo
intensity is 0 dB. The FDI imaging with FAS allocates a bandwidth of 3 MHz
for frequency averaging from a total bandwidth (B) of 5 MHz. The FDI
imaging without FAS allocates half bandwidths for frequency averaging
from total bandwidths of 4, 5, and 6 MHz. Each error bar denotes thestandard deviation, where 10 simulation data with random white noise areused.

using low-SNR frequency-components that makes theconventional FDI imaging unreliable. Because the Capon
method minimizes the output power, the unreliable performance of the conventional FDI method results in the underestimation of echo intensity. In contrast, FDI imaging with
FAS enabled the estimation of echo intensity with an average
estimation error within 2.3 dB and with small variations.
Under this condition, the stabilization factor FS is equal to
1=3. In all cases, the normalized echo intensity estimated by
FDI imaging with FAS is larger than −4.77 dB. This result is
consistent with the results of the theoretical investigation
shown in Sect. 2.2. In a longitudinal section of an artery, thedepths and echo intensities of an arterial wall were similar.
Therefore, in a B-mode image there was a high lateralcontinuity at the region of an arterial wall, as shown in Fig. 8.
FDI imaging estimates the echo intensities in each scan line
separately. Therefore, the low performance of the conventional FDI imaging in estimating echo intensity should
increase the variation of the estimated echo intensity of anarterial wall, causing a low lateral continuity at a region ofan arterial wall. The high performance of the proposed FDI
imaging in echo intensity estimation improved the lateralcontinuity in a FDI image, as shown in Fig. 8(c). These
results indicate the eﬃciency of FAS in estimating echo
intensity and in improving continuity in the lateral direction.
Figure 5 shows the intensity estimated by FDI imaging
with and without RC, where the slope angles of the target
interfaces are 0 and 10 deg, and the bandwidths for frequency
averaging and imaging are 3 and 2 MHz, respectively. Eachsignal that returned from two interfaces was constructedusing Eq. (22), where the signal included no noise. FDI
imaging without RC used a single reference signal that
returned from a horizontal interface. FDI imaging with RC
used six reference signals that returned from six interfaces
with slope angles of 0, 2, 4, 6, 8, and 10°. Under high SNR
conditions, the conventional FDI imaging and FDI imaging(b)
Fig. 5. Intensity of two interfaces estimated by the conventional FDI
imaging, the FDI imaging with FAS, and the FDI imaging with FAS and RC,
where the slope angles of the two interfaces are (a) 0 and (b) 10°. Each signalthat returned from two interfaces was constructed using Eq. (22), where thesignal included no noise. The target depths are 15.0 and 15.2 mm.

with FAS estimated similar intensity proﬁles, as shown in
Fig. 5(a). This is consistent with the results shown in
Figs. 3(b) and 3(e). FAS improves the accuracy of estimatingecho intensity; however, it is insuﬃcient when the slope
angle of the target interface is diﬀerent from that of thereference. Figure 5 indicates that FDI imaging with RC
achieves robustness in terms of spatial resolution and echo
intensity estimation for various target slope angles.
3.2

Agar phantom images acquired using FDI imaging
We experimentally investigated the performance of the
proposed FDI imaging using a 0.15-mm-thick agar membrane phantom, where an anatomist measured the membranethickness microscopically. Figures 6 and 7 show ultrasoundimages of an agar membrane phantom acquired using theconventional B-mode imaging, the conventional FDI imaging
and the proposed FDI imaging with FAS and RC. Because
the conventional B-mode imaging had an image extent of
0.29 mm in the range direction, it failed to depict the pairof interfaces between the 0.15 mm agar membrane and thegelatin. The conventional FDI imaging and the proposed
method allocated 2 and 3 MHz for frequency averaging fromthe total bandwidths of 4 and 5 MHz, respectively. The
conventional FDI imaging has a higher spatial resolution thanthe B-mode imaging; however, its echo intensity estimation

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Jpn. J. Appl. Phys. 54, 07HF05 (2015)

H. Taki et al.

(a)

(a)

(b)

(b)

(c)

(c)
Fig. 7. Ultrasound image of a 10-deg-sloped agar membrane acquired by(a) the conventional B-mode imaging, (b) the conventional FDI imaging, and(c) the proposed FDI imaging with FAS and RC. The dynamic range of eachultrasound image is 50 dB, and the agar membrane is 0.15 mm thick in the
microscopy image.

