IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 61, no. 11, November 20141779

Effect of Subaperture Beamformingon Phase Coherence Imaging
Hideyuki Hasegawa and Hiroshi Kanai
Abstract—High-frame-rate echocardiography using unfocused transmit beams and parallel receive beamforming is apromising method for evaluation of cardiac function, such as
imaging of rapid propagation of vibration of the heart wall
resulting from electrical stimulation of the myocardium. In
this technique, high temporal resolution is realized at the expense of spatial resolution and contrast. The phase coherence
factor has been developed to improve spatial resolution andcontrast in ultrasonography. It evaluates the variance in phases of echo signals received by individual transducer elements
after delay compensation, as in the conventional delay-andsum beamforming process. However, the phase coherence factor suppresses speckle echoes because phases of speckle echoes
fluctuate as a result of interference of echoes. In the present
study, the receiving aperture was divided into several subapertures, and conventional delay-and-sum beamforming was
performed with respect to each subaperture to suppress echoesfrom scatterers except for that at a focal point. After subaperture beamforming, the phase coherence factor was obtained
from beamformed RF signals from respective subapertures.
By means of this procedure, undesirable echoes, which caninterfere with the echo from a focal point, can be suppressedby subaperture beamforming, and the suppression of the phasecoherence factor resulting from phase fluctuation caused bysuch interference can be avoided. In the present study, theeffect of subaperture beamforming in high-frame-rate echocardiography with the phase coherence factor was evaluated usinga phantom. By applying subaperture beamforming, the average intensity of speckle echoes from a diffuse scattering medium was significantly higher (−39.9 dB) than that obtained
without subaperture beamforming (−48.7 dB). As for spatial
resolution, the width at half-maximum of the lateral echo amplitude profile obtained without the phase coherence factor
was 1.06 mm. By using the phase coherence factor, spatial
resolution was improved significantly, and subaperture beamforming achieved a better spatial resolution of 0.75 mm thanthat of 0.78 mm obtained without subaperture beamforming.

I. Introduction

Echocardiography is a widely used modality for
diagnosis of the heart. Because of the temporal
resolution, which is much better than those of computed tomography (CT) and magnetic resonance imaging(MRI), echocardiography is indispensable for evaluationof cardiac function in clinical situations. In addition to
the morphological observation of cross-sectional imagesof the heart based on ultrasonography, ultrasonic meth-

Manuscript received February 27, 2014; accepted July 31, 2014.
The authors are with the Graduate School of Biomedical Engineeringand the Graduate School of Engineering, Tohoku University, Sendai,
Japan (email: hasegawa@ecei.tohoku.ac.jp).
DOI http://dx.doi.org/10.1109/TUFFC.2014.006365

ods for measurements of the myocardial strain and strain
rate [1]–[4] have been developed and used for evaluationof cardiac function. Also, it has been recently reported
that the propagation of myocardial electrical excitation,
which has been visualized by ultrasonic measurement ofelectrical-stimulation-induced myocardial motion, can beobserved by further increasing the temporal resolution inechocardiography [5], [6]. The measurement of such propagation phenomenon would be useful for detection of a siteof myocardial infarction. The electrical excitation propagates in Purkinje fibers and ventricular muscle at typicalvelocities of 2 to 4 m/s [7], [8], and the corresponding
propagation velocities of myocardial contraction of 0.9
to 4 m/s have been measured by ultrasound [5]. In thosecited studies, frame rates of several hundred hertz, whichwere much higher than the several tens of hertz in conventional echocardiography, were realized by sparse scan (lowdensity of scan lines) and ECG gating (requiring several
cardiac cycles to obtain an entire image).
To realize high-frame-rate echocardiography without
decreasing the density of scan lines and ECG gating, Lu
et al. used plane waves in transmission to illuminate awider region by one emission and to reconstruct an imageof the illuminated region [9] based on diffraction tomography [10]–[12]. Recently, a diverging beam, which emulates a spherical wave from a virtual point source behindan array, has been found to be usable to illuminate aneven wider region than a plane wave, and diverging beamtransmission and parallel receive beamforming have beenshown to be feasible in high-frame-rate echocardiography[13]–[17].
Recent developments in high-frame-rate ultrasonography commenced with linear arrays [18]–[21]. Using parallel
beamforming, temporal resolution has been significantly
improved, but spatial resolution was degraded by the useof unfocused transmit beams. To improve spatial resolution, coherent plane-wave compounding has been introduced [22]. In this technique, beamformed RF signals at
the same spatial point, which were obtained by transmitting plane waves from different directions, were coherently
averaged. By means of this procedure, the synthesized
point spread function became narrower (i.e., had better
spatial resolution) than those formed by individual transmissions. In the case of a linear array, the size of the aperture is large, i.e., the width of a plane wave is large, andplane waves can be compounded coherently even when thesteering angle is relatively large. On the other hand, inechocardiography using a phased array, ultrasound must
be insonified from a narrow acoustic window between ribs
and, thus, the size of the aperture, corresponding to the0885–3010 © 2014 IEEE

