Journal of Medical Ultrasonics (2022) 49:555–567
https://doi.org/10.1007/s10396-022-01243-1

ORIGINAL ARTICLE–PHYSICS & ENGINEERING

Application of low‑complexity generalized coherence factor to in vivo
data
Masanori Hisatsu1,2· Shohei Mori3 · Mototaka Arakawa2,3 · Hiroshi Kanai3,2Received: 5 April 2022 / Accepted: 14 June 2022 / Published online: 30 August 2022
© The Author(s), under exclusive licence to The Japan Society of Ultrasonics in Medicine 2022

Abstract
Purpose Beamforming using the generalized coherence factor (GCF) reduces sidelobe artifacts and provides an excellent
contrast-to-noise ratio. We previously proposed ­GCFreal, a method to calculate GCF without generating analytic signals, and­GCFbin, a method to calculate GCF by binarizing the received signals. In this study, we applied these methods to in vivo dataand showed the effect of the computational complexity reduction on contrast performance.
Methods Channel RF data were acquired from the human liver and gallbladder. We set up several observation points ineach data set and investigated the mechanism that causes the differences in contrast performance among the methods basedon the signals and their power spectra in the channel direction.
Results For GCF and G­ CFreal, the obtained values were almost the same. However, there were large differences in G
­ CFbinfrom GCF when the signals from the focus point or from outside the focus point were received on different channels. Thisis because the amplitudes of the signals with high coherence and those with low coherence were changed by binarizing thesignals.
Conclusion While ­GCFbin can significantly reduce the computational complexity, there are differences in the values of­GCFbin and GCF due to binarizing of the received signals. However, this difference resulted in ­GCFbin being superior to
GCF in terms of artifact reduction. This is owing to the elimination of amplitude information in G
­ CFbin, which makes it a
new efficient coherence factor with different characteristics from GCF.
Keywords Ultrasound imaging · Adaptive beamforming · Generalized coherence factor · In vivo data

Introduction
In ultrasonography, the contrast performance of ultrasoundimages is important, because diagnosis is often based onminute changes in brightness between the lesion and normal tissues. In delay-and-sum (DAS) beamforming, which
is a standard beamforming technique in medical ultrasoundimaging, unnecessary signal components from outside
the receiving focus point remain due to sidelobes. These
unnecessary signals are displayed as artifacts on the B-mode* 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

image and reduce the contrast. Apodization, which weights
a preset window function onto the transmitted and received
signals of individual elements, is a general method for reducing sidelobe components. However, apodization degrades
the lateral resolution and signal-to-noise ratio.
Another factor that reduces the visibility of lesion tissue is speckle [1, 2], which occurs on the B-mode images.
Speckle, which is generated by the interference of ultrasound waves from many scatterers, is a variation in thebrightness values that are not directly related to the structure of the body. When speckle occurs, the contrast-tonoise ratio (CNR) [3], which indicates contrast performance, decreases, and the visibility of lesion tissue isdegraded.
Various adaptive beamforming techniques have been
proposed to reduce unnecessary signals in the received
signals [4–6]. A beamforming technique based on acoherence factor (CF) [7–14] has been proposed as aneffective method to reduce unnecessary signals caused

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by sidelobes with low computational complexity. In thistechnique, the brightness values of pixels dominated byunnecessary signals are reduced by weighting the signals after DAS with a CF [7, 15, 16], which represents
the coherence among the received signals of individual
elements. One of the factors, the generalized coherence
factor (GCF) [8, 9], focuses on the depiction of diffused
scattering media and is superior to other factors in termsof CNR, because it reduces sidelobe artifacts withoutemphasizing speckle [17].
We previously proposed ­G CF real [18], a method to
calculate GCF values without generating analytic (i.e.,
IQ) signals for the received signals of individual elements, and ­G CF bin [19], a method that further reduces
the computational complexity of G
­ CF real by binarizing
the received signals. We applied ­G CF real and ­G CF bin to
RF data acquired from phantoms and confirmed thatthe improvements in contrast performance were equivalent to those of conventional GCF. Compared to GCF,
­GCFbin is much more feasible to implement in commercial
ultrasound systems due to its low computational complexity. However, due to the binarization of the signals,
the ­GCFbin value is different from the conventional GCF
value. In this study, we applied these methods to in vivo
data of the human liver and gallbladder, and by referring to the signal values (analytical signal, I signal, andbinarized signal) in the channel direction and their power
spectra, we discussed the mechanism that causes the difference in each method and its effect on the B-mode
image.