(d)Fig. 6. (Color online) Ultrasound images of a horizontal agar membraneacquired by (a) a conventional B-mode imaging, (b) the conventional FDI
imaging, and (c) the proposed FDI imaging with FAS and RC, and(d) microscopy image of the membrane. The dynamic range of eachultrasound image is 50 dB, and the agar membrane is 0.15 mm thick in the
microscopy image. The arrows in the microscopy image indicate the interface
between gelatin and agar.

accuracy is lower than that of the B-mode imaging, resulting
in low continuity in the lateral direction, as described in ourprevious work.29) In contrast, the proposed FDI imaging with
FAS and RC showed the pairs of interfaces in front of andbehind the horizontal agar membrane and sloped agar
membranes. These results are consistent with the performance of FDI imaging shown in Figs. 3(b) and 3(e).
To investigate the performance of the proposed FDI
imaging in estimating target depth, we examined 57 scanlines in the 15-mm-wide region in Fig. 6. As shown in
Fig. 6(d), the surface of the agar membrane was ﬂat. The
median agar membrane thickness estimated using the
proposed FDI imaging was 0.17 mm, and the thickness
estimation error was 0.02 mm. The average and standard
deviation of the depth of the near gelatin-agar interface
estimated by the conventional FDI imaging were 14.46 and
0.104 mm, respectively. In contrast, those estimated by the
proposed FDI imaging were 14.42 and 0.028 mm, respectively. The standard deviation of the depth estimated using
the proposed FDI method was 26.7% of that estimated using
the conventional FDI method, indicating the robustness of the
proposed imaging method.
We also investigated the underestimation of the proposed
FDI imaging at the echo intensity of the near gelatin-agar
interface. We examined 57 scan lines in the 15-mm-wide

region in Figs. 6 and 7. In the conventional FDI image, 8.8
and 22.8% of all the scan lines had echo intensities lower than
one-quarter of the average echo intensity when the slope
angles were 0 and 10 deg, respectively. In the proposed FDI
image no scan line had an echo intensity lower than onequarter of the average echo intensity in both cases. This result
indicates the eﬃciency of the proposed techniques inacquiring robustness.
3.3 Images of swine femoral arteries acquired using FDI
imaging

We experimentally investigated the performance of the
proposed FDI imaging using a ﬁxed swine femoral artery.
Figure 8 shows ultrasound images of a longitudinal sectionof a ﬁxed swine femoral artery acquired using the conventional B-mode imaging, the conventional FDI imaging, andthe proposed FDI imaging. The conventional FDI imaging
has higher range resolution than the conventional B-mode
imaging; however, it also has low continuity in the lateral
direction. In contrast, the proposed FDI imaging has both
high range resolution and good continuity in the lateral
direction.
We investigated the underestimation of the proposed FDI
imaging at the echo intensity of the far-wall lumen–intima
interface. We examined 57 scan lines in the 15-mm-wide
region in Fig. 8. In the conventional FDI image, 19.3% of all
the scan lines had echo intensities lower than one-quarter of
the average echo intensity. In the proposed FDI image, 5.3%
had low echo intensities. This result also indicates theeﬃciency of the proposed techniques in acquiring robustness.
Figure 9 shows the interfaces at the posterior wall of aﬁxed swine femoral artery acquired using the proposed
FDI imaging, where the interfaces were projected onto a

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Jpn. J. Appl. Phys. 54, 07HF05 (2015)

H. Taki et al.

(a)Fig. 9. (Color online) Interfaces depicted at the posterior wall in an FDI
image projected onto a corresponding microscopy image on a millimeterscale. Red lines indicate a lumen–intima interface and a media-adventitia
interface traced histologically. Blue broken lines indicate the interfaces
depicted in the proposed FDI image using FAS and RC.

