IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

511

Effect of Element Directivity
on Adaptive Beamforming Applied
to High-Frame-Rate Ultrasound
Hideyuki Hasegawa and Hiroshi Kanai
Abstract—High-frame-rate ultrasound is a promising technique for measurement and imaging of cardiovascular dynamics. In high-frame-rate ultrasonic imaging, unfocused ultrasonic beams are used in transmit and multiple focused receiving
beams are created by parallel beamforming using the delay
and sum (DAS) method. However, the spatial resolution andcontrast are degraded compared with conventional beamforming using focused transmit beams. In the present study, theminimum variance beamformer was examined for improvement of the spatial resolution in high-frame-rate ultrasound.
In conventional minimum variance beamforming, the spatial
covariance matrix of ultrasonic echo signals received by individual transducer elements is obtained without considering thedirectivity of the transducer element. By omitting the element
directivity, the error in estimation of the desired signal (i.e.,
the echo from the focal point) increases, and as a result, theimprovement of the spatial resolution is degraded. In the present study, the element directivity was taken into account inestimation of the spatial covariance matrix used in minimum
variance beamforming. The effect of the element directivity
on adaptive beamforming was evaluated by computer simulation and basic experiments using a phantom. In parallel beamforming with the conventional DAS beamformer, the lateral
spatial resolution, which was evaluated from the lateral full
width at half maximum of the echo amplitude profile in thebasic experiment, was 0.50 mm. Using conventional amplitude
and phase estimation (APES) beamforming, the lateral spatial
resolution was improved to 0.37 mm. The lateral spatial resolution was further improved to 0.30 mm using the modified
APES beamforming by considering the element directivity.
Image contrast and contrast-to-noise ratios, respectively, were
−12.3 and 6.5 dB (DAS), −32.8 and −11.3 dB (APES), and−7.0 and 3.1 dB (modified APES).

I. Introduction

M

easurements of cardiovascular dynamics and viscoelasticity are useful for diagnosis of the cardiovascular system. High-frame-rate ultrasound is a promisingtechnique for measurement and imaging of tissue dynamics. High-frame-rate ultrasound using parallel beamforming, which was introduced in the 1980s [1], basically uses
unfocused transmit beams and creates multiple focusedreceiving beams in each transmission. The first practical

Manuscript received January 6, 2015; accepted January 9, 2015.
H. Hasegawa is with the Graduate School of Biomedical Engineering/
Graduate School of Engineering, Tohoku University, Sendai 980-8579,
Japan (e-mail: hasegawa@ecei.tohoku.ac.jp).
H. Kanai is with the Graduate School of Engineering/Graduate Schoolof Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan.
DOI http://dx.doi.org/10.1109/TUFFC.2015.006973

application of high-frame-rate ultrasound was the measurement of the displacement distribution in biological tissue induced by acoustic radiation force [2]. This technique
is very useful for assessment of tissue viscoelasticity noninvasively. Recently, we have shown that high-frame-rate
ultrasound is also useful for B-mode, tissue strain, andblood flow imaging [3]. Currently, various methods basedon high-frame-rate imaging have been developed for measurement of cardiovascular dynamics [4]–[10].
One of the problems of high-frame-rate imaging is thedegradation of spatial resolution owing to the use of unfocused transmit beams and, thus, development of methods
for improvement of spatial resolution is desired to simultaneously realize high temporal and spatial resolutions.
The spatial compound technique [11] is one method for
improvement of the spatial resolution in high-frame-rate
imaging [12]. In the cited study, the image spatial resolution was shown to be significantly improved by coherently
compounding multiple steered plane waves. However, multiple transmissions of plane waves degrades the imaging
frame rate.
Recently, adaptive beamforming, namely, minimum
variance beamforming, has been introduced to ultrasound imaging for improvement of the spatial resolution[13]–[16]. In the beamforming procedure, ultrasonic echo
signals received by individual transducer elements in an
ultrasonic probe are aligned based on the geometricalinformation of the focal point and then averaged. Thisway of beamforming is called the delay and sum (DAS)
method. The weights given to the element echo signals in
the averaging procedure are fixed, and a tapered weighting function, such as the Hann function, is typically used.
In adaptive beamforming, those weights are adaptively
determined using the received ultrasonic echoes, and thisprocedure improves the spatial resolution significantly.
Recently, minimum variance beamforming was combinedwith synthetic transmit beamforming for high-frame-rateechocardiography [17].
In minimum variance beamforming, the spatial covariance matrix of the received element echo signals is
estimated to determine the weights to the element echo
signals. In this procedure, the desired signal (echo fromthe focal point) is suppressed when the desired signal iscontained in the spatial covariance matrix. Sub-array averaging was introduced to remove the desired signal fromthe spatial covariance matrix. Using sub-array averaging,0885–3010 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

512

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

suppression of the desired signal is avoided at the expenseof the spatial resolution [14]. Sub-array averaging is also
contribute to reduce the dimension of the spatial covariance matrix. Furthermore, temporal or depth averaging
is required to obtain speckle statistics similar to that obtained by conventional DAS beamforming [18]. Reductionof computational load, such as reduction of the dimensionof the spatial covariance matrix, is very important for realtime implementation and is studied intensively [19]–[21].
Alternative way to remove the desired signal from thespatial covariance matrix is to estimate the desired signal
from the received element signals. Blomberg et al. proposed the amplitude and phase estimation (APES) beamforming, in which the desired signal is estimated by DAS
beamforming [22]. However, in their study, the directivityof the transducer element is not considered in estimationof the desired signal. In the present study, the element
directivity was incorporated to improve the accuracy inestimation of the desired signal. Such improvement would
reduce the suppression of the desired signal in the APES
beamforming.