Journal of Medical Ultrasonics (2022) 49:555–567

Materials and methods
Generalized coherence factor estimated from real
and binarized signals [18, 19]
Figure 1 shows the system block diagram of the receive beamformer using GCF. The GCF is calculated from the received
signal s(m, n, l) after delay processing and before summationand is used as a weighting value for the signal xin (n, l) after
applying DAS. Here, m(m = 0, 1, ⋯ , M − 1) is the channel
number, n is the sample number in the time direction, and l is
the scan line number.
In the GCF estimator shown in Fig. 1, the analytic signal is[]I(m, n, l) + jQ(m, n, l) = A(m, n, l)exp j2𝜋fnT ,(1)

which is calculated by the Hilbert transform in the nth direction for s(m, n, l). Here, A(m, n, l) is the complex amplitude,
f represents the carrier frequency of the received signal, andT represents the reception sampling period. The GCF value
is calculated from Eq. (2) using the SIQ (k, n, l) obtained by
the discrete Fourier transform (DFT) in the mth direction for
the analytic signals [8]:)(GCF n, l;K0 =Fig. 1  System block diagram for coherence-weighted beamforming using GCF

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∑K0

|

|2

S (k, n, l)|k=−K0 || IQ|∑K−1 ||2Sn, l)|
k=−K || IQ (k,
|
∑ K0
|
|2
S (k, n, l)|k=−K0 || IQ
|
=
,
∑M−1
M ⋅ m=0 |I(m, n, l) + jQ(m, n, l)|2(2)

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557

where k is the frequency index in the channel direction,and k = −K, −K + 1, … , 0, … , K − 1, (K = M∕2) for aneven number M . The GCF value is the ratio of the power
value of the frequency component in the range of [−K0 , K0 ](numerator) to the power value of all frequency components(denominator). The above shows the case of using the Hilbert transform, but the same approach can be applied to thecase of baseband demodulation.
By weighting the signal xin (n, l) by the GCF value, xin (n, l)
including unnecessary signals is suppressed. The index
𝛾(> 0) is used to adjust the effect of the weighting as)]𝛾[(
xout (n, l) = GCF n, l;K0 xin (n, l).
(3)

Adjustment by the power 𝛾 is implemented using a lookup table[ (LUT),
in Fig. 1. The LUT outputsa)( as outlined)]𝛾(tabled GCF n, l;K0
value for the input GCF n, l;K0
value.
To reduce the computational complexity of calculating
GCF values, we proposed ­GCFreal, a method that calculates
GCF values from real signals without generating an analytic signal for each channel [18]. The power spectrum ofS(k, n, l) obtained by DFT in the mth direction for real signals
is expressed by the following equation using SIQ (k, n, l):

SIQ (k, n, l)SIQ (−k, n, l) =
[
] M−1
[
]
∑
[
] M−1
2mkπ ∑
2mkπ
1,exp
j4𝜋fnT
A(m,
n,
l)exp
−j
A(m, n, l)exp j
M
M
M2
m=0
m=0

(7)

where there is a component of frequency 2f in then th direction. 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), followed by adding low-pass filters(LPFs) to the numerator and denominator in the nth direction for reducing the cross terms, ­GCFreal is expressed as�GCFreal n, l;K0

�

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

h=−Nf

f

(8)

Equation (8) 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.
To further reduce the amount of computation, the input real
signal s(m, n, l) is binarized as