(b)

(a)
(c)
Fig. 8. Ultrasound images of a ﬁxed swine femoral artery acquired using(a) the B-mode imaging, (b) the conventional FDI imaging without FAS and
RC, and (c) the proposed FDI imaging with FAS and RC.

corresponding microscopy image. For this study, weinvestigated 20 scan lines in the 5-mm-wide central regionin Fig. 9. The interfaces shown using the proposed FDI
imaging were suﬃciently close to those traced microscopically. In this investigation, we selected two peak positionsin the region 1 mm deep in the posterior arterial wall for eachscan line of the ultrasound images. When there was only one
peak intensity position or the interval between the two peak
positions was not within the range from 0.20 to 0.50 mm, we
determined that a complete failure had occurred at the scanline, and excluded the scan line from the calculation of theaverage and the standard deviation of arterial wall thickness.
The complete failure occurrence ratios were 5, 10, and 5% in
the B-mode, conventional FDI, and proposed FDI images,
respectively. The average and the standard deviation ofarterial wall thickness measured microscopically were 0.3217
and 0.0128 mm, respectively, and the results estimated using
the proposed FDI imaging were 0.3242 and 0.0232 mm,
respectively. In contrast, those estimated using the B-mode
imaging were 0.3100 and 0.0316 mm, respectively. These
results show the high performance of the proposed FDI
imaging in depicting arterial walls.

(b)

(c)
Fig. 10. Interpolated B-mode image of a normal living human carotid
artery in vivo obtained using a commercial ultrasonographic device. Images
were acquired using (a) the B-mode imaging, (b) the conventional FDI
imaging, and (c) the proposed FDI imaging with FAS and RC.

3.4 High-range-resolution ultrasound imaging of a human
carotid artery in vivo

We applied the proposed FDI imaging with FAS and RC to
raw IQ data of six carotid arteries in vivo, where each FDI
image was constructed from single-frame IQ data. Figure 10

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Jpn. J. Appl. Phys. 54, 07HF05 (2015)

H. Taki et al.

Fig. 11. Ultrasound images of ﬁve normal living human carotid arteries in vivo depicted using the proposed FDI imaging. This method is applied to a single
frame of IQ data obtained using a commercial ultrasonographic device.

shows ultrasound images of a human carotid artery in vivoacquired using the B-mode imaging, conventional FDI
imaging and proposed FDI imaging. The proposed FDI
method also provided high-range-resolution images of thisartery and the ﬁve other human carotid arteries used in thisstudy. These results verify that the proposed method canstably acquire a high-range-resolution image of normal living
human carotid arteries. Figure 11 shows images of theother human carotid arteries obtained using the proposed
FDI method. These results verify that the proposed method
enabled the stable acquisition of a high-range-resolution
image of a normal living human carotid artery. The calculation time for a ROI of 1 × 2 cm (i.e., 1001 range
samples × 75 scan lines) was approximately 0.06 s=frame,
and the calculations were performed using a desktop PC witha single CPU (Intel Xeon 3.33 GHz) and 6 GB RAM. This
result shows that the proposed FDI imaging is suitable forreal-time high-resolution vascular ultrasound imaging.
4.

Conclusions

We reported a high-range-resolution FDI imaging employing
FAS and RC. FAS ensures the robust depiction of arteryinterfaces when there is a thin layer close to the arterial wall.
The RC technique uses multiple reference signals to suppress
the deterioration of the imaging performance caused byvariation in the echo waveform. The proposed FDI imaging
could depict a horizontal 0.15-mm-thick agar membrane
stably, and the standard deviation of the estimated depth
was suppressed to 26.7% of that obtained using the conventional FDI method. The proposed method also succeededin suppressing the underestimation of the echo intensity
eﬀectively, and in the observation of an agar membrane anda swine artery from 0 to 5.3% of the scan lines with echo
intensities lower than one-quarter of the average echo
intensity, where 8.8 to 22.8% of the scan lines had low echo
intensities when a conventional FDI method was employed.
The proposed method also enabled the acquisition of highrange-resolution images of six living human carotid arteries.
The proposed method required 0.06 s=frame using a desktop
PC with a single CPU for a ROI of 1 × 2 cm. These results
indicate that the proposed FDI imaging has the potential toproduce real-time high-range-resolution ultrasound vascular
images that will enable major improvements in ultrasoundmedical diagnoses.
Acknowledgments

This work was partly supported by the Innovative TechnoHub for Integrated Medical Bio-Imaging of the Projectfor Developing Innovation Systems, from the Ministry of
Education, Culture, Sports, Science and Technology, Japan(MEXT), and by MEXT=JSPS KAKENHI Grant Number
25870345.

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