Journal of Medical Ultrasonics (2021) 48:259–272
https://doi.org/10.1007/s10396-021-01089-z

ORIGINAL ARTICLE—PHYSICS & ENGINEERING

Low‑complexity generalized coherence factor estimatedfrom binarized signals in ultrasound beamforming
Masanori Hisatsu1,2· Shohei Mori3 · Mototaka Arakawa2,3 · Hiroshi Kanai2,3Received: 18 November 2020 / Accepted: 17 March 2021 / Published online: 22 April 2021
© The Japan Society of Ultrasonics in Medicine 2021

Abstract
Purpose In coherence-based beamforming (CBB) using a generalized coherence factor (GCF), unnecessary signals causedby sidelobes are reduced, and an excellent contrast-to-noise ratio (CNR) is achieved in ultrasound imaging. However, the
GCF computation is complex compared to the standard delay-and-sum (DAS) beamforming. In the present study, we propose
a method that significantly reduces the number of GCF computations.
Methods In the previously proposed G­ CFreal, generation of the analytic signal for each element in the conventional GCF
could be omitted. Furthermore, in GCF estimated from binarized signals (GCFB) proposed in the present study, the GCF
value is calculated after the received signal of each element is binarized to reduce the computational complexity of the GCF.
Results The values of GCFB and G­ CFreal estimated from simulation and experimental data were compared. We also evaluated the image quality of B-mode images weighted by GCFB and ­GCFreal. Compared with G­ CFreal, GCFB was superior in
reducing unnecessary signals but tended to reduce the brightness of the diffused scattering media. The CNR improvement
was comparable for both methods.
Conclusion Generalized coherence factor estimated from binarized signals exhibits excellent CNR improvement compared to
DAS. CNR improvements yielded by GCFB and ­GCFreal may depend on the observation target; however, under the conditionsof the present study, comparable performances were obtained. Because GCFB can significantly reduce the computational
complexity, it is potentially applicable in clinical diagnostic equipment.
Keywords Ultrasound imaging · Adaptive beamforming · Generalized coherence factor

Introduction
In delay-and-sum (DAS) beamforming, which is the standard beamforming technique for medical ultrasound imaging, signal components from undesired positions remain
because of sidelobe components. These unnecessary signals
cause artifacts and contrast degradation in B-mode images.
Apodization, which weights a preset window function to
the received signals of individual elements, is applied as a
general method to reduce the sidelobe components at the* Masanori Hisatsu
masanori.hisatsu.uc@fujifilm.com
1

FUJIFILM Healthcare Corporation, 3‑1‑1
Higashikoigakubo, Kokubunji, Tokyo 185‑0014, Japan

2

Graduate School of Biomedical Engineering, Tohoku
University, Sendai, Miyagi 980‑8579, Japan

3

Graduate School of Engineering, Tohoku University, Sendai,
Miyagi 980‑8579, Japan

expense of lateral resolution and signal-to-noise ratio (SNR)[1]. Generally, apodization is not applied (set the weights
of all elements to 1) in the deep region to prevent SNR
degradation.
Numerous adaptive beamforming techniques have been
proposed to reduce the unnecessary signals contained inreceived signals [2–4]. Coherence-based beamforming(CBB) [5–12], which is one of the techniques, is effective
in reducing unnecessary signals caused by sidelobes withlow computational complexity. In CBB, the coherence factor (CF) [5, 13, 14], which represents the coherence among
the received signals, is weighted to the signal after DAS to
reduce the brightness value of the pixel where the unnecessary signal is dominant.
Speckle noises [15, 16] are generated in B-mode imagesof the human body owing to the interference of sound waves
from many scatterers. Speckle noise is a variation of thebrightness value that is not directly related to the structurein the human body. In ultrasound diagnosis, lesions are often

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observed from minute changes in brightness, and the speckle
noises interfere with diagnosis by lowering the contrast-tonoise ratio (CNR) [17]. When applying CBB, it is necessary
to focus on the CNR as well as the effect of reducing unnecessary signals. The generalized coherence factor (GCF) [6,7, 18], which is one of the factors used for CBB, focuses on
the depiction of diffused scattering media, and has a significantly better CNR than other factors [19].
Recently, high-performance beamforming techniques
including CBB have been realized in real time by improving
the performance of field-programmable gate arrays (FPGA),
central processing units (CPUs), and graphics processing
units (GPUs) [20, 21]. The synthetic transmit aperture(STA) [22–27] technique, which realizes dynamic-transmit
focusing, can also be realized with commercial ultrasonicdiagnostic equipment. However, the STA technique requires
dozens of times more DAS processing for each transmission. Therefore, a technology with a lower computational
complexity is required to incorporate CBB into the STA.
In contrast, ultrasonic diagnostic equipment has been madesmaller and more portable. To achieve high image quality
with limited computing power for such a model, it is necessary to reduce the computational complexity of CBB, making it possible to expand the image quality with a wider
range of models.
The aim of this study is to reduce the computational
complexity of the GCF [6], which has better CNR thanother factors used in CBB. With the GCF, it is necessary to
generate an analytic signal for the received signal of eachelement and perform a discrete Fourier transform (DFT) in
the element direction at each sample point. Therefore, thecomputational complexity is high compared to the standard
DAS beamformer. We have shown in a previous study [28]that generation of the analytic signals can be omitted, and
the GCF value can be calculated from real signals. In thepresent study, we propose a method that further reduces thecomputational complexity of the GCF value calculation bybinarizing the real input signals. Moreover, the performancedifference between the proposed method and conventional
GCF is verified, and the validity of the proposed method is
evaluated.