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width of a plane wave, is limited. Under such conditions, it
is difficult to compound plane waves at different steering
angles, and the effect of compounding is degraded.
To improve spatial resolution and contrast in ultrasonography, the minimum variance beamforming method
has been developed [23]. This method improves the spatial resolution significantly by minimizing the power of
echo signals coming from undesired directions (i.e., except
for the focal point). In minimum variance beamforming,
Synnevåg also introduced sub-array averaging for controlling the trade-off between the robust solution and thespatial resolution [24]. This method requires calculationof the covariance matrix of the complex echo signals received by individual transducer elements after delay compensation as in conventional delay-and-sum beamforming
process, and the inverse matrix of the covariance matrix
must be obtained. Therefore, although minimum variancebeamforming is a promising method for improvement of
spatial resolution, it is computationally intensive.
There is another technique, namely, the phase coherence factor (PCF) [25], which would also be effective for
improvement of spatial resolution and contrast in highframe-rate echocardiography. However, speckle echoes tend
to be suppressed by the phase coherence factor, whereasstrong echoes tend to be enhanced. In echocardiography,
specular reflection from valves and the interface between
the heart wall and blood should be visualized, but speckle
echoes from the inside of the heart wall should also be
visualized. Therefore, in the present study, a strategy foruse of the phase coherence factor was proposed for avoiding suppression of speckle echoes from a diffuse scattering
medium.
II. Principles
A. Phase Coherence Factor
The phase coherence factor [25] is used for weighting
beamformed RF echoes to improve spatial resolution andcontrast in ultrasonography. The weight is determined byevaluating the variance in phases of ultrasonic RF echoes
received by individual transducer elements. The phasevariance is evaluated after delay compensation as in aconventional delay-and-sum beamforming process. Whenan echo comes from a scatterer exactly located at a focal
point of the beamformer, echoes received by individual
elements are perfectly aligned after the application of delay compensation and, thus, the phase variance among
elements would be zero, corresponding to high phase coherence factor (maximum is 1). Because of this propertyof the phase coherence factor, echoes from spatial points
except for a focal point will be suppressed because of focusing errors resulting in increased phase variance, andspatial resolution and contrast will be improved.
To obtain phases of echo signals received by individual
elements, in the present study, for computational efficiency, the complex signal gi(t) of the echo signal si(t) received

by the ith element (i = 1, 2, …, N ) was obtained using theshort-time Fourier transform with respect to the ultrasonic center frequency f0 instead of the analytic signal
obtained by the Hilbert transform. The short-time Fouriertransform was used with a Hann window of 0.512 μs in
length. Under this condition, the first nulls of the power
spectrum of the Hann window in estimation of the Fourier
coefficient at the ultrasonic center frequency of 3 MHz
were located at −0.125 and 6.25 MHz. Although a shorter
window can increase the frequency bandwidth of its main
lobe, components at negative frequencies would be included to estimate the Fourier coefficient at 3 MHz. Therefore,
in the present study, one of the first nulls was placed close
to 0 MHz. By estimating the Fourier coefficient only at
the ultrasonic center frequency, the computational load
was significantly lower than the Hilbert transform. In delay compensation in conventional delay-and-sum beamforming, subsample time delay τs was compensated bymultiplying the estimated complex signal gi(t) byexp ( j2π f0τs). The phase coherence factor PCF was evaluated using the phase ϕi of gi(t) · exp ( j2π f0τs). However,
the estimated phases ϕi have discontinuity when the estimated phase value crosses the +π and −π boundary, despite the fact that phases close to ±π are similar. To avoid
this pitfall, the auxiliary phase φiA was also obtained,
where +π was added to ϕi if ϕi < 0 and −π is added if ϕi> 0. The standard deviations σ1 and σ2 across the receiving aperture were estimated with respect to ϕi and φiA,
respectively, and the smaller standard deviation (σ1 or σ2)
was used as the standard deviation σ of the phases of
echoes received by individual elements. Using the estimated standard deviation σ, the coherence factor PCF wasestimated as
PCF = 1 −

σ
,
σ0

(1)

where σ0 is the nominal standard deviation of π /31/2 of a
uniform distribution between −π and π [25].
B. Problem in Conventional Phase Coherence Imaging
One important consideration in this procedure is thatechoes from multiple scatterers should overlap in the signal received by each element. Let us consider the case inwhich an echo from a scatterer exactly located at a focal
point of a beamformer is much stronger than other echoes,
namely, out-of-focus echoes. Fig. 1(1-a) shows RF echoes
received by individual elements and their phases obtained
after delay compensation in a conventional delay-and-sum
beamforming process. The red dashed lines in Fig. 1 show
the focal point. In such a case, the contribution of outof-focus echoes is negligible because the echo from the
focal point is dominant, and phases of signals received byindividual elements reflect the phase of the dominant echo
from the focal point. Therefore, the phases are similar
at the focal point and the phase variance is low, i.e., thephase coherence factor is high.