II. Materials and Methods(1)

where T denotes the transpose. The lateral position of themth transducer element is defined by xm and the range
position z of every transducer element is zero. By defining the position of the receiving focal point to be (xf, zf),
the output uDS of the DAS beamformer is expressed asfollows:(2)

where H is the Hermitian operator. In (2), wDS shows theweights for the element signals used in DAS beamforming. In the present study, for an easy comparison between
the physical meanings of the adaptive and conventional
DAS beamformers, rectangular apodization is considered
in conventional DAS beamforming. In the case of rectangular apodization, (2) is expressed as follows:
w DS =

a
a Ha

=

I −1a
,
a HI −1a

B. Adaptive Beamforming
As in conventional DAS beamforming, the output uMVof the adaptive beamformer, namely, minimum variancebeamformer, is expressed as follows:u MV = w H
MVS.

(3)

where I is the identity matrix, and a is called the steeringvector, expressed as(5)

The minimum variance beamformer determines theweight wMV so as to minimize the variance P of the output uMV [13], [14]. The variance (power) P of the output
uMV is expressed as follows:2

Let us define the complex signal of the ultrasonic echo
received by the mth transducer element of an ultrasonicprobe by sm (m = 0, 1, 2, ..., M − 1), where M is the total
number of elements in the aperture. The M signals areordered in a vector as follows:u DS = w H
DSS,

where f0 is the ultrasonic center frequency, and c0 is the
speed of sound.

H
P = E[ u MV ] = E[w MV
SS Hw MV ] = w H
MVRw MV,

A. Conventional Delay and Sum (DAS) Beamforming

S = (s 0 s 1 … s M −1) T,

2
2 


 exp  −j 2π f 0 (x 0 − x f ) + z f  
 


c0
 

 a 0  
2
2 



f
x
−
+
2
π
(
x
)
z

0
1
f
f


 
a 1   exp  −j
a = 
c0  , (4)=   
a M −1  22
 2π f 0 (x M −1 − x f ) + z f   
 exp  −j
c0
 



(6)

where E[∙] denotes the expectation, and R is the spatial
covariance matrix and expressed as follows:
R = E[SS H].

(7)

This minimization problem can be expressed as follows:H
min w H
MVRw MV, subject to w MVa = 1.
w MV

(8)

The solution to (8) is expressed as follows:
w MV =R −1a.
a HR −1a(9)As can be seen in (9), the weight wMV determined by
the minimum variance beamformer has a form very similar to that of the DAS beamformer expressed by (3). In(3), the identity matrix is used as the covariance matrix.
This means that undesired signals, which are suppressedby the DAS beamformer, are uncorrelated with each other(i.e., the covariance matrix of such components becomesthe identity matrix). On the other hand, in minimum variance beamforming, the spatial covariance matrix, whichcorresponds to the undesired signals to be suppressed,
is determined from the measured signal S. However, themeasured signal S contains the desired signal (i.e., theecho from the focal point). Therefore, the desired signal
would also be suppressed when the spatial covariance matrix defined by (7) is used. To overcome this problem, theAPES beamformer, which removes the desired signal fromhasegawa and kanai: adaptive beamforming applied to high-frame-rate ultrasound513

the covariance matrix, has been introduced [22]. In APES
beamforming, the weight wAPES is determined as follows:
w APES =Q −1a,a HQ −1a(10)where Q = R − GGH, and G = [g0 g1 g2 ... gM−1]T. The
G corresponds to the desired signal, and in [22], all of theelements gm (m = 0, 1, ..., M − 1) of vector G are estimated as gm = aHS/M.
C. Consideration of Element Directivity
in Adaptive Beamforming
In the APES beamforming proposed in [22], the directivity of each transducer element is not considered (thetransducer element is assumed to be omnidirectional).
However, each element should have directivity owing to
its finite size. Therefore, more components arising fromthe desired signal will remain in the covariance matrix
Q when the accuracy in estimation of the desired signal
is degraded due to the element directivity. Consequently,
the desired signal in the output uAPES will be suppressed.
In the present study, the directivity of each transducer
element was considered to improve the accuracy in estimation of the desired signal G (i.e., the echo from the focal
point) for a better removal of the desired signal from thecovariance matrix.
As shown in Fig. 1, the direction from the mth transducer element to the focal point (xf, zf) is defined by θm.
The directivity D(θm) of the mth transducer element (m =0, 1, 2, ..., M − 1) is expressed as follows [23]:D(θm ) =sin (πl
sin θmλπlsin θmλ)θm = tan(),

x f − xm,
zf

D(θm )a HS
M −1∑i =0 D(θi)

.

(14)

u mAPES = w H
mAPESS.

(15)

(11)

(12)

l is the width of each transducer element, and λ is theultrasonic wavelength.
In the modified APES beamforming proposed in thepresent study, the vector G = [g0 g1 g2 ... gm−1 gm gm+1 ...
gM−1]T corresponding to the estimate of the desired signal
is obtained as follows:
gm =

Q −1a
,
a HQ −1aw mAPES =

where
−1

Fig. 1. Illustration of geometry. Directivity function D(θm) was calculated by (11) at l = 150 µm and λ = 200 µm.

(13)

On the basis of (10), the weight wmAPES and the output
umAPES of the modified amplitude and phase estimation
beamformer are obtained using the vector G obtained by(13).