Conventional methods
Figure 1a shows the system block diagram for CBB using
GCF. The focused beam is generated from received signals
in the number of channels connected to the ultrasound diagnostic apparatus. The received signals in the channels areconverted to digital signals discretized in the time direction by analog-to-digital converters (ADC) and delayed toin phase for waves from the focus point. The GCF is calculated from the received signals after delay processing andbefore summation, and then used as a weighting value for the

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Journal of Medical Ultrasonics (2021) 48:259–272

signal xin (n, l) after applying DAS [6]. Here, n is the sample
number in the time direction and l is the scan line number.
By weighting the GCF value to the signal xin (n, l), xin (n, l)
including unnecessary signals is suppressed and output as asignal xout (n, l). This process is applied at each focus point
corresponding to (n, l) and repeated at all positions. However, as the GCF decreases to a very small value around thestrong scatterer, the brightness of the surrounding diffused
scattering medium is significantly reduced, and a dark region
artifact (DRA) is generated [29]. Therefore, to apply GCF
to a B-mode image, it is necessary to adjust the reduction
effect. In the present study, similar to the sign coherence factor (SCF) [8], the index p in Eq. (1) was used as the weight:

xout (n, l) = [GCF(n, l)]p xin (n, l).

(1)

Adjustment by the power p is implemented using alook-up table (LUT), as outlined in Fig. 1a. If p < 1 is set
to weaken the reduction effect in DRA, the relationshipbetween GCF(n, l) and [GCF(n, l)]p is as shown in Fig. 1b.
Calculation of the GCF value is described next. Whenthe analytic signal generated from the received signal of thechannel number m(m = 0, 1, ⋯ , M − 1) is represented byI(m, n, l) + jQ(m, n, l), the GCF is calculated from Eq. (2)using the Fourier coefficient SIQ (k, n, l) obtained by the DFTof I(m, n, l) + jQ(m, n, l) in the m-th direction [6]:��

GCF n, l;K0 =

M⋅

∑ K0

�

�2

S (k, n, l)�
k=−K0 �� IQ
�

∑M−1

2
m=0 �I(m, n, l) + jQ(m, n, l)�

,(2)

where k is the frequency index in the m-th direction, andk = −K, −K + 1, … , 0, … , K − 1, (K = M∕2) for an evennumber M . The GCF value is the ratio of the power value ofall frequency components (denominator) to that of the DC
vicinity components represented by [−K0 , K0 ](numerator).
Figure 2a shows the block diagram for calculating the GCF
value using Eq. (2). Generation of the analytic signal in eachchannel requires processing such as mixers and filters at ahigh sampling frequency in the n-th direction. Therefore,
when these processes are applied to all the channel signals,
the computational complexity increases significantly. Therefore, we proposed a method for calculating the GCF value
from real signals without generating analytic signals [28].
When generation of the analytic signal is omitted and the
GCF value is calculated from the real signals, a frequency
component that is twice the frequency of the received signal
is generated in the n-th direction. It was demonstrated that
­GCFreal obtained by removing this component using a lowpass filter (LPF) was equivalent to the GCF in Eq. (2). In
Eq. (2), replacing the analytic signal I(m, n, l) + jQ(m, n, l)with the real signal s(m, n, l), and SIQ (k, n, l) with S(k, n, l),Journal of Medical Ultrasonics (2021) 48:259–272

261

Fig. 1  a System block diagram for coherence-based beamforming and b input/output of the LUT

then adding LPFs to the numerator and denominator in then-th direction, ­GCFreal is expressed as�

GCF real n, l;K0

�

�
�∑
��
K0
fLPF (h) ⋅� S(k, n − h, l)�2
k=−K0
=∑
�
� ∑
�� .
Nf
M−1
f (h) ⋅ M m=0 � s(m, n − h, l)�2h=−N LPF
∑Nf

h=−Nf

f

(3)

Equation (3) shows the case where a finite impulse
response low-pass filter (FIR-LPF) with coefficients
fLPF (h), (h = −Nf … Nf ) is used as the LPF.