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In the present study, a controlled phase coherence factor PCF0.5 at γ = 0.5 was examined.

Fig. 1. RF echoes and their phases obtained from (1) a strong scattererand (2) a weak scatterer; RF echoes and their phases are obtained byindividual (a) elements and (b) subapertures.

On the other hand, when an echo from a focal point isweak, e.g., echoes from a diffuse scattering medium, contributions of out-of-focus echoes cannot be negligible. Fig.
1(2-a) shows RF echoes from a diffuse scattering medium
and their phases. As can be seen in Fig. 1(2-a), RF echoes
are not aligned even after delay compensation because
out-of-focus echoes are not negligible and interfere withthe echo from the focal point. In such a case, the phasevariance would be high, i.e., a low phase coherence factor,
even when a weak echo coming from the focal point exists.
C. Strategies for Avoiding Suppression of Speckle Echoesin Phase Coherence Imaging
For avoiding undesirable suppression of weak echoesfrom a diffuse scattering medium, in the present study,some strategies for evaluation of the phase variance were
examined, as described subsequently.
1) Controlled PCF [25]: A method for avoiding suppression of speckle echoes, which should be mentioned first,
is to weaken the effect of the phase coherence factor by
introducing a control parameter γ as follows [25]:PCF γ = 1 −

γ
σ.
σ0

(2)

2) PCF With Subaperture Beamforming [26]: In the caseof a diffuse scattering medium, the interference between
an echo from a focal point and out-of-focus echoes significantly influences the phase estimated from the echo
signal received by each element. Therefore, out-of-focus
echoes must be suppressed to estimate the phase of anecho from the focal point. To suppress the contributionsof out-of-focus echoes, a receiving aperture consisting of
N elements was divided into M subapertures. Each subaperture performs conventional delay-and-sum beamformingwith respect to an assigned focal point. By subaperture
beamforming, echoes from scatterers except for that at
the focal point can be suppressed. Figs. 1(1-b) and 1(2-b)
show RF echoes and their phases obtained after subaperture beamforming. For the strong echo from the focal
point [Fig. 1(1-b)], there is no significant change in the
RF echoes and phases at the focal point between preand post-subaperture beamforming because out-of-focus
echoes are negligible. On the other hand, in the case of the
weak echo from a diffuse scattering medium shown in Fig.
1(2-b), there is a significant change in RF echoes between
pre- and post-subaperture beamforming. By subaperture
beamforming, an echo from the focal point was enhanced,
and the differences in phases at the focal point became
smaller than those before subaperture beamforming.
In the present study, non-overlapping and overlapping
subapertures were examined. Hyun et al. showed that subaperture beamforming could be used for efficient calculation of spatial coherence in the use of a 2-D matrix array[27]. They showed that the short-lag spatial coherence
estimated without subaperture beamforming showed thebest performance but subaperture beamforming led to no
significant degradation of the performance. Overlapping
subapertures were used in [28] for improving estimation ofaberration in received ultrasonic echoes.
In the case of non-overlapping subapertures, each subaperture consists of N/M elements. On the other hand,the number of subapertures and the number of elements ineach subaperture can be assigned independently. However,in comparison between non-overlapping and overlapping
subapertures, the same number of elements in each subaperture was used and the number of subapertures was set
at N − M + 1 (the subaperture was shifted by one element) in the case of overlapping subapertures. The phasecoherence factor was estimated using the phases of thesubaperture output signals based on (2).
3) PCF With Reduced Number of Elements: The estimation of the phase coherence factor with subapertures beamforming significantly reduces the number of phase data
for estimating the phase variance. Using a smaller number of phase data increases the variance in the estimatedphase variance (see appendix). The increased variance inestimation of the phase variance would increase the casein which the phase variance evaluated from echoes from