}| 2
|1{
∗
|S(k, n, l)|2 = || SIQ (k, n, l) + SIQ(−k, n, l) ||
|
| 2{
}
2
1 |
| ∗
|2
|
∗
∗
=
(−k, n, l)|(k, n, l)SIQ(−k, n, l) + |SIQ
|SIQ (k, n, l)| + SIQ (k, n, l)SIQ (−k, n, l) + SIQ
|
|
|
4 |
|
|2
Replacing |SIQ (k, n, l)| in Eq. (2) with |S(k, n, l)|2 in||
Eq. (4), Eq. (2) can be rewritten as()
GCF I n, l;K0 =

∑K 0

|

|2

S (k, n, l)|k=−K0 || IQ
|

+

∑K0

[
]
Re SIQ (k, n, l)SIQ (−k, n, l)[] .
∑K−1 ||2 ∑K−1Sn, l)| + k=−K Re SIQ (k, n, l)SIQ (−k, n, l)k=−K || IQ (k,
|
k=−K0

(5)

As the first terms in the numerator and denominator of
Eq. (5) are the same as those of Eq. (2), they are expressed||2
as GCF terms. Furthermore, |SIQ (k, n, l)| in the GCF term||is expressed as

2
|M−1
]|
[
1 || ∑
2mkπ |||2|.
A(m, n, l)exp −j|SIQ (k, n, l)| = 2 |||M ||M | m=0||(6)

Thus, the GCF term in the nth direction exhibits a gradualchange based on the envelope amplitude A(m, n, l). On theother hand, SIQ (k, n, l)SIQ (−k, n, l) in the second term (crossterm) of each of the numerator and denominator in Eq. (5)is expressed byu(m, n, l) ={(4)

−1 if s(m, n, l) < 0.
+1 if s(m, n, l) ≥ 0(9)

In Eq. (8), by replacing s(m, n, l) with u(m, n, l) , andS(k, n, l) with U(k, n, l) obtained by DFT of u(m, n, l), we obtain��
GCFbin n, l;K0 =

∑ Nf

h=−Nf

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

M2

.

(10)

Compared with the GCF in Eq. (2), the number of multiplications and additions in ­GCFbin is greatly reduced [19].

Experimental setup
The experimental RF data were collected from the liver andgallbladder of a 33-year-old healthy male using ultrasonicdiagnostic system ProSound α10 (Aloka, Tokyo, Japan) with aconvex probe (UST-9130, center frequency 3.5 MHz, radius ofcurvature 60 mm). In this study, the transmit center frequency
was set at 3.5 MHz, and the depth of the transmitting focus

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was 105 mm. The echo signals were received by 96 channels, and the RF data were sampled at a sampling frequencyof 20 MHz. The number of scan lines of the images was 210
and 312 for the liver and gallbladder data, respectively. As in aprevious study [19], we set the channel number to M = 96, theDC vicinity range to K0 = 1, and the LPF order to 2N f = 20.
Under this condition, the number of multiplications of ­GCFbin
was less than 1/100 of that of GCF.
GCF weighting can reduce sidelobe artifacts without
speckle enhancement. However, dark region artifacts [20]are generated around strong scatterers. For the liver data,
we selected an image in which sidelobe artifacts and dark
region artifacts were generated by the diaphragm, which wasa strong scatterer. For the gallbladder data, we selected animage that included the homogeneous part of the liver andthe hypoechoic part of the gallbladder so that contrast performance could be evaluated. This study was approved by
the institutional ethical committee and was performed with
the informed consent of the subject.
Figure 2a, b shows the B-mode images of the liverand gallbladder obtained with DAS, respectively. The
dynamic range of the display was 80 dB. The sidelobe
artifact generated by the diaphragm is indicated by the

Journal of Medical Ultrasonics (2022) 49:555–567

arrow in Fig. 2a. Figure 2c, d shows the scan line data
before scan conversion. The horizontal axis shows the scanline number, and the vertical axis shows the depth. The
red points, from A to E, indicate the points, where thesignals were observed. At these points, we investigated themechanism that causes the difference between the methods by observing the signals (analytic signal, I-signal, andbinarized signal) in the channel direction used to calculate
the GCF in Eq. (2), the ­GCFreal in Eq. (8), and the ­GCFbinin Eq. (10). Since the purpose was to investigate the difference in methods, it did not matter if the depths of theobservation points were different.