Generalized coherence factor estimatedfrom binarized signals (GCFB)In the present study, we propose a method that further
reduces the computational complexity of Eq. (3), whichcalculates the GCF value without the generation of analytic signals. The input real signal s(m, n, l) is binarized asu(m, n, l) ={−1 if s(m, n, l) < 0,
+1 if s(m, n, l) ≥ 0,

(4)

and the DFT for u(m, n, l) in the m-th direction is given by

]
[
2mkπ
.
u(m, n, l)exp −j
M
m=0

M−1

U(k, n, l) =∑(5)

Because u(m, n, l) is 1 or − 1, Eq. (5) can be calculated
by adding and subtracting complex exponential functions.
Replacing the real signal s(m, n, l) with the binary signalu(m, n, l), and S(k, n, l) with U(k, n, l), Eq. (3) is expressed as
�
�∑
��
K0
2
U(k,
n
−
h,
l)�
f
⋅
�
(h)
LPF
�
�
h=−Nf
k=−K0
GCFB n, l;K0 = ∑
�
� ∑
�� .
Nf
M−1
2
f
M
u(m,
n
−
h,
l)�
⋅
�
(h)
m=0
h=−N LPF
∑ Nf

f

(6)

The denominator is a fixed value because | u(m, n, l)| = 1,
so LPF can be omitted, and Eq. (6) becomes
2

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Journal of Medical Ultrasonics (2021) 48:259–272

Fig. 2  System block diagram for a conventional GCF and b GCFB estimators

��
GCFB n, l;K0 =

∑ Nf

h=−Nf

�
�∑
��
K0
fLPF (h) ⋅� U(k, n − h, l)�2
k=−K
0

M2

.

(7)

The computational complexity of GCFB can be reduced
compared to ­GCFreal because (1) the DFT of Eq. (5) can becalculated only by addition and subtraction, (2) the addition
and LPF of the denominator in Eq. (6) can be omitted, and(3) the division of Eq. (7) can be replaced with multiplication of the fixed value 1∕M 2 . The configuration for calculating the GCFB from Eq. (7) is shown in Fig. 2b, which
is simpler than the configuration of the conventional GCF
shown in Fig. 2a.

Comparison of computational load of conventional
GCF, ­GCFreal, and GCFB
Table 1 shows the number of multiplications and additions required to calculate the GCF, G­ CFreal, and GCFB
values for each spatial sample. Here, it is assumed thatthe order 2Nf of the Hilbert transform filter required in
the conventional GCF is similar to the order of the LPF

13used in Eq. (3) or Eq. (7). For G­ CF real and GCFB, thefrequency components were calculated only on the positive side because the frequency spectrum of a real signal
is positive–negative symmetric. To demonstrate the calculation complexity of each method, an example where
the channel number M = 96 , DC vicinity range K0 = 1,
and Hilbert transform or LPF order 2Nf = 20 is shown.
For ­GCFreal, the number of multiplications and additions
is approximately 1/6 of those for GCF. Furthermore, for
GCFB, the number of multiplications is 1/20 or less of
those for ­G CF real. For GCFB, the calculation complexity can be further reduced by replacing the division in
Eq. (7) with multiplication of 1∕M 2 . Especially in ASICs
and FPGAs, the circuit scale can be condensed by reducing
the number of such operations. However, reduction of thecalculation depends on the algorithm of the compiler andconfiguration of the processor.
In apodization, which is generally used to reduce thesidelobe components, the signal of each channel is weighted
using a window function; therefore, multiplications by the
number of channels are required. GCFB can be realized witha smaller number of multiplications.

Journal of Medical Ultrasonics (2021) 48:259–272

263

Table 1  Computational load in conventional GCF, G­ CFreal, and GCFB

Hilbert transform
DFT
Numerator in Eq. (2) or (3) or (7)(without LPF)
Denominator in Eq. (2) or (3) or(7) (without LPF)
LPF in Eq. (3) or (7)Total (M = 96, K0 = 1, Nf = 10)

GCF

GCFreal

GCFB

Multiplication Addition

Multiplication Addition

Multiplication Addition

M (2Nf+ 1)
4M (2K0 + 1)
2 (2K0 + 1)

2MNf–
2 (2M − 1) (2K0 + 1) 2M (K0 + 1)
4K0 + 12 (K0 + 1)––
2 (M – 1) (K0 + 1) –3K0 + 12 (K0 + 1)–
2 (M − 1) (K0 + 1)
3K0 + 1

2M + 1

2M − 1

M+1

M−1

–

–

–
3367

–
3262

2 (2Nf + 1)
527

4Nf
519

2Nf + 1
25

2Nf
404

When baseband demodulation is used to generate theanalytic signals in GCF instead of the Hilbert transform,
multiplication of the mixers and LPFs for both the real (I)and imaginary (Q) parts is required, and the calculation
complexity in this part increases. Instead, the calculation
complexity can be reduced by lowering the sampling rate of
the subsequent processing. However, regardless of whether
the Hilbert transform or baseband demodulation is used,
the number of calculations becomes large compared to thesubsequent processing. Therefore, the total number of calculations is smaller when the analytic signal generation isomitted [28]. Second-order sampling can be used to generate
approximate analytic signals with a low number of calculations, but it is not considered in the present study because
it limits the sampling rate of the ADC and causes serious
errors in wideband transmission [30].