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diffuse scattering medium becomes low. This means thatspeckle echoes from a diffuse scattering medium are more
likely visualized compared with the case in which a larger
number of phase data are used. To examine the effect of
the number of phase data on phase coherence imaging, inthe present study, the phase coherence factor was also estimated using a smaller number of elements (and, therefore,
phase data). The number of elements corresponds to thenumber of subapertures in the non-overlapping case.
III. Experimental Results
A. Basic Experiments Using Phantom
In the present study, a custom-made ultrasound system (RSYS0002, Microsonic, Tokyo, Japan), which enables 96-channel simultaneous transmit and is able toacquire ultrasonic RF echoes from 96 elements, was usedwith a commercial 3.75-MHz phased array probe (UST52101, Hitachi-Aloka, Tokyo, Japan). The total numberof elements and the element pitch of the phased arrayprobe were N = 96 and 0.2 mm, respectively. Ultrasonic echoes received by individual elements were sampled
at 31.25 MHz at 12-bit resolution for off-line processing(receive beamforming, estimation of phase coherence factor, etc.). An ultrasound imaging phantom (model 54GS,
Computerized Imaging Reference Systems Inc., Norfolk,
VA) was used for evaluation of spatial resolution and effects of subaperture beamforming on speckle echoes froma diffuse scattering medium. The phantom includes finewires and cyst phantoms in a diffuse scattering medium.
Fig. 2(a) shows a B-mode image of the phantom obtained by parallel receive beamforming described in [14]with transmissions of diverging waves in 15 directions.
The virtual point source was 100 mm behind the array,and the angular interval between transmit beams was 6°.
The lateral amplitude profile of the B-mode image at a
range distance of 42 mm is shown in Fig. 3. To evaluate
spatial resolution, the width at half-maximum of the amplitude profile of an echo from a wire was calculated fromthe data shown in Fig. 3. The width at half-maximum wl
was estimated to be 1.06 mm. For consideration of the effects of subaperture beamforming on speckle echoes froma diffuse scattering medium, ratio ra between the peak
amplitude of an echo from a wire to the average echo amplitude in the diffuse scattering medium (corresponding to
the region indicated by lateral angle θ of −45° < θ < −5°in Fig. 3) was evaluated. Also, the mean over standard
deviation μ /σ of the echo amplitude profile in −45° <θ < −5° was obtained for evaluation of image blurring.
The ratio ra and mean over standard deviation μ /σ were
evaluated to be −32.3 dB and 7.2 dB, respectively, forparallel beamforming without the phase coherence factor.
In the B-mode image obtained without the phase coherence factor, speckle echoes can be observed, but the imageis blurred by undesired signals, such as electrical noise andechoes originating from side lobes, which would increase
the mean μ of echo amplitudes.
Fig. 2(b) shows a B-mode image of the phantom obtained with the phase coherence factor with no subaperture beamforming. In Fig. 2(b), although the lateral spatial resolution is improved by using the phase coherence
factor, speckle echoes in a diffuse scattering medium aresignificantly suppressed. Lateral spatial resolution wl was
0.78 mm. Amplitude ratio ra and mean over standard deviation μ /σ were evaluated to be −48.7 dB and −0.3 dB,
respectively. The mean over standard deviation μ /σ wasdecreased because the speckle echoes were more visualized
by the phase coherence factor and the standard deviation
σ was increased.
Figs. 2(c), 2(d), 2(e), and 2(f) show B-mode images
obtained with controlled coherence factor, coherence factors estimated with non-overlapping subapertures, reduced number of elements, and overlapping subapertures,
respectively. With respect to the controlled phase coherence factor, the spatial resolution wl was 0.92 mm. The
amplitude ratio ra and mean over standard deviation μ /σ
were −36.5 dB and 6.34 dB, respectively. Although the increased ra of −36.5 dB shows the enhancement of speckle
echoes, the increased wl and μ /σ show the degraded spatial resolution and image blurring, respectively.
Then, phase coherence factors obtained with non-overlapping subapertures and reduced number of elements
were compared. The number of elements in each non-overlapping subaperture was N/M (where M is the numberof subapertures and N is the total number of elements).
In Fig. 2(d), M = 4. In Fig. 2(e), the number of elements
used for estimation of the phase coherence factor was 4,
where each element was located at the position corresponding to the center of each of the non-overlapping subapertures in Fig. 2(d). In Fig. 2(d), spatial resolution wl,
amplitude ratio ra, and mean over standard deviation μ /σ
are 0.75 mm, −39.9 dB, and 3.6 dB, respectively. In Fig.
2(e), spatial resolution wl, amplitude ratio ra, and meanover standard deviation μ /σ are 0.77 mm, −39.4 dB, and5.3 dB, respectively. In terms of speckle-echo visualization, non-overlapping subaperture and reduced numberof elements showed similar performances. However, thephase coherence factor estimated with non-overlapping
subapertures achieved better spatial resolution (smallerwl) with less blurring (lower μ /σ). Figs. 4(a), 4(b), and4(c) summarize estimated spatial resolution {wl}, amplitude ratios {ra}, and means over standard deviation,{μ /σ}, respectively.
As shown in Fig. 4(a), the spatial resolution wl evaluated from an echo from a fine wire (strong scatterer) was
further improved by subaperture beamforming. A strong
echo from a strong scatterer located at a focal point is alsointerfered by weak echoes from diffuse scattering medium,
which is surrounding the strong scatterer. Although theeffect of such interference is smaller than that between
echoes both from weak scatterers in diffuse scattering medium, the phase variance estimated with respect to thehasegawa and kanai: effect of subaperture beamforming on phase coherence imaging