D. Sub-Aperture Beamforming for Reductionof Computational LoadIn the present study, the modified APES beamformer
along with sub-aperture beamforming was also examined
for reduction of the computational load. The output yk of
the kth sub-aperture (k = 0, 1, 2, ... K − 1) consisting ofMsub = M/K elements is expressed as follows:****
y k = (a M
aM
aM
… aM
)
sub ⋅ksub ⋅k +1
sub ⋅k + 2
sub ⋅k + M sub −1s M sub ⋅k




 s M sub ⋅k +1 ×  s M sub ⋅k + 2 





 s M ⋅k +M −1 sub= a kHS k.

			

sub

		(16)

514

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

In the present study, the output umAPESsub of the modified APES beamforming with sub-aperture beamforming
was obtained as follows:u mAPESsub = w mAPESsubY,

(17)

where
T

Y = ( y 0 y 1 … y K −1 ) ,

(18)

C −1J
,
J HC −1J(19)

w mAPESsub =C = YY H − VV H,(20)
T

V = ( v 0 v 1 … v K −1 ) ,K −1∑i =0 y i ,
vk =
K −1
∑i =0 bi
bk

bk =

(21)
(22)

M sub −1

∑ D(θM ⋅k +i),
sub

i =0

(23)

and J is a K dimensional vector of ones. Using sub-aperture beamforming, the dimensions of the covariance matrix C are reduced to K × K. The difference between theprocedures of the proposed method with and without subaperture beamforming is illustrated in Fig. 2.
E. Evaluation of Image Quality
In the present study, the quality of an obtained B-mode
image was evaluated by methods described in [24], [25].
1) Spatial Resolution: The spatial resolution was definedas the lateral full-width at half-maximum of the amplitude
profile of an echo from a point scatterer (point scatterer insimulation, fine wire in experiments).
2) Contrast: Contrast C was evaluated as follows:C =µ B − µl,
µB + µl(24)2where uB and µl are mean gray levels in background andlesion, respectively.
3) Contrast-to-Noise Ratio (CNR): Contrast-to-noise
ratio was evaluated as follows:
CNR =µB − µl22 ,σB + σl(25)2where σ B2 and σ l2 are variance of gray levels in backgroundand lesion, respectively. Both in simulations and experiments, anechoic cyst phantoms were adopted as the lesion,and diffuse scattering medium was adopted as background.

Fig. 2. Illustration of the proposed method with and without sub-aperture beamforming.

F. Method of Simulation
In the present study, the proposed method was evaluated by computer simulation and basic experiments usinga phantom. In simulation, the scatterer distribution was
generated by modifying the program, cyst_pht.m, provided by Field II [26]. The simulated phantom includes
strong point scatterers and anechoic cysts. An in-house
software was used for simulation of echoes from the generated scatterer distribution because Field II simulation
does not incorporate with the element directivity. In thein-house software, the echo signal received by the jthtransducer element sj(t) is obtained as follows:Ms j(t) =N1∑∑ ri + r j AnD(θi)D(θ j )h(t − τ TBF,i − τ i − τ j ),			
i =1 n =1

		(26)

hasegawa and kanai: adaptive beamforming applied to high-frame-rate ultrasoundFig. 3. Illustration of geometry in computer simulation.

where θi and θj are insonification and scattering angles
illustrated in Fig. 3, M is the number of transmitting elements, N is the number of scatterers, and An is the scattering strength of the nth scatterer. The element directivity D(∙) is obtained by (11). Each scatterer is located at(xn, zn) as illustrated in Fig. 3. Using the location of thetransmitting and receiving elements (xi,0) and (xj,0), thedistances ri from the transmitting element to the scatterer
and that rj from the scatterer to the receiving element are
expressed as follows:ri =(x i − x n)2 + z n2,

(27)

rj =

(x j − x n)2 + z n2 .

(28)

In the present study, the time delay τTBF,i applied tothe ith transmitting element by the transmitting beamformer was set at zero because plane wave transmission
was considered. The propagation delays τi and τj duringtransmission and reception are expressed as τi = ri/c0 andτj = rj/c0, respectively, where c0 is speed of sound. The ultrasonic pulse h(t) emitted from each transducer element
is expressed as follows:515

improvement of the imaging spatial resolution. A linear
array ultrasonic probe at a nominal center frequency of
10 MHz (UST-5412, Aloka, Tokyo, Japan) was used, andultrasonic echo signals received by individual transducer
elements were acquired by a modified ultrasound scanner(α-10, Aloka) at a sampling frequency of 40 MHz. The
beamforming procedure was performed off-line on the ultrasound echo signals received by the individual elements
using an in-house software based on Matlab (The MathWorks Inc., Natick, MA, USA). The element pitch of thelinear array was 0.2 mm, but the width l of each transducer element was not known. Therefore, the width l was
assumed to be 0.15 mm.
The transmit-receive sequence is described in [3]. In thepresent study, the number of emissions of plane waves forcreation of one image frame was set at 4, and each plane
wave was emitted using 96 transducer elements. In eachtransmission, 24 focused receiving beams were created atintervals of 0.2 mm, and the aperture used to create one
focused receiving beam consisted of M = 72 elements.
Consequently, one image frame consisting of 24 × 4 = 96
focused receiving beams was obtained by four emissionsof plane waves.
To obtain a complex element signal sm of the mth element, in the present study, the discrete Fourier transform
at f0 = 8.9 MHz was applied to the real echo signal received by the mth element at every moment in time (corresponding to range distance) with a Hann window whose
length was 0.225 µs. The computational cost of this procedure is similar to that of the quadrature demodulationand very effective to obtain the complex signal sm.
In the present study, the time delay compensation defined by the steering vector a was performed by time shifting the obtained complex signal sm. However, sm is thediscrete signal sampled at 40 MHz. Therefore, the residual
sub-sample time delay Δτm was compensated by multiplying the time-shifted version of sm by exp(2πf0 Δτm).
After this time delay compensation, the steering vector abecomes a vector of ones.