Evaluation methods
Comparison of ­GCFreal and GCFB values
Because the signal binarization in the proposed method isa special process, it is difficult to express the general relationship between S(k, n, l) and U(k, n, l). Consequently, it isdifficult to theoretically predict how the binarization process will affect the weighting of the received signal. Therefore, we focus on the effect of reducing unnecessary signals
caused by sidelobes, and the ability to visualize diffused
scattering media. As shown in Fig. 3, the G­ CFreal and GCFB
values were compared for the following two cases using thereceived signal of each channel generated by simulation
and acquired from a phantom using an ultrasonic diagnostic
apparatus.
(a) A receiving focus region around one scatterer.
(b) A receiving focus point in a diffused scattering
medium.
We evaluated the effect of binarization by comparing­GCFreal. We used a convex probe, which is mainly used forFig. 3  Geometry for generating received signals in the simulation. a
Receiving focus region for one scatterer. b Receiving focus point in adiffused scattering medium

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Journal of Medical Ultrasonics (2021) 48:259–272

observing the abdomen, where there are many regions ofdiffused scattering media.
Evaluation of B‑mode images weighted by ­GCFreal and GCFB
The contrast performances of B-mode images obtained with
­GCFreal and GCFB were evaluated using the following contrast and CNR values:( )𝜇Contrast = 20log10 1 ,(8)𝜇2�𝜇1 − 𝜇2 �� ,CNR = √�2
𝜎 1 + 𝜎2 2(9)where 𝜇i and 𝜎i are the mean value and standard deviationof the envelope signal in region i , respectively. As shown in
Eq. (1), when the GCF value is weighted to the signal after
DAS, the weighting effect is adjusted by the power of p. The­ CFreal and GCFB are defined as pGCFreal andp-values for G
pGCFB, respectively. pGCFreal is determined so that DRA does
not occur near a strong scatterer. Moreover, pGCFB is determined in the same region so that the mean value of ­GCFrealwith pGCFreal and that of GCFB with pGCFB are equal. The
contrast and CNR values are calculated from the signals ofboth methods adjusted by these coefficients.

Simulations and experimental setup
RF data generation by simulation(10)

rf (n) = n∕fs ⋅ c∕2,where n is the sample number in the time direction, fs isthe sampling frequency of the receiving signal, and c is thesound velocity. To consider the propagation and delay times,
we converted to the Cartesian coordinate system in which
the origin was set on the probe surface, the 𝜃 = 0◦ direction
was the z axis, and the azimuth direction was the x axis, as
shown in Fig. 3a.( The )coordinates of the scatterer (xq , zq ) andreceiving focus xf , zf are represented by()
xq = R + rq sin 𝜃q ,()(11)
zq = R + rq cos 𝜃q − R,()
xf (n, l) = R + rf (n) sin 𝜃f (l),()
zf (n, l) = R + rf (n) cos 𝜃f (l) − R.

(12)

The signal obtained by delaying the received signal fromthe scatterer (xq , zq ) is represented by
Me
∑
( (
(
)
)
s� m, n, l, xq , zq =G −𝜏 mT , m, xq , zq
mT =Ms())+𝜏d mT , m, xfTx (l), zfTx (l), xf (n, l), zf (n, l) ,

(13)

where

[
]
[
]
G(t) = exp −2{π𝜎t}2 ⋅ cos 2πf0 t(14)

is a Gaussian pulse with center frequency f0 and − 6 dB
bandwidth 𝜎.
√
)
(
( ( )
)2 ( ( ))2
𝜏 mT , m, xq , zq =xe mT − xq + ze mT − zq ∕c+
√
(
)2 (
)2
xe (m) − xq + ze (m) − zq ∕c(15)

The signal change in the channel direction that occurs basedon the scatterer and receiving focus positions is generated
simply. As shown in Fig. 3a, b polar coordinate system(R + r, 𝜃) is set based on the center of the curvature of theis the propagation time until the sound wave transmitted
convex probe surface; here, R is the radius of the curvaturefrom the element with a number mT (= Ms , Ms + 1, … , Me ) isof the convex probe, r is the distance from the probe surface,reflected by the scatterer (xq , zq ) and received by the receivand 𝜃 is 0° in the vertical direction of the probe. The positioning element with number m.
of the scatterer with number q is represented by (R + rq , 𝜃q ).
()
𝜏d mT , m, xfTx (l), zfTx (l), xf (n, l), zf (n, l)
√
√
(16)
( ( )
)2 ( ( )
)2
/
(
)2 (
)2
=
xe mT − xfTx (l) + ze mT − zfTx (l) ∕c − rfTx c + rf (n)∕c +xe (m) − xf (n, l) + ze (m) − zf (n, l) ∕c
Considering the receiving focus point (R + rf (n), 𝜃f (l)) ,where rf (n) is the receiving focus distance and 𝜃f (l) is theazimuth angle of the l -th scanning line,rf (n) is represented by