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Fig. 2. B-mode images of phantom: (a) without the phase coherence factor, (b) with the conventional phase coherence factor, (c) with the controlled
phase coherence factor (γ = 0.5), (d) with the phase coherence factor with 4 non-overlapping subapertures (24 elements/subaperture), (e) with thephase coherence factor estimated by 4 elements, and (f) with the phase coherence factor with 73 overlapping subapertures (24 elements/subaperture).

strong echo from the focal point would increase, whichleads to suppression of the peak amplitude (at the focal
point) of the strong echo. As a result, the spatial resolution, which was evaluated as the width at half-maximumof the echo amplitude, was degraded slightly when thephase coherence factor was estimated without subaperture beamforming (corresponding to a reduced numberof elements). Using subaperture beamforming, such weakechoes interfering with the strong echo at the focal point
were suppressed, and the spatial resolution was improved.
As shown in Fig. 4(b), amplitude ratios {ra}, which aresimilar at all numbers of subapertures and number of elements, show that phase coherence factors estimated with
non-overlapping subapertures and reduced number of ele-

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Fig. 3. Lateral amplitude profiles of B-mode images at range distance of
42 mm. Profiles were obtained without phase coherence factor (PCF),
with conventional PCF, with controlled PCF, with PCF obtained by
4 non-overlapping subapertures (24 elements/subaperture), with PCF
obtained by reduced number of elements (4 elements), and with PCF
obtained by 73 overlapping subapertures (24 elements/subaperture).

ments realized similar levels of speckle-echo visualization.
However, it should be noted that the average echo amplitude is also increased by random noise, such as electrical noise. This result suggests that the average echo
amplitude in a diffuse scattering medium depends on thenumber of data used for estimation of the phase coherence
factor. By reducing the number of data for estimation of
the phase coherence factor, the variance in estimation of
the phase variance becomes higher, as described in the
appendix, and the difference between the phase coherence
factor of the coherent echo and that of the incoherent
component, e.g., echoes from diffuse scattering medium,
electrical noise, etc., is possibly decreased more. As a result, the increase in the difference between relative magnitudes of the coherent echo and the incoherent component
was suppressed by decreasing the number of data used for
estimation of the phase coherence factor.
In an ultrasound imaging, echo speckles increase thestandard deviation in the echo amplitude profile. On theother hand, random noise, such as electrical noise, leads tonoisy images; i.e., the mean of the echo amplitude profile
in an ultrasound image increases. In Fig. 4(c), the meanover standard deviation μ /σ obtained with subaperture
beamforming was lower than that obtained with reduced
number of elements (without subaperture beamforming).
This means that subaperture beamforming realizes moreenhancement of speckle echoes. As shown in Fig. 4(b),the average echo amplitudes in diffuse scattering medium
are similar, and more enhancement of speckle echoes (notrandom noise) is possible by the phase coherence factor
obtained with subaperture beamforming.
Therefore, by evaluating the mean over standard deviation, it can be confirmed whether speckle echoes orFig. 4. Basic experimental results obtained with phase coherence factors, which were estimated with non-overlapping subapertures and reduced number of elements. (a) Lateral widths at half-maxima {wl} ofecho amplitude profiles (wl obtained without the phase coherence factor(PCF) was much larger (1.06 mm) and not indicated in the figure). (b)Amplitude ratios {ra}. (c) Mean to standard deviation of echo amplitude
profile.

random noise is enhanced. In Fig. 4(c), the mean overstandard deviation μ /σ obtained with subaperture beamforming was lower than that obtained with reduced number of elements (without subaperture beamforming). Thismeans that subaperture beamforming realizes more sup-hasegawa and kanai: effect of subaperture beamforming on phase coherence imaging