III. Experimental Results 2πt  0.5 − 0.5 cos  sin(2π f 0t) (0 ≤ t < Tp)			
h(t) =  Tp 
A. Simulation Experiments(otherwwise),
 0
Figs. 4(a), 4(b), and 4(c) show B-mode images of the		(29)
phantom obtained by conventional DAS beamforming,
where f0 is the center frequency of ultrasound set at 8 APES beamforming, and modified APES beamforming
MHz, and Tp is the ultrasonic pulse duration correspond- proposed in the present study, respectively. The signaling to three cycles at ultrasonic center frequency. The ele- to-noise ratio of the simulated RF signal was 40 dB. Fig.
ment pitch and kerf were set at 0.2 and 0.05 mm, respec- 5 shows lateral amplitude profiles at a range distance of
tively. The signal-to-noise ratio of the simulated element 15 mm obtained by the respective methods. The lateralRF signal was controlled by adding random noise.
spatial resolutions evaluated from the lateral full widths
at half maxima of the lateral amplitude profiles were 0.26
G. Experimental Setup
mm (DAS), 0.27 mm (APES), and 0.24 mm (modified
APES). In conventional APES beamforming, the accuracy
An ultrasound imaging phantom (model 54GS, CIRS in estimation of the desired signal (the echo from the foInc., Norfolk, VA, USA) was used for evaluation of the cal point) is degraded due to the lack of the information

{

}

516

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

Fig. 4. B-mode images of simulated phantom obtained by (a) delay andsum beamforming (DAS), (b) amplitude and phase estimation beamforming (APES), and (c) modified amplitude and phase estimation
beamforming (mAPES).

on the element directivity, and the desired signals cannot
be removed from the spatial covariance matrix R. As aresult, the desired signals are also suppressed by adaptive
beamforming (particularly present with respect to strong
echoes from wires). On the other hand, by considering
the element directivity, more parts of the desired signals
contained in the spatial covariance matrix R are removed,
and as a result, the undesired signals are suppressed but
the desired signals are not suppressed, as shown in Fig.
4(c).
In addition, C and CNR were estimated for evaluationof the image contrast. A rectangular region (from 19.3 to21.2 mm in the range direction, from 14 to 16 mm in thelateral direction) was assigned as the lesion, and a rectangular region (from 19.3 to 21.2 mm in the range direction,from 8 to 10 mm in the lateral direction) was assigned as
background (diffuse scattering medium). Obtained results(C, CNR) were (−8.5 dB, 6.6 dB; DAS), (−25.1 dB, −2.7
dB; APES), and (−6.1 dB, 2.1 dB; modified APES). In
conventional APES beamforming, C and CNR are significantly degraded due to suppression of the desired signals.
Using the proposed modified APES beamforming, C and

Fig. 5. Lateral amplitude profiles at a range distance of 15 mm in Bmode images shown in Fig. 4 obtained by delay and sum beamforming (DAS), amplitude and phase estimation beamforming (APES), andmodified amplitude and phase estimation beamforming (mAPES).

CNR are better than conventional APES beamforming
but similar to DAS beamforming. In the modified APES
beamforming, the spatial resolution was improved by suppressing the undesired signals. The suppression of the undesired signal also deepens dips between speckle echoes
as shown in Fig. 4(c). The improvement in the spatial
resolution yields a smaller speckle size, and the smaller
speckle size reduces the mean gray level in diffuse scattering medium. Also, the deeper dips between speckle echoes
increases the variance of gray levels. As a result, the C
and CNR obtained by the modified APES beamforming
did not outperform those obtained by DAS beamforming.
Table I shows lateral full widths at half maxima, C, and
CNR obtained at different signal-to-noise ratios. Similartendencies were observed at three different signal-to-noise
ratios, but the conventional APES beamformer was more
influenced by noise.
In the present study, the feasibility of sub-aperture
beamforming was also examined. Fig. 6 shows B-mode
images obtained by (top) APES beamforming and (bottom) modified APES beamforming, respectively, with (a)24 sub-apertures, (b) 12 sub-apertures, and (c) 4 sub-apertures. Even with sub-aperture beamforming, the quality of the B-mode images could be significantly improved

TABLE I. Lateral Full Widths at Half Maxima (FWHM), Contrast, and Contrast-To-Noise Ratios(CNRs) Obtained at Different SNRs Using Delay and Sum (DAS), Amplitude and Phase Estimation(APES), and Modified Amplitude and Phase Estimation (mAPES) Beamforming.
SNR [dB]

Beamformer

40

DAS
APES
mAPES
DAS
APES
mAPES
DAS
APES
mAPES

30

20

FWHM [mm]Contrast [dB]

CNR [dB]

0.26
0.27
0.24
0.26
0.28
0.24
0.26
0.27
0.24

−8.5
−25.1
−6.1
−8.6
−27.8
−6.1
−8.7
−31.7
−6.2

6.6
−2.7
2.1
6.6
−5.9
2.1
6.5
−9.4
2.1

hasegawa and kanai: adaptive beamforming applied to high-frame-rate ultrasoundFig. 6. B-mode images of simulated phantom obtained by (top) amplitude and phase estimation beamforming and (bottom) modified amplitude and phase estimation beamforming. (a) 24 sub-apertures, (b) 12
sub-apertures, (c) 4 sub-apertures.