Results
Differences of ­GCFreal from GCF and of G
­ CFbinfrom GCF
Figure 3a, b shows the differences of G
­ CFreal values from
GCF values:

Fig. 2  B-mode images of a liver and b gallbladder. Scanline data before scan conversion of c liver and d gallbladder data

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559

Fig. 3  Difference of G
­ CFreal from GCF in a liver and b gallbladder data. Difference of ­GCFbin from GCF in c liver and d gallbladder data

)
)
(
(
)
(
ΔGCF real n, l ; K 0 = GCF real n, l ; K0 − GCF n, l ; K0 ,(11)
and Fig. 3c, d shows the differences of G
­ CFbin values from
GCF values:
)
)
(
(
)
(
ΔGCF bin n, l ; K 0 = GCF bin n, l ; K0 − GCF n, l ; K0 ,(12)estimated from the liver and gallbladder data shown in
Fig. 2. Here, as in Fig. 2c, d, the data are displayed using
the scanning line data before scan conversion.
ΔGCF bin (n, l;1) was larger than ΔGCF real (n, l;1) . In
Fig. 3c, d, ΔGCF bin (n, l;1) was negative in structures,such as the diaphragm and gallbladder wall, as well as in
the homogeneous part of the liver; thus, the ­GCFbin values were smaller than the GCF values in these areas. In
the area shown with the black arrow in Fig. 3c, because
ΔGCF bin (n, l;1) was positive, ­GCFbin values were larger than
GCF values. For such characteristic positions, the points ofinterest from A to E, indicated by the red dots, were set.
In Figs. 2c and 3c, A represents the homogeneous part ofthe liver, where ΔGCF bin (n, l;1) was a positive value. B

represents the position, where the blood vessel wall existed
in the homogeneous part of the liver and ΔGCF bin (n, l;1)
was large on the negative side. C represents the position of
the strong scatterer on the diaphragm. In Figs. 2d and 3d, D
represents the homogeneous part of the liver, and E represents the hypoechoic region in the gallbladder.

Signals in channel direction and their frequency
spectraThe signals after delay processing in the channel direction
at point A are shown in Fig. 4a1. Three signals are shown:
the I (in-phase) signal, the Q (quadrature-phase) signal, andthe binarized signal for the I signal. The GCF value is theratio of the power value in the vicinity of DC to the total
power value; thus, the GCF value does not change even if theamplitude value of the signal is normalized. Therefore, here,
the amplitude value of the binarized signal was normalized
and displayed so that the total power value was the same as
the I signal. When the channel number m was larger than 60,

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Journal of Medical Ultrasonics (2022) 49:555–567

Fig. 4  a1–e1 Signals in the channel direction and a2–e2 their frequency spectra at each observation point indicated by A to E

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561

Fig. 4  (continued)

the signals from the strong scatterer at point C were mixed,
and the amplitude value of the I and Q signals became high.
Figure 4a2 shows the frequency spectra obtained with
DFT in the channel direction for the signals in Fig. 4a1.
GCF is calculated from the spectrum of the analytic signals, ­GCFreal is calculated from the spectrum of the I signals, and ­GCFbin is calculated from the spectrum of thebinarized signals. In the spectrum of the analytic signals,
the frequency component was large near k = 15, and thiscomponent was from the strong scatterer at point C. In the
spectrum of the binarized signals, the frequency component (around k = ±15) due to the strong scatterer decreased
and the component in the vicinity of DC increased compared to the spectrum of the I signals. Consequently, thevalues of GCF, ­GCFreal, and ­GCFbin were 0.01, 0.01, and0.21, respectively, which showed that ­GCFbin was larger
than GCF and ­GCFreal.
Figure 4b1 shows the received signals at point B. The
amplitude values were high at channel numbers 30 to 80,
and the fluctuation was gradual. As the signals in thispart were dominant, in the frequency spectrum shown in
Fig. 4b2, the frequency component was concentrated in
the vicinity of DC in each signal. However, because theamplitude value is not considered in the binarized signal,
the influence of the signals at m < 30 whose amplitude wassmall and the sign changes became large, and the highfrequency component increased. Consequently, the valuesof GCF, G­ CFreal, and G­ CFbin were 0.84, 0.84, and 0.55,
respectively, showing that ­GCFbin was smaller than GCF
and ­GCFreal.
Figure 4c1 shows the signals in the channel direction atpoint C of the strong scatterer of the diaphragm. The coherence of the signals was high, and the frequency spectrum ofeach signal was concentrated in the vicinity of DC, as shownin Fig. 4c2. However, because of the generation of high-frequency components due to binarization, the values of GCF,