pression of random noise. As shown in Fig. 4(b), the average echo amplitudes in diffuse scattering medium are similar, and more enhancement of speckle echoes (not random
noise) is possible by the phase coherence factor obtainedwith subaperture beamforming.
In Fig. 4, spatial resolution wl, amplitude ratio ra, andmean over standard deviation μ /σ are also evaluated withrespect to ultrasound images obtained using Hann apodization in each subaperture beamforming. Subaperture
apodization controls the effect of suppression of out-offocus echoes by changing the effective size of subaperture,
which is similar to controlling the effect of the coherence
factor by changing the filter coefficient (corresponding to
the cut-off direction of arrival) in [29]. Subaperture apodization weakens the effect of subaperture beamforming
because apodization reduces the effective subaperture size.
As shown in Fig. 4, although the phase coherence factor
obtained with apodized subapertures also improves speckle-echo visualization, as indicated by the amplitude ratio
ra, the spatial resolution wl and the mean over standard
deviation μ /σ are degraded by subaperture apodization.
In Fig. 4, it is shown that subaperture beamforming isuseful for improving the spatial resolution and visualization of speckle echoes. However, subapertures do not overlap, and the number of subapertures are limited, particularly at a large number of elements in each subaperture.
To evaluate the effect of the number of subapertures, theresults were also obtained with non-overlapping and overlapping subapertures, as shown in Fig. 5.
Using overlapping subapertures, the spatial resolution
wl was degraded at a large number of elements in each
subaperture. In the case of overlapping subapertures witha large number of elements, the information from subapertures are not independent, and the echo signals fromelements, which are located around the center of the total aperture, are used many times (corresponding to thenumber of subapertures) to obtain the phase coherence
factor. This can be considered as the aperture data being
apodized by a weighting function whose weight is higharound the central of the aperture when we regard the
beamformed signals from respective subapertures as thesignals from array elements. The effective aperture size ofthe array is reduced by such apodization and, therefore,
the lateral spatial resolution is degraded, as shown in Fig.
5(a), using overlapping subapertures. Also, for random
noise, the randomness among noises contained in the signals from subapertures is degraded using overlapping subapertures even when noises contained in the signals fromindividual elements are random. As a result, the effect of
averaging of the signals from subapertures on suppressionof random noise is degraded, and the mean over standard
deviation deviation μ /σ is larger than that obtained with
non-overlapping subapertures.
In summary, subaperture beamforming in estimationof the phase coherence factor can improve the spatial
resolution and speckle-echo visualization, and the effectof the phase coherence factor can be controlled in various ways, such as introducing a control parameter, re-1785

Fig. 5. Basic experimental results obtained with phase coherence factors,
which were estimated with non-overlapping and overlapping subapertures. (a) Lateral widths at half-maxima {wl} of echo amplitude profiles(wl obtained without the phase coherence factor (PCF) was much larger(1.06 mm) and not indicated in the figure). (b) Amplitude ratios {ra}. (c)Mean to standard deviation of echo amplitude profile.

ducing the number of elements, subaperture apodization,and using overlapping subapertures. Introducing a control
parameter, reducing the number of elements, and subaperture apodization improve speckle-echo visualization
but degrade the spatial resolution. The use of overlapping subapertures slightly degrades the spatial resolution