by considering the element directivity. Using sub-aperture
beamforming, the dimensions of the covariance matrix are
reduced, and the computational load can be significantly
decreased. As can be seen in the lower image of Fig. 6(c),a good B-mode image can be obtained even with only
4 sub-apertures. Lateral amplitude profiles at a range
distance of 15 mm obtained by APES beamforming andmodified APES beamforming are shown in Figs. 7(a) and
7(b), respectively. In Fig. 7, the signal-to-noise ratio of thesimulated RF signal was set at 40 dB.
Fig. 8 shows lateral full widths at half maxima (spatial resolution), contrast, and CNR at different numbersof sub-apertures and signal-to-noise ratios obtained by
APES beamforming and modified APES beamforming.
The evaluated performance metrics show that APES
beamforming is more influenced by noise. The contrast
obtained by modified APES beamforming is totally better than APES beamforming, but the CNRs obtained by
APES beamforming with smaller numbers of sub-apertures were better than those obtained by modified APES

517

Fig. 7. Lateral amplitude profiles at a range distance of 15 mm in Bmode images shown in Fig. 6 obtained by (a) amplitude and phase estimation beamforming and (b) modified amplitude and phase estimation
beamforming.

beamforming. In modified APES beamforming, the spatial
resolution was not influenced by sub-aperture beamforming, but contrast and CNR were degraded slightly.
B. Basic Experiments
Figs. 9(a), 9(b), and 9(c) show B-mode images of thephantom obtained by conventional DAS beamforming,
APES beamforming, and modified APES beamforming
proposed in the present study, respectively. Fig. 10 shows
lateral amplitude profiles at a range distance of 21 mm
obtained by the respective methods. The lateral spatial
resolutions evaluated from the widths at half maxima of
the lateral amplitude profiles were 0.50 mm (DAS), 0.37mm (APES), and 0.30 mm (modified amplitude and phaseestimation). Similar tendency compared with the simulation experiment was obtained.
For evaluation of the image contrast, a phantom including an anechoic cyst was measured. Figs. 11(a), 11(b), and518IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

Fig. 8. Performance metrics obtained by (left) amplitude and phase estimation beamforming and (right) modified amplitude and phase estimation beamforming at different numbers of sub-apertures and signal-to-noise ratios (SNRs). (a) Lateral full widths at half maxima, (b) contrast, (c)contrast-to-noise ratios.

11(c) show B-mode images obtained by DAS beamforming, APES beamforming, and modified APES beamforming, respectively. A rectangular region (from 44.3 to 46.2
mm in the range direction, from 1 to 5 mm in the lateral
direction) was assigned as the lesion, and a rectangularregion (from 44.3 to 46.2 mm in the range direction, from
8 to 12 mm in the lateral direction) was assigned as background (diffuse scattering medium). Obtained results (C,CNR) were (−12.3 dB, 6.5 dB; DAS), (−32.8 dB, −11.3
dB; APES), and (−7.0 dB, 3.1 dB; modified APES). Results similar to those in simulation experiments were obtained.
The feasibility of sub-aperture beamforming was also
examined. Fig. 12 shows B-mode images of the string
phantom obtained by (top) APES beamforming and (bottom) modified APES beamforming, respectively, with (a)24 sub-apertures, (b) 12 sub-apertures, and (c) 4 sub-apertures. Even with sub-aperture beamforming, the qualityof the B-mode images could be significantly improved byconsidering the element directivity. As can be seen in thelower image of Fig. 12(c), a good B-mode image can beobtained even with only 4 sub-apertures. Lateral amplitude profiles at a range distance of 21 mm obtained by
APES beamforming and modified APES beamforming areshown in Figs. 13(a) and 13(b), respectively.
Fig. 14 shows B-mode images of the cyst phantom obtained by APES beamforming and modified APES beamforming, respectively, with (a) 24 sub-apertures, (b) 12
sub-apertures, and (c) 4 sub-apertures. A good B-mode
image can be obtained even with only 4 sub-apertures.
Figs. 15(a), 15(b), and 15(c) show lateral full widths
at half maxima, contrast, and CNRs obtained by APES
beamforming and modified APES beamforming. The tendencies similar to those in the simulation experiments
were observed. The evaluated performance metrics were
improved by sub-aperture beamforming with a smallerhasegawa and kanai: adaptive beamforming applied to high-frame-rate ultrasound519

Fig. 9. B-mode images of string phantom obtained by (a) delay and sum
beamforming (DAS), (b) amplitude and phase estimation beamforming(APES), and (c) modified amplitude and phase estimation beamforming(mAPES).

Fig. 11. B-mode images of cyst phantom obtained by (a) delay and sum
beamforming (DAS), (b) amplitude and phase estimation beamforming(APES), and (c) modified amplitude and phase estimation beamforming(mAPES).

number of sub-aperture in APES beamforming. In modified APES beamforming, the performance metrics weremuch less influenced by the number of sub-apertures; thespatial resolution was slightly improved by a smaller number of sub-apertures. The contrast and contrast-to-noise
ratio were slightly degraded by a smaller number of subapertures, as in the simulation experiments.

