Ultrasound in Med. & Biol., Vol. 39, No. 4, pp. 681–691, 2013
Copyright Ó 2013 World Federation for Ultrasound in Medicine & Biology
Printed in the USA. All rights reserved
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http://dx.doi.org/10.1016/j.ultrasmedbio.2012.10.019

d Original Contribution

SUPPRESSION OF GRATING LOBE ARTIFACTS IN ULTRASOUND IMAGESFORMED FROM DIVERGING TRANSMITTING BEAMS BY MODULATIONOF RECEIVING BEAMSAKINLOLU PONNLE,* HIDEYUKI HASEGAWA,*y and HIROSHI KANAI*y* Graduate School of Engineering, Tohoku University, Sendai, Japan; and y Graduate School of Biomedical Engineering,Tohoku University, Sendai, Japan(Received 20 October 2011; revised 22 October 2012; in final form 30 October 2012)

Abstract—In linear array transducers, owing to regular spacing of the array elements, grating lobes exist in transmission and reception. In ultrasonic imaging involving the use of diverging (unfocused) transmitting beams andsteered receiving beams by linear transducer arrays, aperture apodization and spatial combination of steered
receiving beams from multiple transmissions are not sufficient to suppress receive-grating lobe artifacts. To
further suppress receive-grating lobe artifacts in reconstructed B-mode images, we propose a technique of modulating the receiving beams by a factor that is governed by the envelope of a corresponding signal, which is formedby filtering the receiving beam with a zero-phase low-pass filter with a cut-off frequency that is determined by thereceiving beam steering angle. This technique suppressed receive-grating lobe artifacts without significant loss inspatial resolution in offline reconstructed B-mode images from simulation, phantom and in vivo imaging of the
carotid artery. In a simulation of point scatterers, a relative reduction in grating lobe artifacts of 40 dB was realized
in images from diverging beam scanning. (E-mail: ponnleakinlolu@yahoo.co.uk) Ó 2013 World Federation for
Ultrasound in Medicine & Biology.
Key Words: Receive-grating lobe, Diverging transmitting beam, Zero-phase low-pass filter, Bidirectional filtering,
Modulated receiving beam.

because of the reception of echoes from several directions
that the transmission beam insonifies. These backscattered echoes may contain signals of different frequency
components when pulsed ultrasound is used for imaging.
Because the receive-grating lobe angle varies with thefrequency of the incoming signals, a receiving beam
formed for a given direction may have a wide frequency
spectrum containing echo signals from the desired direction as well as directions of the grating lobes. Althoughgrating lobe intensity can be reduced by apodization(De Jong et al. 1985) and by combining receiving beams
from multiple transmissions (Ponnle et al. 2011), thesemeasures are not sufficient.
A method of adjustable frequency scanning to
reduce grating lobe artifacts in scanning a field of viewusing a scan format has been described previously by
Wright et al. (1996; U.S. Patent No. 5549111). In thispatent, the carrier frequency of the imaging pulse transmitted into the body is highest in the center portion of
the scan and is reduced in a controlled fashion as the steering angle is increased without modification of the pulse
shape itself. This arrangement permits a combination of

INTRODUCTION
In linear array transducers, owing to regular spacing of
the array elements, grating lobes exist in transmission
and reception if the inter-element pitch is wider thana wavelength (Barthez et al. 1997; De Jong et al. 1985;
Kremkau 2006; Kremkau and Taylor 1986). The
receive-grating lobe angle depends on the steering angleof the main receiving lobe, inter-element pitch and thewavelength. In applications in which an unfocused,wide beam is transmitted—such as in synthetic aperture
imaging, parallel receive beam forming (Jensen et al.
2006; O’Donnell 1990; Thomson 1984), explososcan,ultrafast ultrasound imaging (Delannoy et al. 1979;
Fink et al. 2002; Shattuck et al. 1984), or multi-element
diverging transmission beam scanning (Ponnle et al.
2011)—the effect of receive-grating lobes is significant

Address correspondence to: Akinlolu Ponnle, Department ofElectronic Engineering, Graduate School of Engineering, Tohoku
University, 6-6-05 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579,
Japan. E-mail: ponnleakinlolu@yahoo.co.uk
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Fig. 1. Illustration of the transmission and reception scheme of
the multi-element diverging beam scanning from a linear arraytransducer.