13

represents the sum of the transmitting delay time given to
the element with the number mT and the receiving delay
time given to the element with number m.(xe (m), ze (m)) represents the element position with number m.rfTx represents
the transmission focus distance, and the azimuth angle of theJournal of Medical Ultrasonics (2021) 48:259–272

265transmission focus is 𝜃f (l), which is the same( as the receiving)
focus. The transmission focus coordinate xfTx , zfTx in the
Cartesian coordinate system is()
xfTx (l) = rfTx + R sin 𝜃f (l),()(17)
zfTx (l) = rfTx + R cos 𝜃f (l) − R.
As shown in Fig. 3b, when focusing on a diffused scattering medium, the delayed signals are generated by superimposing the received signals from Q scatterers at different
positions as follows:Q∑()
ssim (m, n, l) =s� m, n, l, xq , zq .

(18)of curvature 60 mm, element pitch 0.38°) was used, andthe number of channels was M = 96 . In this measurement,
an image was formed from 312 received scan lines in therange of a 60° viewing angle. Both the transmitting andreceiving apertures for forming the scan line were set withthe scan line as the center. Table 2 lists the transmitting
and receiving conditions.

Results
Comparison of ­GCFreal and GCFB values for one
scatterer

q=1

The ­GCFreal value is calculated by substituting the real
signal ssim (m, n, l) into s(m, n, l) in Eq. (3). The GCFB value
is calculated from Eq. (7) after substituting ssim (m, n, l) intos(m, n, l) in Eq. (4). In the simulation, the amplitude values of the received signals from the anechoic region are
all zero. In this case, because the signal values are all + 1
according to Eq. (4), the ­GCFreal and GCFB values are 1.
To avoid this, random noise with a maximum of − 40 dB
relative to the amplitude of the Gaussian pulse in Eq. (14)
was added to the signal for each channel. In the simulation,
the same conditions were used as the experimental dataacquisition conditions presented later (Table 2). The center
frequency f0 and − 6 dB bandwidth 𝜎 of the Gaussian pulse
were set to 3 MHz and 1.5 MHz, respectively, according
to the experimental data.
Experimental RF data acquisition
The experimental RF data were acquired using the ultrasonic diagnostic system ProSound α10 (Hitachi, Tokyo,
Japan) with ultrasonic multipurpose phantom 403GS-LE(Gammex, WI, USA) as the measurement object. A convex probe (UST-9130, center frequency 3.5 MHz, radius

Table 2  Input data conditions in the simulations and the experiments
Parameter
Transmit
Number of element
Focus depth [mm]Apodization function
Center frequency [MHz]Band width [MHz]Receive
Number of element
Sampling frequency [MHz]

Value
76
105
Hamming
5396
20

In the present study, all the verifications were performed
under the condition of K0 = 1, which was suitable for
reducing unnecessary signals in a previous study [28].
Figure 4 shows the simulation data. Figure 4a–c show thevalues of DAS, ­GCFreal, and GCFB, respectively, wherethe vertical axis is the depth rf (n) and the horizontal axis
is the angle 𝜃f (l) of the receiving focus point, when there
is one scatterer at ( rq , 𝜃q) = (46.2 mm, 0°). For 𝜃f (l) , only
the positive side is shown because the result is positive–negative symmetric. For DAS, the amplitude value ofthe envelope is displayed in decibels. Similarly, Fig. 4d–f
show the values of DAS, G­ CFreal, and GCFB, respectively,
when there is one scatterer at ( rq , 𝜃q) = (65.8 mm, 0°), andFig. 4g–i show those when there is one scatterer at ( rq , 𝜃q
) = (85.3 mm, 0°). Since ­GCFreal and GCFB are evaluation
values of coherence, they are large over a wider range
in the depth direction than DAS, which represents theamplitude value. In Fig. 4a, b, it can be observed that in
the region where the DAS value increased because of thesidelobe, the ­GCFreal value also increased. However, thissidelobe influence was hardly observed in Fig. 4c. Similartendencies were observed at all depths (Fig. 4d–i). These
results suggest that GCFB is more effective at reducing theunnecessary signals caused by the sidelobe components
than ­GCFreal.
Figure 4j shows the values of G
­ CF real and GCFB at
the scatterer depth indicated by dashed line 1 in Fig. 4b.
◦
When 𝜃f (l) < 0.5 , the phases among the channels wereroughly aligned or changed slowly, so that the G­ CFreal and
GCFB values were both close to 1. However, there wasa region where the GCFB value was approximately 0.2
lower than that of G
­ CFreal. This is because high-frequency
components in the channel direction are generated in binarized signals in the case of GCFB. In addition, ­GCFreal◦
and GCFB increase again around 𝜃f (l) = 0.4 , because thesignal is concentrated on the component of k = 1. Moreo◦ver, when 𝜃f (l) > 1 , while G­ CFreal was approximately 0,
GCFB fluctuated by a small value because of the influenceof binarization. Figure 4k shows the G­ CFreal and GCFB