only undesired signals should be contained in the spatial
covariance matrix. However, the spatial covariance matrix
is estimated by the measured signals, which contain thedesired signal (echo from the focal point), and the desired
signal would be suppressed by the adaptive beamforming process if no procedure for suppression of the desired
signal contained in the spatial covariance matrix is used.
In conventional minimum variance beamforming, the desired signal contained in the spatial covariance matrix is
suppressed by sub-array averaging [14]. The APES beamformer proposes an alternative way for suppression of thedesired signal contained in the spatial covariance matrix.
The APES beamformer estimates the desired signal basedon the concept of DAS beamforming and removes it fromthe spatial covariance matrix [22]. However, the conventional APES beamformer does not incorporate with theelement directivity, and thus, the desired signal remains
in the covariance matrix. In conventional APES beamforming described in [22], sub-array averaging was also
used to further suppress the residual desired signal in thespatial covariance matrix. Using the conventional APES
beamformer with sub-array averaging, B-mode images,
which are significantly better than those obtained by DAS
beamforming, can be obtained. Figs. 16(a) and 16(b) show
B-mode images of the string and cyst phantoms obtainedby conventional APES beamforming with sub-array averaging and diagonal loading. Each sub-array is composed of
L = 48 elements (72 elements in the total aperture), anddiagonal loading corresponding to 0.05/L of the received
power [22] was used. As shown in Fig. 16, B-mode images
obtained by conventional APES beamforming with subarray averaging are much better than those obtained by
DAS beamforming shown in Figs. 9 and 11.
In the present study, the accuracy in estimation of thedesired signal contained in the spatial covariance matrix

IV. Discussion
In minimum-variance-based adaptive beamforming, thecomponents in the received signals, which correlate withthe spatial covariance matrix, are suppressed. Therefore,

Fig. 10. Lateral amplitude profiles at a range distance of 21 mm obtainedby delay and sum beamforming (DAS), amplitude and phase estimation
beamforming (APES), and modified amplitude and phase estimation
beamforming (mAPES).

520

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

Fig. 12. B-mode images of string phantom obtained by (top) amplitude
and phase estimation beamforming and (bottom) modified amplitude
and phase estimation beamforming. (a) 24 sub-apertures, (b) 12 subapertures, (c) 4 sub-apertures.

Fig. 13. Lateral amplitude profiles at a range distance of 21 mm obtainedby (a) amplitude and phase estimation beamforming and (b) modified
amplitude and phase estimation beamforming.

was improved by considering the element directivity. As
a result, good B-mode images could be obtained without sub-array averaging, which was required for conventional APES beamforming [22]. The feasibility of the
proposed method was examined through simulations andbasic experiments. Sub-array averaging was not used forevaluation of the effect of the element directivity itself.
In the proposed modified APES beamformer, in which
the element directivity was taken into account, the spatial
resolution and the image contrast were improved without sub-array averaging. In terms of the computationalload, sub-aperture beamforming was used to increase thecomputational efficiency. The image spatial resolution isdegraded when the computational load is reduced by subarray averaging used in conventional adaptive beamforming (reduction of the size of the covariance matrix) [14]. In
the present study, it was shown that sub-aperture beamforming did not degrade the spatial resolution and wascomputationally effective.

In the field of audible sound, the element directivityof a microphone array has been taken into account for
determining the invariant (not adaptive) weights for individual elements in the beamforming process [27], [28]. In
medical ultrasound imaging, the element directivity has
not been considered in general. We have shown that theperformance of the adaptive beamformer can be improvedby considering the element directivity.
The adaptive beamformer suppresses the components
contained in the covariance matrix, which is estimatedfrom the received ultrasonic echo signals. Therefore, thedesired signals should be removed from the covariance matrix. The accuracy in estimation of the desired signal isdegraded if the element directivity is not considered. The
amount of the desired signal component, which remains
in the covariance matrix, is dominant when the desired
signal is a strong echo, such as an echo from a wire in
the experiment in the present study. In such a case, thedominant component contained in the covariance matrix

hasegawa and kanai: adaptive beamforming applied to high-frame-rate ultrasound521

Fig. 14. B-mode images of cyst phantom obtained by (top) amplitude
and phase estimation beamforming and (bottom) modified amplitude
and phase estimation beamforming. (a) 24 sub-apertures, (b) 12 subapertures, (c) 4 sub-apertures.

becomes the residue of the desired signal. As a result, thestrong echoes (desired signal) were particularly suppressedby adaptive beamforming when the element directivity
was not considered.
In conventional APES beamforming, the estimation of
the desired signal corresponds to DAS beamforming withrectangular apodization. Therefore, the side lobe components, which are undesired signals, are also estimated andremoved from the covariance matrix. Therefore, the side
lobe components are not suppressed so much in conventional APES beamforming.
By considering the element directivity, the accuracy inestimation of the desired signal (i.e., the echo from the
focal point) is improved, and more parts of the desired signal are removed from the covariance matrix. On the other
hand, the accuracy in estimation of the side lobe components is degraded by considering the element directivity
because the directivity shown by (11) assumes the direction of the signal to be the direction of the focal point,whereas the side lobe components originate from the otherFig. 15. Lateral full widths at half maxima (a), contrast (b), andcontrast-to-noise ratios obtained by amplitude and phase estimation(APES) beamforming and modified APES with different numbers of
sub-apertures.

directions. As a result, the side lobe components remain in
the covariance matrix and are suppressed by the modified
APES beamformer proposed in the present study.
Conventional adaptive beamforming is often used withthe sub-array averaging technique [15]. Sub-array averaging avoids the desired signals being suppressed and reduces the computational load but degrades the spatial resolution. In the modified APES beamformer, sub-aperture
beamforming reduces the computational load but does notdegrade the spatial resolution. Such characteristics of themodified APES beamformer are very practical to realize
high temporal and spatial resolutions simultaneously. Un-

522

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 62, no. 3, March 2015

Fig. 16. B-mode images of (a) string and (b) cyst phantoms obtained byconventional APES beamforming with sub-array averaging (48 elementsin each sub-array) and diagonal loading corresponding to 0.05/L of thereceived power.