high-frequency imaging operation (high resolution) in thecentral portion of the image with a wide field of view thatsuppresses grating lobe artifacts in the outer portions of
the image, but with reduced lateral resolution.
A means of reducing the grating lobe by decreasing
the imaging frequency on a scan-line–by–scan-line basis
was described by Yamaguchi et al. (1986; U.S. Patent No.
4631710). In this patent, a variable bandpass filter (containing a wideband amplifier, a variable high-pass filter
and a variable low-pass filter) is described whose characteristics are controlled as a function of steering angle. As
described, the filter can be applied to a combination ofeach output from a pulse or transmitter, each reception
signal from a receiving transducer element, a composite
receiving beam and original transmission or excitation
signal. Providing one such device per transmission
channel and/or one per receive channel is prohibitively
complex and electronic component intensive. The
approach also suffers from an inherent loss of signal-tonoise ratio because useful energy is lost.
Using angular compounding for strain imaging,
Hansen et al. (2006) applied low-pass filtering to thereceive-beam–formed radiofrequency (RF) signals after
transmitting conventional focused beams at large steering
angles from a linear transducer array to reduce grating
lobe artifacts, but at the cost of spatial resolution.
In this work, a wide multi-element diverging (unfocused) transmitting beam from a linear array transducer
with scanning in a linear sequential fashion (across thearray) was used. The ultrasonic RF echo data received
by the elements in the receiving sub-aperture withineach transmitting event are used for offline creation ofmany steered receiving beams at regular angular inter-

Volume 39, Number 4, 2013vals. The maximum steering angle of receiving beams
in each transmission beam is limited to 665 degrees
with an inter-beam angular separation of 0.5 degrees.
The steered receiving beams were then processed further,and a B-mode image was reconstructed from combinations of many steered receiving beams from multiple
transmissions per frame.The transmission and reception
principle is illustrated in Figure 1. In the figure, eachpoint V is the virtual acoustic (point) source behind theactual array surface (Gammelmark and Jensen 2003;
Karaman et al. 1995; Lockwood et al. 1998; Nikolov
et al. 1999); fd is the axial distance from the array surface
to the virtual acoustic source V; F is the beam-spreadangle; and Ne is the number of active elements thatcompose the transmitting sub-aperture.
To further suppress receive-grating lobe artifacts inoffline-reconstructed B-mode images from diverging
transmission beam scanning, we proposed a method of
modulating each steered receiving beam by a varying
factor governed by the envelope of a corresponding signal,
which was formed by filtering the receiving beam througha zero-phase (ZP) low-pass filter (LPF) with a cut-off
frequency dependent on the main receiving beam steering
angle. The receiving beams are modulated rather thanusing the low-pass–filtered signals to keep the phase information of the receiving beams unaffected and to preserve
the spatial resolution of the reconstructed image.
Reconstructed B-mode images from simulated scanning of point scatterers in water and from scanning of thetransverse cross-section of a silicone-rubber tube
phantom in water, as well as in vivo scanning of carotid
artery, show that receive-grating lobe artifacts are significantly suppressed in the images in which the proposed
technique was applied without a loss of spatial resolution.

Principle
For a linear array transducer, the location (angle qg)of receive grating lobes is obtained as (Huang et al. 2004):


ml
21
sin qs 2; ðm 5 61; 62; 63; ::: Þ
qg 5 sinp(1)
where p is the inter-element pitch, l is the receive-signal
wavelength, qs is the steering angle of the main receiving
lobe and m is a signed integer that is the order of thegrating lobes. The location of the main receiving lobe
corresponds to the value of m 5 0.
Considering the first order grating lobe (m 5 61),l21
qg 5 sin
sin qs 6 :(2)
pBecause l is real,Suppression of grating lobe artifacts in ultrasound images d A. PONNLE et al.

col 5 p sin qg 1sinjqs j 5 ;
f

683

(3)

where co is the speed of ultrasound in the medium.
Therefore, the receive-grating lobe angle qg, thereceiving beam steering angle qs, and the inter-element
pitch p are related to the receive-signal frequency f by:f5co
p sin qg 1sinjqs j(4)Considering a receiving beam at steering angle qs, as
qg increases (from 0 degrees), f decreases until qg 5 90
degrees at f 5 fc (cut-off frequency). This implies thatat frequencies .fc, grating lobes exist at different angles
between 0 and 90 degrees. This finding is illustrated in
Figure 2 for a main receiving beam at 0 degrees, having
different directions of first-order receive-grating lobes,
qg at different frequencies.
Cut-off frequency
At the cut-off frequency, the grating lobe angle is 90
degrees. Substituting 90 degrees for qg in eqn (4), the cutoff frequency fc can be expressed as:
fc 5copð11sinjqs jÞ(5)Given a steering angle qs, the cut-off frequency canbe determined. It should be noted that in this approach,the center frequency of the transmitted pulse is constant,
but the steered receiving beams formed in each transmitting event are low-pass filtered with different cut-off
frequencies determined by the respective receiving
beam steering angles. There could be a large overlap in
the frequency range between the grating lobes at various
angles because there are multiple cut-off frequencies andreceiving beam steering angles are different.
Zero-phase low-pass filtering by bidirectional recursive
filtering
A ZP filter is a non-causal filter that can be used ona finite sequence of signal data. It is a special filter inwhich the slope of the phase response with frequency iszero. It is possible to implement a ZP filter offline byusing a recursive infinite impulse response (IIR) filter inbidirectional filtering operation; this squares the amplitude response and zeros the phase response (Gustafsson
1996; Smith 1997). It is desirable that the LPF have as
maximally flat a magnitude frequency response as
possible in the passband and stopband, as well as a steep
frequency roll-off toward zero in the transition band.
In this work, ZP filtering was performed by first
designing a seventh-order Butterworth (IIR) LPF(Selesnick and Burrus 1996; Shenoi 2006; Shenoi and