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Journal of Medical Ultrasonics (2021) 48:259–272

Fig. 4  Comparison of G
­ CFreal and GCFB values around scatterers inthe simulation data. a DAS, b ­GCFreal, and c GCFB values for the
scatterer at r = 46.2 mm. d DAS, e ­GCFreal, and f GCFB values forthe scatterer at r = 65.8 mm. g DAS, h ­GCFreal, and i GCFB values

for the scatterer at r = 85.3 mm. ­GCFreal and GCFB values at j dashedline 1 and k dashed line 2 in b. l s(m, n, l) and u(m, n, l) at the positionindicated by the arrow in b

values at the depth indicated by dashed line 2 in Fig. 4b.
­GCFreal exhibited a higher value than GCFB when 𝜃f (l) wasin the range of 0.5 to 2.0° because of the influence of thesidelobes. Figure 4l shows the real s(m, n, l) and binarizedu(m, n, l) signals in the channel direction at the position
affected by the sidelobe indicated by the arrow in Fig. 4b.
Here, the amplitude values of u(m, n, l) were normalized
so that the power values of both signals were equal. Ins(m, n, l) used to calculate ­GCFreal, the received signal fromthe scatterer was dominant in the channel of m > 60 . The­G CF real value increased because of this signal, and thesidelobe component was not sufficiently reduced.

Figure 5a is a B-mode image constructed from theobtained experimental data. The ­GCFreal and GCFB values around the three wires surrounded by yellow squares
are shown in Fig. 5b–g. The vertical axis is the depth rf (n),�
and the horizontal axis is 𝜃f (l) , where the azimuth angle
relative to the scanning line passing through each wire�(0°) is shown as 𝜃f (l) . Figure 5b, c show the G­ CFreal and
GCFB values around the wire at r = 46.2 mm, Fig. 5d, eshow the values at r = 65.8 mm, and Fig. 5f, g show thevalues at r = 85.3 mm.
Figure 5h shows the G­ CFreal and GCFB values at dashedline 1 shown in Fig. 5b. Similar to the simulation results,
�◦
GCFB was slightly lower than GCF at 𝜃f (l) < 0.5 , where

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Journal of Medical Ultrasonics (2021) 48:259–272

Fig. 5  Comparison of ­GCFreal and GCFB values around wire targets
in the experimental data. a B-mode image of the data. b ­GCFreal and c
GCFB values for the wire at r = 46.2 mm. d ­GCFreal and e GCFB values for the wire at r = 65.8 mm. f ­GCFreal and g GCFB values for the267­ CFreal and GCFB values at h dashed line 1 andwire at r = 85.3 mm. G
i dashed line 2 in b. j s(m, n, l) and u(m, n, l) at the position indicatedby the arrow in b

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the signal coherence was high. ­GCFreal was approximately�
0 at 1◦ < 𝜃f (l) < 3◦. When the signal after DAS is weighted
using this value, the amplitude is significantly reduced anda DRA occurs. However, the value of GCFB was slightly
larger than that of G
­ CFreal in this region, which suppressed
the occurrence of DRA. Figure 5i shows the ­GCFreal and
GCFB values at dashed line 2 in Fig. 5b. Similar to thesimulation results, it can be confirmed that ­GCFreal waslarge because of the influence of the sidelobe components
�
at 0.5◦ < 𝜃f (l) < 1◦ . Figure 5j shows the real s(m, n, l) andbinarized u(m, n, l) signals at the positions affected by thesidelobe indicated by the arrows in Fig. 5b. Similar to
Fig. 4l, the amplitude values of u(m, n, l) were normalized so that the power values of both signals were equal.
Similar to the simulation results, in the case of ­GCFreal, thereceived signal from the wire was dominant in the channel
at the end (m > 70).

Fig. 6  Comparison of ­GCFreal and GCFB at diffused scattering medium. a ­GCFreal and GCFB values in the diffused scattering
medium for the simulation data. b Changes in ­GCFreal and GCFB val-

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Journal of Medical Ultrasonics (2021) 48:259–272

Comparison of ­GCFreal and GCFB values for diffused
scattering media
Figure 6a shows the G­ CFreal and GCFB values at the receiving focus points in the diffused scattering media in thesimulation data. The scatterer density was set to 100/mm2
to generate sufficiently dense scatterers with respect to thewavelength (0.5 mm). The mean value after repeating thesimulation 100 times by changing the arrangement of thescatterers at each depth is shown. The G­ CFreal and GCFB
values changed depending on the depth and increased near
the transmission focus depth (105 mm). This is because theinfluence of the signals from the scatterers near the focus
point was more dominant as the transmission beam width
became narrower, and the coherence of the signals among
the channels increased. The GCFB values were smaller thanthe ­GCFreal values, and when they were used as the weightvalues, the brightness of the diffused scattering media waslower than that of ­GCFreal.
Figure 6b shows the ­GCFreal and GCFB values when thenoise level given to each channel was changed at rf (n) =100 mm in a diffused scattering medium. The noise level isues relative to the noise level. c Regions for estimating G­ CFreal and
GCFB values for the experimental data. d ­GCFreal and GCFB values
in diffused scattering media shown in c