der the computational environment in the present study,
the computation time required for proposed beamformingwith 4 sub-apertures (18 elements in each sub-aperture)was 1/20 of that required for proposed beamforming without sub-apertures (72 elements in total aperture). Calculation of the inverse matrix of the spatial covariance matrix
of a large dimension is a significant computational load,
and the sub-aperture beamforming is effective to reducethe dimension of the spatial covariance matrix.
One of the problems of the proposed modified APES
beamformer is the excessive suppression of speckle echoesfrom diffuse scattering medium. As can be seen in Fig. 10,
the difference between amplitudes of echoes from a strong
scatterer (wire) and those of a diffuse scattering medium
was significantly increased to about 60 dB. Although sucha problem should be overcome in the future work, theproposed modified APES beamformer is effective for improvement of the spatial resolution in ultrasound imaging
and is also computationally effective when working with
sub-aperture beamforming.
V. Conclusions
In the present study, the APES beamformer was modified so that the accuracy in estimation of the desired signal is improved when the spatial covariance matrix was

estimated. Although ultrasonic attenuation during propagation was not considered, the spatial resolution and image contrast were improved significantly compared withconventional DAS and APES beamforming. Further study
on incorporating with ultrasonic attenuation would realize
more accurate estimation of the desired signal and additional improvement of the image quality.
In addition, sub-aperture beamforming was implemented for reduction of computational load. In minimum
variance beamforming, sub-array averaging was used for
reduction of computational load. However, sub-array averaging degraded the spatial resolution of an obtained ultrasound image. In contrast, sub-aperture beamforming usedin the proposed modified APES beamformer did not degrade the spatial resolution. Also, as seen in Fig. 12, subaperture beamforming seems to improve the penetration
depth. A larger number of elements in each sub-aperture
realized a better penetration depth. The improvement of
the signal-to-noise ratio of the output signal from each
sub-aperture can be considered as a reason for the improvement in the penetration depth.
As described above, the proposed modified APES
beamformer has preferable characteristics, i.e., providing
better spatial resolution and contrast than conventional
beamformer even with a 4 × 4 spatial covariance matrix.
Further study should be conducted for real-time implementation of the proposed method. A GPU-based system
is a potential candidate for real-time implementation [29].
References[1]	D. P. Shattuck, M. D. Weinshenker, S. W. Smith, and O. T. vonRamm, “Explososcan: A parallel processing technique for high speed
ultrasound imaging with linear phased arrays,” J. Acoust. Soc. Am.,
vol. 75, no. 4, pp. 1273–1282, 1984.
[2] M. Tanter, J. Bercoff, L. Sandrin, and M. Fink, “Ultrafast compound imaging for 2-D motion vector estimation: Application totransient elastography,” IEEE Trans. Ultrason. Ferroelectr. Freq.
Control, vol. 49, no. 10, pp. 1363–1374, 2002.
[3]	H. Hasegawa and H. Kanai, “Simultaneous imaging of artery-wallstrain and blood flow by high frame rate acquisition of RF signals,”IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 55, no. 12, pp.
2626–2639, 2008.
[4]	Y. Honjo, H. Hasegawa, and H. Kanai, “Two-dimensional trackingof heart wall for detailed analysis of heart function at high temporaland spatial resolutions,” Jpn. J. Appl. Phys., vol. 49, no. 7, art. no.
07HF14, 2010.
[5] J. Provost, A. Gambhir, J. Vest, H. Garan, and E. E. Konofagou, “Aclinical feasibility study of atrial and ventricular electromechanicalwave imaging,” Heart Rhythm, vol. 10, no. 6, pp. 856–862, 2013.
[6]	D. Shahmirzadi, R. X. Li, and E. E. Konofagou, “Pulse-wave propagation in straight-geometry vessels for stiffness estimation: Theory,
simulations, phantoms and in vitro findings,” J. Biomechan. Eng.,
vol. 134, no. 11, art. no. 114502, 2012.
[7]	H. Hasegawa, K. Hongo, and H. Kanai, “Measurement of regional
pulse wave velocity using very high frame rate ultrasound,” J. Med.
Ultrasound, vol. 40, no. 2, pp. 91–98, 2013.
[8] J. Bercoff, G. Montaldo, T. Loupas, D. Savery, F. Mézière, M. Fink,
and M. Tanter, “Ultrafast compound Doppler imaging: Providing
full blood flow characterization,” IEEE Trans. Ultrason. Ferroelectr.
Freq. Control, vol. 58, no. 1, pp. 134–147, 2011.
[9] B. Y. Yiu and A. C. Yu, “High-frame-rate ultrasound color-encoded
speckle imaging of complex flow dynamics,” Ultrasound Med. Biol.,vol. 39, no. 6, pp. 1015–1025, 2013.