­GCFreal, and ­GCFbin were 0.91, 0.90, and 0.79, respectively,
and only ­GCFbin was smaller.
Figure 4d1 shows the signals at point D in the liver homogeneous part in the gallbladder data. The IQ signals showeda gradual change in the channel direction. Figure 4d2 showsthese frequency spectra, which depicted that the frequency
component was distributed in the vicinity of DC in eachsignal. In addition, as demonstrated in Fig. 4c2, the highfrequency component was increased as a result of binarization. Consequently, the values of GCF, G­ CFreal, and G­ CFbinwere 0.31, 0.31, and 0.23, respectively, and only G­ CFbin was
smaller.
Point E in the hypoechoic region in the gallbladder wasa position, where signals from surrounding structures suchas the gallbladder wall were mixed. As demonstrated inFig. 4e1, signals fluctuated drastically in the channel direction due to the scattered waves from the surrounding structures. As shown in Fig. 4e2, the frequency spectrum of eachsignal was like white noise, and the ratio of the power value
in the vicinity of DC to the total power value was small. The
values of GCF, G­ CFreal, and ­GCFbin were as small as 0.02,
0.02, and 0.03, respectively, and the differences among eachmethod were also small.

B‑mode images weighted by each method
B-mode images weighted by GCF, ­GCFreal, and ­GCFbin forthe liver data are shown in Fig. 5a–c, and those for the gallbladder data are shown in Figs. 5d–f. The dynamic range
was set to 80 dB, as in Fig. 2a, b. For each of GCF, G­ CFreal,and ­GCFbin, the values 𝛾GCF = 0.2 , 𝛾real = 0.2 , 𝛾bin = 0.26
adjusted by phantom data [18, 19] were used as the adjustment coefficient 𝛾 in Eq. (3). These 𝛾 values were adjusted sothat the average brightness value of the dark region artifact[20] generated by the strong scatterer of the phantom was
the same for each method. The B-mode images weighted by

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Fig. 5  B-mode images weighted by a, d GCF, b, e ­GCFreal, and c, f ­GCFbin

GCF and G­ CFreal were almost the same. In the liver data, thedark region artifact generated by the diaphragm, indicatedby the arrow in Fig. 5a, remained in GCF and G­ CFreal, but it
was not recognizable in ­GCFbin (Fig. 5c).
For the regions of interest indicated by the squares inFig. 5b and d, the contrast and CNR [3] values were calculated using

13

Contrast = 𝜇1 − 𝜇2 ,(13)

�𝜇1 − 𝜇2 �� .
CNR = √�2
𝜎 1 + 𝜎2 2

(14)

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563

Table 1  Contrast values of the sidelobe artifact part concerning thehomogeneous part of the liver

Contrast [dB]