Journal of Medical Ultrasonics (2021) 48:259–272

expressed as the mean value of DAS in the absence of noiseas 0 dB. The values of G
­ CFreal and GCFB decreased with
the increase in noise level, making the difference between
the two small.
The results of the experimental data are shown in Fig. 6c,d. Figure 6c is a B-mode image constructed by DAS. The
mean ­GCFreal and GCFB values calculated for each region
indicated by the yellow circles are shown in Fig. 6d. Similar to the simulation results, the GCFB values were smaller
than the G­ CFreal values. It can also be confirmed that thedifference between the ­GCFreal and GCFB values decreased
as the values decreased. In the experimental data, because
the SNR decreased as a result of attenuation with depth, the­GCFreal and GCFB values were smaller than the simulation
results in Fig. 6a, and were highest at 85 mm shallower than
the transmission focus.

B‑mode images and CNR values by CBB
Figure 7a–c show the B-mode images yielded by DAS and
CBB using ­GCFreal and GCFB, obtained from the acquired
experimental data. The dynamic range of the display was
80 dB. For G­ CFreal, pGCFreal was set to 0.2 to avoid the269
Table 3  Contrast and CNR values of the B-mode image generatedusing each method

Region 1: red
Region 2: yellow
Region 1: green
Region 2: yellow

Contrast [dB]
CNR
Contrast [dB]
CNR

DAS

GCFreal

GCFB− 13.9
2.47
− 5.2
0.98

− 17.7
2.87
− 7.9
1.38

− 17.9
2.92
− 7.8
1.35

occurrence of DRA around the wire indicated by the arrow
in Fig. 7a. As a result of adjusting pGCFB so that the meanvalue of GCFB in the region near the wire was similar tothat of ­GCFreal, pGCFB was set to 0.26. Figure 7b, c show
the images adjusted using these p-values. Moreover, Fig. 7dshows the azimuth brightness profile of each image averaged in the depth direction for the region shown by the yellow square in Fig. 7b. In the case of ­GCFreal and GCFB,
the brightness of the diffused scattering medium was lower
than that of DAS, but more than that, the brightness of theanechoic region was significantly reduced owing to theunnecessary signal reduction effect. Table 3 shows the contrast and CNR values of each image calculated from Eqs. (8)and (9), with the red and yellow squares shown in Fig. 7aFig. 7  B-mode images generated by a DAS and those weighted by b ­GCFreal and c GCFB. d Lateral profiles of the anechoic region shown by thesquare in b

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as regions 1 and 2, and with the green and yellow squares
shown in Fig. 7a as regions 1 and 2, respectively. In thecase of ­GCFreal and GCFB, both the contrast and CNR weresuperior to DAS, and the same degree of contrast improvement was observed.

Discussion
The advantages of GCFB over ­G CF real are discussed
below. For signals such as those shown in Figs. 4l and5j, positive signals near m = 90 , which are considered tobe signals from the strong scatterer around the receiving
focus point, are dominant. Consequently, the DAS value
increases even though there is no scatterer at the focus
point. This is the influence of the sidelobe component. In
this case, because the DC component increases, the numerator of Eq. (3) also increases, making the G­ CFreal value
large and similar to that of DAS. However, in the case of
GCFB calculated from the binarized signal u(m, n, l) , theamplitude value of the signal is not considered, and thesignal received by more channels becomes dominant. For
example, for the signal shown in Fig. 4l, because there
is no scatterer at the receiving focus point, all signals at
m < 60 , which are not signals from the scatterer, are noise.
Because the GCFB uses binarization, these noise signals
become dominant. The effect is relatively weak because
the number of receiving channels is small for signals nearm = 90 . Consequently, the GCFB value is smaller thanthat of G­ CFreal, which considers the amplitude, at the position where the sidelobe component is generated in DAS.
As shown in Fig. 5j, when the focus point is in a diffused
scattering medium, the signals from the diffused scattering medium are received by all channels. However, somechannels receive signals from the wire located at a position different from the focus point. Therefore, the calculated GCFB value is significantly influenced by the diffused scattering medium, and the influence of the sidelobe
component can be relatively suppressed. From the above,
when the signal caused by the sidelobe is larger than theoriginal signal of the receiving focus point and becomes
an unnecessary signal, GCFB has an excellent reduction
effect compared to ­GCFreal.
Similarly, even in the vicinity of a strong scatterer
where DRA is likely to occur, the influence of the signal
from the focus point is stronger than that from the strong
scatterer at a position different from the focus point in
GCFB. Therefore, the value does not decrease as significantly as ­GCFreal, and GCFB suppresses the occurrence of
DRA more than ­GCFreal.
From the above, GCFB is superior to ­GCFreal in reducing unnecessary signals and can suppress the occurrenceof DRA. The wider the bandwidth, the fewer the channels