hasegawa and kanai: adaptive beamforming applied to high-frame-rate ultrasound[10]	H. Takahashi, H. Hasegawa, and H. Kanai, “Echo speckle imagingof blood particles with high-frame-rate echocardiography,” Jpn. J.
Appl. Phys., vol. 53, no. 7, art. no. 07KF08, 2014.
[11]	S. K. Jespersen, J. E. Wilhjelm, and H. Sillesen, “Multi-angle compound imaging,” Ultrason. Imaging, vol. 20, no. 2, pp. 81–102, 1998.
[12] G. Montaldo, M. Tanter, J. Bercoff, N. Benech, and M. Fink, “Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 3, pp. 489–506, 2009.
[13] J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE, vol. 57, no. 8, pp. 1408–1418, 1969.
[14] J. F. Synnevåg, A. Austeng, and S. Holm, “Adaptive beamforming
applied to medical ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 8, pp. 1606–1613, 2007.
[15] I. K. Holfort, F. Gran, and J. A. Jensen, “Broadband minimum variance beamforming for ultrasound imaging,” IEEE Trans. Ultrason.
Ferroelectr. Freq. Control, vol. 56, no. 2, pp. 314–325, 2009.
[16] J. F. Synnevåg, A. Austeng, and S. Holm, “Benefits of minimumvariance beamforming in medical ultrasound imaging,” IEEE Trans.
Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 9, pp. 1868–1879,
2009.
[17]	A. Rabinovich, Z. Friedman, and A. Feuer, “Multi-line acquisition
with minimum variance beamforming in medical ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 60, no.
12, pp. 2521–2531, 2013.
[18] J. F. Synnevåg, C.-I. Nilsen, and S. Holm, “Speckle statistics inadaptive beamforming,” in Proc. IEEE Ultrasonics Symp., 2007, pp.
1545–1548.
[19] J. F. Synnevåg, A. Austeng, and S. Holm, “A low-complexity data
dependent beamformer,” IEEE Trans. Ultrason. Ferroelectr. Freq.
Control, vol. 58, no. 2, pp. 281–289, 2011.
[20] B. M. Asl and A. Mahloojifar, “A low-complexity adaptive beamformer for ultrasound imaging using structured covariance matrix,”IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 59, no. 4, pp.
660–667, 2012.
[21] K. Kim, S. Park, J. Kim, S.-B. Park, and M. Bae, “A fast minimum
variance beamforming method using principal component analysis,”IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 61, no. 6, pp.
930–945, 2014.
[22]	A. E. A. Blomberg, I. K. Holfort, A. Austeng, J. F. Synnevåg, S.
Holm, and J. A. Jensen, “APES beamforming applied to medical
ultrasound imaging,” in 2009 IEEE Int. Ultrasonics Symp. Proc., pp.
2347–2350.
[23] F. J. Pompei and S. Wooh, “Phased array element shapes for suppressing grating lobes,” J. Acoust. Soc. Am., vol. 111, no. 5 pt. 1, pp.
2040–2048, 2002.
[24] M. C. van Wijk and J. M. Thijssen, “Performance testing of medical
ultrasound equipment: Fundamental vs. harmonic mode,” Ultrasonics, vol. 40, no. 1–8, pp. 585–591, 2002.
[25] J. M. Thijssen, G. Weijers, and C. L. de Korte, “Objective performance testing and quality assurance of medical ultrasound equipment,” Ultrasound Med. Biol., vol. 33, no. 3, pp. 460–471, 2007.
[26] J. A. Jensen, “Field: A program for simulating ultrasound systems,”
Med. Biol. Eng. Comput., vol. 34, suppl. 1, pt. 1, pp. 351–354, 1996.
[27] M. R. P. Thomas, J. Ahrens, and I. Tashev, “Optimal 3D beamforming using measured microphone directivity patterns,” in International Workshop Acoust. Sig. Enhancement, 2012.
[28] M. R. P. Thomas, J. Ahrens, and I. J. Tashev, “Beamformer design using measured microphone directivity patterns: Robustness tomodeling error,” in APSIPA Ann. Summit Conf., 2012.

523[29] J. P. Åsen, J. I. Buskenes, C.-I. C. Nilsen, A. Austeng, and S. Holm,“Implementing Capon beamforming on a GPU for real-time cardiac
ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 61, no. 1, pp. 76–85, 2014.

Hideyuki Hasegawa was born in Oyama, Japan, in 1973. He received the B.E. degree fromTohoku University, Sendai, Japan, in 1996. He received the Ph.D. degree from Tohoku University
in 2001. He is presently an associate professor in
Graduate School of Biomedical Engineering, Tohoku University. His research interest is medical
ultrasonic imaging and measurements of tissue
dynamics and viscoelasticity. Dr. Hasegawa is amember of the IEEE, the Acoustical Society ofJapan, the Japan Society of Ultrasonics in Medicine, and the Institute of Electronics, Information and Communication
Engineers.

Hiroshi Kanai was born in Matsumoto, Japan,
on November 29, 1958. He received a B.E. degreefrom Tohoku University, Sendai, Japan, in 1981,
and M.E. and the Ph. D. degrees, also from Tohoku University, in 1983 and in 1986, both in electrical engineering. From 1986 to 1988 he was with
the Education Center for Information Processing,Tohoku University, as a research associate. From1990 to 1992 he was a lecturer in the Department
of Electrical Engineering, Faculty of Engineering,Tohoku University. From 1992 to 2001 he was an
associate professor in the Department of Electrical Engineering, Facultyof Engineering, Tohoku University. Since 2001 he has been a professor in
the Department of Electronic Engineering, Graduate School of Engineering, Tohoku University. Since 2008 he has been also a professor in the
Department of Biomedical Engineering, Graduate School of Biomedical
Engineering, Tohoku University. From 2012 he has been a dean of Graduate School of Engineering, Tohoku University.
His present interests are in transcutaneous measurement of the heart
wall vibrations and myocardial response to propagation of electrical potential and cross-sectional imaging of elasticity around atherosclerotic
plaque with transcutaneous ultrasound for tissue characterization of thearterial wall.
Dr. Kanai is a member of the Acoustical Society of Japan, a fellow of
the Institute of Electronics Information and Communication Engineering of Japan, a member of the Japan Society of Ultrasonics in Medicine,Japan Society of Medical Electronics and Biological Engineering, andthe Japanese Circulation Society. Since 1998, he has been a memberof Technical Program Committee of the IEEE Ultrasonics Symposium.
Since 2008, he has been an International Advisory Board of International Acoustical Imaging Symposium. Since 2011, he has been a Board
member of International Congress on Ultrasonics. Since 2012, he has
been an editor of Journal of Medical Ultrasonics and Japanese Journal of
Medical Ultrasonics. Since 2013, he has been an associate editor of theIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.