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but improves speckle-echo visualization (higher amplitude
ratio ra) compared with the use of non-overlapping subapertures, particularly at a large number of elements ineach subaperture. Therefore, the phase coherence factor
obtained with overlapping subapertures might be a useful strategy. However, the use of overlapping subapertures
requires a significant additional computational cost, andthe phase coherence factor obtained with non-overlapping
subapertures shows good performance and seems effective
for improvement of the spatial resolution while preserving
speckle echoes.
B. In Vivo Measurement of Human Heart
Fig. 6(a) shows a B-mode image of the heart of a26-year-old healthy male. By weighting beamformed RF
signals using the conventional phase coherence factor, undesirable signals in the cardiac lumen are suppressed, as
shown in Fig. 6(b). However, speckle echoes inside theheart wall are also suppressed significantly.
Figs. 6(c), 6(d), 6(e), and 6(f) show B-mode images obtained with controlled coherence factor, coherence factors
estimated with 4 non-overlapping subapertures, reduced
number of elements of 4, and 73 overlapping subapertures(sizes of subapertures were same as those of 4 non-overlapping subapertures), respectively. By introducing thecontrol parameter, the effect of the phase coherence factor
was weakened, and speckle echoes inside the heart wall
could be visualized. However, undesired echoes in the cardiac lumen were hardly suppressed.
As can be seen in Figs. 6(d), 6(e), and 6(f), undesirable
echoes in the cardiac lumen could be suppressed by thephase coherence factors estimated with non-overlapping
subapertures, reduced number of elements, and overlapping subapertures while preserving speckle echoes inside
the heart wall. However, there are slightly more undesirable signals in the cardiac lumen in the case of the reduced
number of elements shown in Fig. 6(e).
As shown in Figs. 6(d) and 6(f), subaperture beamforming realizes good performance in suppressing undesirable signals while preserving speckle echoes inside theheart wall, whereas the larger speckle size in Fig. 6(f)shows the slight degradation of the spatial resolution by
overlapping subapertures as described in Section III-A.
From these results, it was also shown in the in vivo measurement that subaperture beamforming improves visualization of speckle echoes in phase coherence imaging.
IV. Discussion
As described in the present paper, the phase coherence
factor is very useful for improvement of spatial resolution and contrast in high-frame-rate echocardiography.
However, the phase coherence factor suppresses speckle
echoes significantly, and, therefore, a strategy for avoiding
suppression of speckle echoes has been proposed. In thepresent study, the phase coherence factor was obtainedwith subaperture beamforming to suppress the influenceof out-of-focus echoes.
As shown in Fig. 4(a), the spatial resolution wl evaluated from an echo from a fine wire (strong scatterer) was
further improved by subaperture beamforming. For interpretation of such slight improvement of the lateral spatial
resolution owing to subaperture beamforming, we haveconducted a simple simulation experiment. In this simulation, it was assumed that an ultrasonic echo from a point
target was received by 96 elements at element pitches of
0.2 mm. The point scatterer was located at 40 mm in range
distance and 0° in lateral direction. The ultrasonic center
frequency was set at 3 MHz and a Hanning envelope with
3 cycles at the ultrasonic center frequency was assumed.
White noise was added to the simulated ultrasonic signals
at a signal-to-noise ratio of 38.4 dB. In this simulation,echoes from diffuse scattering medium surrounding thepoint scatterer were assumed to be random.
Fig. 7(a) shows the lateral profiles of non-normalized
amplitudes of beamformed RF signals obtained withoutphase coherence factor (PCF) (red line), with PCF without subaperture beamforming (green line), and with PCF
with 6 subapertures (blue line). As shown in Fig. 7, thepeak echo amplitude obtained with PCF without subaperture beamforming is slightly decreased by the increaseof the phase variance resulting from random signals. Suchrandom signals are suppressed by subaperture beamforming before evaluation of PCF, and the suppression of thepeak amplitude is avoided.
Fig. 7(b) shows the lateral profiles of normalized amplitudes. By avoiding the suppression of the peak amplitude, the width at half-maximum of the profile obtainedwith PCF with subaperture beamforming is found to be
decreased slightly. This phenomenon can be considered
as follows: When the location of the focal point coincides
with that of the scatterer (corresponding to the peak of
the lateral profile in Fig. 7), the phases of all echo signals
are the same and the phase variance is zero if there isno noise. Therefore, all the noise components work to increase the phase variance. In other words, the phase variance is purely dependent on the random signals.
On the other hand, when the location of the focal point
does not coincide with that of the scatterer, the phasevariance is dependent on both the geometrical mismatch
between the focal point and the scatterer and the random signals. Therefore, the increase of the phase variancecaused by noise would be smaller than that at the peak of
the lateral profile. As a result, a larger suppression of theecho amplitude resulting from the random signals occurs
at the peak of the lateral profile, and the width at halfmaximum increases, as shown in Fig. 7(b), when subaperture beamforming is not used.
In Fig. 4(b), although amplitude ratio ra obtained with
non-overlapping subapertures was increased by decreasing
the number of non-overlapping subapertures, the lateral
spatial resolution wl was degraded when the number ofsubapertures was less than 8. By reducing the number ofsubapertures, a greater number of elements could be used

hasegawa and kanai: effect of subaperture beamforming on phase coherence imaging

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Fig. 6. B-mode images of a 26-year-old healthy male: (a) without the phase coherence factor, (b) with the conventional phase coherence factor, (c)with the controlled phase coherence factor (γ = 0.5), (d) with the phase coherence factor with 4 non-overlapping subapertures (24 elements/subaperture), (e) with the phase coherence factor estimated by 4 elements, and (f) with the phase coherence factor with 73 overlapping subapertures (24elements/subaperture).

for subaperture beamforming, and greater suppression ofout-of-focus echoes could be realized. Therefore, the phasecoherence factor of an echo from a diffuse scattering medium could be estimated more correctly, and speckle echoes

were enhanced (corresponding to the increased amplitude
ratio ra and the reduced mean over standard deviation
μ /σ ). Spatial resolution was also improved (corresponding to small wl) by more suppression of out-of-focus echoes

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 61, no. 11, November 2014

Fig. 8. Spatial resolution wl at a range distance of 61 mm obtained with
non-overlapping subapertures.

Fig. 7. (a) Non-normalized and (b) normalized lateral profiles of amplitude of an echo from a point scatterer obtained by simulation
experiment.