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Journal of Medical Ultrasonics (2021) 48:259–272

that receive the signal from the strong scatterer, and thestronger this tendency becomes. This feature generally
holds regardless of the measurement target.
The disadvantages of GCFB versus G­ CF real are discussed below. As can be observed in Figs. 4j and 5h, both
GCFB and ­GCFreal have values close to 1 near 𝜃f (l) = 0◦ ,where the receiving focus and scatterer position match.
However, in the vicinity of 𝜃f (l) = 0.3◦ , where the receiving focus is slightly shifted from the scatterer, a slightphase change occurs in the signal in the channel direction. High-frequency components are generated in the frequency spectrum in the channel direction by binarizing thesignal, such that GCFB has a smaller value than G­ CFreal.
The advantage of GCF is that it becomes a large value
and the brightness can be maintained even when there isa slight phase change, whereas GCFB may reduce suchsignals. However, if p < 1 is adjusted so that DRA does
not occur in GCF, a larger GCF value leads to a smallerchange in [GCF(n, l)]p with regards to the change in the
GCF value, as shown in Fig. 1b. Therefore, for a signal
with high coherence, even if there is a slight difference
between the GCFB and ­G CF real values, the difference
between the two after adjustment with the p-values (< 1)is small, having a slight effect on the image quality.
Similarly, for a signal from the diffused scattering
medium, as a result of the scattered waves interfering witheach other, a phase change occurs in the channel direction[6], and high-frequency components increase because ofbinarization. Therefore, as shown in Fig. 6a, d, GCFB has
smaller values than ­GCFreal, which may reduce the brightness. Because the GCFB value in the diffused scattering
medium is not as large as the GCFB value at the strong scatterer, the brightness value decreases, as shown in Fig. 7d,even if it is adjusted by the p-value.
As mentioned above, GCFB is superior to ­GCFreal interms of its ability to reduce unnecessary signals generated by sidelobes; however, the brightness value of the
diffused scattering medium is also reduced. Consequently,
the contrast and CNR calculated from the diffused scattering medium and the hypoechoic regions are equivalent tothose of G
­ CFreal, as shown in Table 3. However, because
the contrast and CNR depend on the degree of reduction inbrightness in the diffused scattering medium and the degreeof reduction in unnecessary signals, the performances of
GCFB and ­GCFreal are considered to depend on the observation target.
Additionally, since GCF is a process that reduces thebrightness of unnecessary signals, the resolution of an image
generated using GCF is not inferior to that of DAS. However, since the noise component is also reduced, it may givethe impression that spatial high-frequency components aresuppressed.

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271

Table 4  Relationship between coherence factors

Ethical approval This article does not contain any studies with humanor animal subjects performed by any of the authors.

Input signal

Only the DC component

Components around DC

GCF (K0 > 0)
Real signal
CF, i.e. GCF (K0 = 0)
Binarized signal SCF, i.e. GCFB (K0 = 0) GCFB (K0 > 0)

In the present study, to evaluate the effect of binarization, GCFB was verified with G­ CFreal as a comparator.
Because GCF and ­GCFreal have equivalent values [28], it
is considered that the same results can be obtained by comparing GCF and GCFB. In the case of the sign coherence
factor (SCF) [8], which is one of the coherence factors, thephase of the signal is binarized to 0° and 180° in calculating the phase coherence factor (PCF) [8], which indicatesthe variance value of the phase in the channel direction.
Similar to the proposed method, the phase variance value
is calculated using the mean value of the binarized signals.
It is considered that SCF and GCFB (K0 = 0) are similar
because the process of calculating the variance value fromthe mean value of binarized signals is considered to be similar to adjusting the effect (a conversion such as the p-value).
Table 4 summarizes these relationships, and SCF using binarized signals is a special case of GCFB (K0 = 0). By evaluating up to the DC vicinity component (K0 > 0) in GCF, thevariation in values can be suppressed in diffused scattering media, and CNR values superior to CF and SCF can beobtained. This effect can also be achieved with GCFB.

Conclusions
In the present study, we proposed a GCFB that binarizes the
input real signals to reduce the number of GCF computations. Focusing on the effect of reducing unnecessary signals
and the ability to visualize diffused scattering media, thevalidity of the proposed method was verified using simulation and experimental data. From the results, the contrast
performance was superior to DAS in the case of both theconventional method and GCFB. The performance of bothmethods for improving the CNR may depend on the observation target. Under the conditions in the present study,
comparable performance was achieved with both methods.
Because GCFB can significantly reduce the computational
complexity by binarization, it is potentially applicable forclinical diagnostic equipment.

Declarations
Conflict of interest The authors declare that they have no conflicts ofinterest.

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