Fig. 2. Illustration of a main receiving beam (at 0 degrees) andassociated different first-order receive-grating lobe angles (qg)at different frequencies.

Agrawal 1980) with cut-off frequencies as determinedby eqn (5). The designed filter was then used on thereceiving beam data in a bidirectional recursive filtering
operation to cancel out the phase shifts.
The impulse response of the seventh-order Butterworth (IIR) LPF (at a cut-off frequency of 7.5 MHz anda sampling frequency of 40 MHz) with and without the
ZP operation is shown in Figure 3 (a, b) and the corresponding frequency magnitude/phase responses areshown in Figure 3 (c, d). In Figure 3b, the ZP-LPF removes the time shift and makes the impulse response
symmetrical in time, though only positive time samples
are shown. Also in Figure 3d, it can be observed thatwhile the phase varies non-linearly with frequency for
the IIR filter, the resulting phase shift by the ZP-LPF is
maintained at almost zero throughout the pass band.
Proposed modulating technique
To keep the phase information of the receiving
beams unaffected and to preserve the spatial resolutionof the reconstructed image, the receiving beams are
modulated rather than using the LPF signals for image
reconstruction. The receiving beams are modulated indirectly by the output of the ZP-LPF according to the
proposed technique shown in Figure 4. The modulating
signal RF(n,q) is obtained by operation A1 defined by:RF ðn; qÞ 5yf ðenvÞ ðn; qÞif yf ðenvÞ ðn; qÞ,yenv ðn; qÞyenv ðn; qÞ1otherwise(6)

where yenv(n,q) is the envelope of the original receiving
beam signal y(n,q), and yf(env)(n,q) is the envelope of the684

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Fig. 3. Characteristics of the seventh-order Butterworth (IIR)
low-pass filter (cut-off frequency of 7.5 MHz at sampling
frequency of 40 MHz): (a) Impulse response without zero phase
operation, (b) Impulse response with zero phase operation, (c)frequency response, (d) phase response.

ZP-LPF signal yf(n,q). The output signal ym(n,q) is themodulated receiving beam signal given byym ðn; qÞ 5 RF ðn; qÞ3yðn; qÞ(7)where q is the beam steering angle.

Fig. 4. Proposed modulating technique. env. det. 5 envelope
detection.

Volume 39, Number 4, 2013

Operation A1 as defined by eqn (6) allows for modulation of the receiving beams without affecting the resolution of the final B-mode image. In addition, the seriesof modulating weights could be represented as a direct
current (d.c.) signal with some arbitrary alternating
current (a.c.) signals riding on it. Therefore, the multiplication shows that the overall bandwidth of the modulated
receiving beams is still comparable to the frequency bandof the original receiving beam, but the peaks and troughsin the spectra are slightly modified.
The modulating signal RF(n,q) as determined byoperation A1, when multiplied with the original receiving
beam y(n,q), brings down the average amplitude level ofy(n,q) close to that of the ZP-LPF signal for comparison;
it also ensures that y(n,q) is not completely modulated by
the entire ZP-LPF envelope. Comparing the ZP-LPF
signal with the original receiving beam signal, the amplitude of the receive-grating lobe and depth side-lobe
signals in the ZP-LPF signal would be relatively reduced.
Therefore, the proposed modulating technique attempts
to modify the amplitude variations of the original
receiving beam signal y(n,q) to follow the amplitude variations of the ZP-LPF signal in time portions of the original signal, in which the amplitude of the ZP-LPF
signal is less than the amplitude of the original signal,
while retaining the level of the original signal in time
portions in which the amplitude of the ZP-LPF signal isgreater. This technique prevents the spreading effect of
the envelope of the ZP-LPF signal in the depth direction
from affecting the modulated receiving beam signalym(n,q).
The offline creation of steered receiving beams,
synthesis of the IIR LPF, bidirectional filtering, beam
modulation and image reconstruction were all performed
using MATLAB software (MathWorks, Natick, MA,
USA).
MATERIALS AND METHODS
Simulations
Three columns of six point-scatterers of equal
strength—separated by a lateral distance of 14 mm witheach point-scatterer in each column positioned at axial
depths of 10, 12, 14, 16, 18 and 20 mm in water—were
simulated, and virtual (simulated) diverging transmitting
beam scanning at a beam-spread angle F of 90 degrees
with a simulated 192-element linear array transducer
was performed using Field II program developed by
Jensen (Jensen 1996). A transmitting sub-aperture of 36
elements was used, thereby making 157 transmissions
per frame possible. The scatterers were positioned, andthe columns were distanced apart to enable visualizationof the grating lobe artifacts of the point-scatterers
and how much they affect (i.e., blur) the image of theSuppression of grating lobe artifacts in ultrasound images d A. PONNLE et al.