DAS

GCF

GCFreal

GCFbin

8.23

4.76

4.72

3.81

Here, 𝜇i and 𝜎i are the mean and standard deviation of theenvelope signal after log compression in region i . Table 1
shows the contrast values of the sidelobe artifact part (yellow) concerning the homogeneous part (green) shown in
Fig. 5b. The larger the value, the stronger the sidelobe artifact. It can be seen that G­ CFbin reduced sidelobe artifact themost. Table 2 shows the contrast values of the dark region
artifact part (red) concerning the homogeneous part (green)
shown in Fig. 5b. The smaller the value, the stronger thedark region artifact. In GCF and ­GCFreal, the brightness ofthe dark region artifact part was greatly reduced comparedto DAS, which did not generate an artifact. It can be seenthat this decrease in brightness was alleviated with ­GCFbin.
Table 3 shows the contrast and CNR values of the hypoechoic part (yellow) of the gallbladder concerning the homogeneous part (red) shown in Fig. 5d. ­GCFbin had the same or
better contrast performance improvement effect than GCF
and ­GCFreal.

Discussion
Spectra of real signals and ­GCFreal values
As mentioned above, GCF and ­GCFreal values were almost
the same, and the contrast performance of the B-mode
images, shown in Table 1, was also the same. Here, we considered the power spectrum of the analytic signals used to
calculate GCF and that of the I signals used to calculate­GCFreal. Because the k th component of the power spectrumof the I signals is calculated from the ±k th components ofthe power spectrum of the analytic signals from Eq. (4),the power spectrum of the I signals has a positive–negative symmetry. Assuming that SIQ (k, n, l)SIQ (−k, n, l) andSIQ ∗ (k, n, l)SIQ ∗ (−k, n, l), which are the components of thecross term, are removed by the LPF in the n th direction in­GCFreal, the k th component of the power spectrum of the I
signals is expressed by

Table 2  Contrast values of the dark region artifact part concerning
the homogeneous part of the liver

Contrast [dB]

DAS

GCF

GCFreal

GCFbin1.46− 4.83− 4.77− 1.14

Table 3  Contrast and CNR values of the hypoechoic part of the gallbladder concerning the homogeneous part of the liver

Contrast [dB]
CNR

1
|S(k, n, l)| =
4
2

DAS

GCF

GCFreal

GCFbin− 15.74
3.11− 19.79
3.57− 19.79
3.58− 20.26
3.67

{

}
|
|2
|2 | ∗|SIQ (k, n, l)| + |SIQ (−k, n, l)| .
|
|
|
|

(15)

Therefore, the k th component of the power spectrum of
the I signals is the average value of the ±k components of thepower spectrum of the analytic signals [because Eq. (15) is
the power value of the I signal only, which is half the power
value of the analytic (IQ) signal, it is multiplied by 1/4]. As
shown in the example in the schematic diagram in Fig. 6a2,
when there is a frequency component at the frequency kʹ inthe power spectrum of the analytic signals, the frequency
component is distributed to ±kʹ in the power spectrum of
the I signals. Therefore, the G­ CFreal value calculated from
the
power
valuesinthepositive–negative
symmetry range[]−K0 , K0 in the power spectrum of the I signals is equivalent
to the GCF value.

Spectra of binarized signals and the mechanismthat causes the difference of ­GCFbin from GCF values
From the power spectrum of the analytic signals and thatof the binarized signals, the difference between the G­ CFbinvalue and the GCF value is discussed below for each pointof interest.
In the case of the analytic signals at point A shown in
Fig. 4a1, the signals from the strong scatterer were dominant in some channels, and the signals from the diffused
scattering medium, which was the receiving focus point,
were dominant in other channels. It can be abstracted as
signals with low coherence and signals with high coherence,
respectively. The schematic diagram is shown in Fig. 6a1.
Let mc (0 < mc < M) be the number of channels that receive
the high-coherence signals and let the amplitude (absolute value) of the analytic signals be a constant value Aco .
The remaining channels ( M − mc ) receive the signals withlow coherence, and amplitude Ain is larger than that of Aco( Aco ∕Ain ≪ 1). Figure 6a2 shows a schematic diagram of thefrequency spectra obtained with DFT of the signals in thechannel direction. Here, the total power value of each spectrum is the same. In the case of the analytic signals shownin Fig. 6a1, the frequency component with high coherence
is concentrated in the vicinity of DC, but the power value issmall, because the amplitude of the analytic signals is small.
The frequency component of the low-coherence part is dis�tributed in the vicinity of the high-frequency k = k (> K0 )