by wider subapertures. The reason for the degradationof the spatial resolution at numbers of subapertures ofless than 8 was considered to be that a small numberof beamformed RF signals was not sufficient to obtain astatistically stable estimate of phase variance. However,the change in spatial resolution {wl} at numbers of subapertures of less than 8 is small, and such a small difference
may be an error. Therefore, the spatial resolution wl was
evaluated at a different range distance of 61 mm, as shownin Fig. 8. In Fig. 8, a similar tendency can be confirmed,
i.e., the spatial resolution wl is also degraded at numbersof subapertures of less than 8.
In the present study, the number of elements in each
subaperture was fixed, not depending on the range distance. The degree of suppression of out-of-focus echoes,
which is achieved by the same number of elements (size)of a subaperture, would depend on the range distanceeven when the distance between the location of a scatterer (source of the out-of-focus echo) and the focal pointis same. Therefore, it would be effective to change thesubaperture size depending on the range distance to ob-tain spatially homogeneous effects of subaperture beamforming. However, the variable subaperture has not been
examined in the present study because the homogeneity of
the image quality was not the main scope of the present
study.
In delay-and-sum beamforming in each subaperture, thesubsample time delay τs was compensated by multiplying
the complex received signal gi(t) by exp( j2π f0τs). In thepresent study, f0 was set at 3 MHz, which was almost thecenter frequency of the received RF echo, whereas thenominal center frequency of the phased array probe was
3.75 MHz. As described in [30], [31], the center frequencyof the received RF echo can vary by ultrasonic frequencydependent attenuation, interference among echoes, etc.
Although more computation is required, the estimation of
the actual center frequency of the received RF echo would
realize more accurate beamforming and estimation of thephase coherence factor.
Furthermore, although speckle echoes can be more visualized by subaperture beamforming, ultrasound imaging
with the phase coherence factor increases the distance inintensity between echoes from specular and diffuse scatterers. In future work, it would also be necessary to investigate a more suitable method than the conventional log
compression technique to appropriately show ultrasoundimages weighted by the phase coherence factors to physicians in clinical situation.
V. Conclusions
To realize high-frame-rate echocardiography, parallel
beamforming has been introduced; however, spatial resolution was degraded by the use of unfocused transmit
beams. Although the phase coherence factor is feasible for
improvement of spatial resolution, speckle echoes from a
diffuse scattering medium are suppressed. In the present
study, a strategy for estimating the phase coherence factor
has been presented for improvement of spatial resolution
in high-frame-rate echocardiography and for avoiding suppression of speckle echoes. One of the reasons for reduc-hasegawa and kanai: effect of subaperture beamforming on phase coherence imaging

tion of the phase coherence factor estimated for a weakecho from a diffuse scattering medium was interference of
echoes. Therefore, by using subaperture beamforming, aweak echo from a focal point in a diffuse scattering medium was enhanced, and the phase variance of echo signals
received by individual transducer elements was reduced.
As a result, suppression of speckle echoes could be successfully avoided without degradation of spatial resolution.
Appendix
Relationship Between Variance of Estimate
and Number of Data
Let us define the phase of the RF echo signal received by
the ith transducer element or subaperture (i = 0, 1, …, K− 1) by ϕi. There would be some degree of correlation
between the phases evaluated from echo signals received
by individual transducer elements, which are scattered bydiffuse scattering medium. However, in this theoreticalconsideration, the phases of echo signals are assumed to
be independent to simply explain the relationship between
the number of phase data and the estimated phase variance. The measured phase includes random noise, whichis assumed to obey the normal distribution. Let us also
define the population mean and standard deviation of themeasured phase ϕi by μϕ and σϕ. Under such conditions,the Cramér–Rao lower bound CLRB(σϕ) in estimationof the population standard deviation σϕ is expressed as[32], [33]CRLB(σ φ2) =1

K × Ei {2∂
ln p(φi ) ∂(σ φ2 )


}

,

(3)

where E[·] represents the expectation operator, and p(ϕ )is the probability density function of the measured phase
ϕi, which is expressed asp(φ) =

 (φ − µ φ)2 
exp
−
.

2σ φ2 2πσ φ2
1(4)

Eq. (3) can be modified as follows:
CRLB(σ φ2)
=

=

=

1

K × Ei 


2

2
φ

2
φ

1
2

1
1
E i  − 2σ 2 + 2σ 4 (φi − µ φ)2 
φ
φ


1

{

∞

2σ φ4
.
K

(5)

}

(

(φ − µ φ)21− 2σ 2
2σ φ4
−∞
φ

K∫
=

{ ∂(∂σ ) ( − 12 ln(2πσ φ2) − 2σ1 (φi − µφ)2 )} )212πσ φ2{exp −(φ − µ φ)2
2σ φ2

} dφ

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As described previously, the variance CRLB(σ φ2) in theestimation of the phase variance σ φ2 can be reduced byincreasing the number of elements or subapertures K.
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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 currently an associate professor in
the 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 Ph. D. degrees, also from Tohoku
University, in 1983 and in 1986, both in electricalengineering. 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. Since 2012, he has been a deanof the Graduate School of Engineering, Tohoku University.
His current 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 a member of the International Advisory Boardof the International Acoustical Imaging Symposium. Since 2011, he has
been a board member of the International Congress on Ultrasonics. Since
2012, he has been an editor of the Journal of Medical Ultrasonics andthe Japanese Journal of Medical Ultrasonics. Since 2013, he has been an
associate editor of the IEEE Transactions on Ultrasonics, Ferroelectrics,
and Frequency Control.