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Journal of Medical Ultrasonics (2022) 49:555–567

Fig. 6  Schematic diagrams of a1–e1 the signals in the channel direction and a2–e2 their frequency spectra at each observation point indicated by A to E

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Journal of Medical Ultrasonics (2022) 49:555–567( k = ±k in the case of the I signal). Because the amplitudeof the analytic signals with low coherence is high, its power
value is large. Therefore, GCF and G­ CFreal values are small.
On the other hand, in Fig. 6a1, the amplitude of the signals
with high coherence becomes relatively large, and that withlow coherence becomes relatively small, due to binarization.
In addition, in the power spectrum of Fig. 6a2, the ­GCFbin
value becomes larger than the GCF and G­ CFreal values dueto the increase in the power value in the vicinity of DC.
At point B, signals with high coherence and signals withlow coherence were mixed and received on different channels, as at point A, but as shown in Fig. 6b1, the relationshipof the amplitude is the opposite ( Ain ∕Aco ≪ 1). In this case,as the amplitude Aco of the signals with high coherence islarger than the amplitude Ain of the signals with low coherence in the analytic signals and I signals, the power value inthe vicinity of DC is also larger than the power value of the�signals with low coherence in the vicinity of k = k (> K0 )
�(k = ±k in the case of the I signal) in the power spectrum, as
shown in Fig. 6b2. However, contrary to point A, the amplitude of the signals with high coherence becomes relatively
small, and that of the signals with low coherence becomes
relatively large, due to binarization. Therefore, the power
value of the DC vicinity component becomes smaller, and­GCFbin becomes smaller than GCF and G­ CFreal. In this case,since the signal from the focus point is dominant, the brightness should not be reduced. Therefore, the smaller value of­GCFbin than GCF is a disadvantage of ­GCFbin.
The signals at points A and B have different amplitudes
for signals with high coherence and signals with low coherence, and they are received by different channels. As a result,­GCFbin is significantly different from GCF and G­ CFreal. On
the other hand, points C to E, which receive signals from thesame source on all channels, are shown below.
In the case of the received signals at points C and D,
although there were differences in the channel directionchanges and the bandwidth of the power spectrum, the frequency components were concentrated in the vicinity of DC
in both cases. Figure 6c1, d1 shows schematic diagrams of
the received signals at points C and D, and Fig. 6c2, d2
shows schematic diagrams of their power spectra. Most of
the frequency components generated by binarization are
considered to appear at |k| > K 0, because K0 is a small number ( K0 = 1 in this study). As a result, the ratio of the power
value of the DC vicinity component to the total power value
decreases, and the ­GCFbin value decreases compared to the
GCF and ­GCFreal values.
Figure 6e1, e2 shows schematic diagrams of the received
signals at point E. In the case of the received signals, thesignals from the focus point are small, and the signals fromoutside the focus point are dominant. With respect to theanalytic signals and I signals, the ratio of the frequency
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component of |k| ≤ K 0 is small. Even if high-frequency
components are generated by binarization, the change inthe power value of |k| ≤ K 0 is small, and the change in the­GCFbin value from the GCF value is small. Similarly, when
the noise component is dominant due to attenuation, both
GCF and G­ CFbin are small due to the high-frequency components [19].

Advantages of ­GCFbin over GCF
The GCF value is determined by the ratio of the frequency components of |k| ≤ K 0 and |k| > K 0 . In general,
the received signals contain both of these frequency components. However, there are cases, where all channels
contain these components in the same way, such as points
C to E, and cases, where each component is received bydifferent channels, such as points A and B. In this paper,
the received signals are classified into these patterns,
and points A–E are selected. In the case of points C toE, the ­GCFbin value changes for the GCF value due to theincrease in the high-frequency components due to binarization. On the other hand, in the case of points A and B,
the dominant signal changes due to binarization, so thechange in the G­ CFbin value for the GCF value tends to belarge. This case is considered below.
Signals like those in Fig. 6a1 are generated when there
is a scatterer at the receiving focus point, and the received
signals from this point are in phase in some channels, but
strong signals from outside the focus point are mixed in theother channels. For such received signals, the GCF value issmall, and weighting with GCF excessively reduces the signal after DAS and causes dark region artifacts [20] aroundthe strong scatterer. The dark region artifacts caused by thediaphragm's strong scatterer are confirmed in Fig. 5a, b. This
artifact is a problem associated with conventional GCF. As
shown in Fig. 5c, because the value of ­GCFbin becomeslarger than that of GCF and G­ CFreal in such a region, theartifacts are not noticeable.
Next, consider the signal in Fig. 6b1. Such received signals are generated when the amplitude of the signals fromthe receiving focus point is large but the signals are notreceived in some channels. For example, it is thought tooccur in the following situations: (1) when the directivity of
the reflected wave is strong due to a continuous structure,such as a blood vessel wall, as in the example of point B;(2) when there is a structure in which sound waves do not
propagate partially between the receiving focus point andthe probe; and (3) when the surface of the probe does notpartially touch the body. These phenomena can occur evenin ordinary examinations. In such situations, the application of ­GCFbin may reduce the signal from the receiving
focus point compared to GCF. On the other hand, sidelobe

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Journal of Medical Ultrasonics (2022) 49:555–567

Conclusion

Fig. 7  Example of received signals at the position affected by thesidelobe

artifacts occur when the signals from the scatterer outside
the focus point are cut off at the edge of the receiving aperture (channel), as shown in Fig. 7, and the DC component
becomes large. Such received signals also correspond to thecase of Fig. 6b1, and because ­GCFbin becomes a smaller
value than GCF, it is considered that the sidelobe artifact
reduction effect of ­GCFbin is superior. In this way, even withthe same signal pattern, there are cases, where it is desirable
to maintain brightness and where it is preferable to reduce it,
depending on the target. Distinguishing them is one of thechallenges of beamforming using coherence factors.
From the above, as dark region artifacts are less likely
to occur with ­GCFbin, the 𝛾 value can be adjusted to further reduce unnecessary signals compared to GCF. This isan advantage of G
­ CFbin. Furthermore, the effect of reducing sidelobe artifacts with ­GCFbin is higher than that with
GCF thanks to binarization. Due to these effects, it can be
confirmed from Tables 1 and 2 that G­ CFbin suppresses dark
region artifacts and reduces sidelobe artifacts more than
GCF. In addition, it is considered that the effect of improving the contrast between the homogeneous part of the liver
and the hypoechoic part of the gallbladder was slightly superior to that of the conventional GCF, as shown in Table 3.
Thus, although G­ CFbin reduced the computational complexity by virtue of binarization of the signal, it was found thatthe image quality of B-mode images was superior to that of
the conventional GCF. It is considered that this is because­GCFbin is calculated only from phase information by removing amplitude information, while GCF is calculated fromphase and amplitude information. Therefore, ­GCFbin is considered to be a new coherence factor that not only reduces
the computational complexity of GCF but also has different
characteristics than GCF.

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In this study, targeting signals in the channel direction andtheir frequency spectra from in vivo data, we considered
the mechanism that causes the differences between G­ CFbin,which reduces the computational complexity of GCF, andGCF.
While GCF and G­ CF real are coherence factors that
include the amplitude values of the signals, the amplitude
information disappears due to binarization of the signals
with ­GCFbin. Therefore, the ­GCFbin value is different fromthe GCF value. However, owing to this difference, G­ CFbinmay be superior in terms of the ability to reduce artifacts.
By removing the amplitude information, ­GCFbin can beconsidered a new coherence factor with different characteristics from GCF.

Declarations
Conflict of interest The authors declare that they have no conflicts ofinterest.
Ethical approval This study was approved by the institutional ethicalcommittee and was performed with the informed consent of the subject.

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