685

Table 1. Parameters for the virtual (simulated) scanningof point-scatterers in water
Parameter

Value

Transmitting frequency (MHz)Sampling frequency (MHz)Transmitting sub-aperture size (elements)
Assumed speed of sound in water (m/s)
Assumed attenuation in water (dB/cm)
Transmitting and receiving apodization
Element excitation

7.5
30
36
1500
0
BoxcarHanning-modulated
sinusoid of 2 cycles
0.2 (one-element pitch)

Interval of centers of transmitting
sub-apertures (mm)Beam-spread angle (degrees)
Virtual source point for the diverging beam90
3.5 mm behind thearray surface

point-scatterers. The position of each column of scatterers, especially the central column, fell within theregion where the grating lobe artifacts of the point scatterers of other columns were prominent. Other simulation
parameters are shown in Table 1.
Silicone-rubber tube phantom scanning
A silicone-rubber tube phantom in water wasscanned in the transverse plane using diverging transmitting beams having a beam-spread angle F of 90 degrees;
36 elements as the transmitting sub-aperture and 96
elements as the receiving sub-aperture per transmission.
Using a 192-element linear array transducer having

Fig. 6. Zoom-in portion of the receiving beam and the modulated receiving beam of Figure 5 (a, d) superimposed after
normalization for comparison.

200-mm inter-element pitch (UST-5545, Aloka Co.,Tokyo, Japan) with a-10 Aloka ultrasound equipment,
157 transmissions were made per frame, as done in thesimulation. The received ultrasonic RF echoes of eachelement were acquired and sampled at a frequency of
40 MHz for offline processing and image reconstruction.
Carotid artery in vivo scanning
Transverse cross-sectional scanning of the carotid
artery of three human subjects (adult men) was performed
using diverging transmitting beams with the same transmission, array transducer, ultrasound equipment anddata acquisition parameters used in the silicone-rubber
tube phantom scanning.
RESULTS

Fig. 5. Waveforms of the (a) receiving beam, (b) its zero-phase
low-pass filtered signal, (c) the modulating signal and (d) themodulated receiving beam for 0 degrees receive-steering angle
for the 79th transmission of 157 transmissions per frame (simulation). Norm.Amp. 5 Normalized amplitude.

Simulations
Figure 5 (a–d) shows the waveforms of the 0-degreesteered receiving beam signal y(n,q), the ZP-LP filteredsignal yf(n,q), the modulating weight RF(n,q) and themodulated receiving beam signal ym(n,q) of the 79th
transmission of the 157 transmissions per frame, y(n,q)
being created from the received RF signals of thereceiving sub-aperture elements. This receiving beam
coincides with the center column of the point scatterers.
The positions of the point-scatterers are indicated by
the arrows in Figure 5a. In Figure 5d (compared with
Fig. 5a), the temporal lengths of signals due to grating
lobes and lateral and depth side-lobes are reduced, but
temporal lengths of signals from the point-scatterers are
retained. This finding can also be observed in Figure 6,
which is a zoom-in portion of the receiving beam andthe modulated receiving beam signals of Figure 5 (a, d)
superimposed after respective normalization for comparison. The two signals are still aligned in time, but the686

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Fig. 7. Power spectra of the corresponding waveforms in
Figure 5.

instantaneous amplitude of the modulated receiving beam
is modified.
Figure 7 shows the power spectra of the signals in
Figure 5 (a, b, d). The frequency band of the ZP-LPF
signal is reduced because of the filtering (cut-off
frequency is 7.5 MHz in this case), but the frequency
band of the modulated receiving beam signal extends
well beyond the cut-off frequency of the ZP-LPF signal.
In addition, the overall frequency band of the modulated

Fig. 8. Reconstructed B-mode image of simulated scanning ofsimulated point-scatterers using diverging beam scanning (a)from receiving beams, (b) from ZP-LPF signals and (c) frommodulated receiving beams (images in 60 dB range).

Fig. 9. (a) Lateral profile at a depth of 14 mm. (b) Depth profile
along the scatterers of the central column. (c) Positions of thepoint-scatterers of (b).

receiving beam is still comparable to the frequency bandof the original receiving beam, although the peaks andtroughs are modified because of the multiplication
between the modulating weights and the original
receiving beam signal, as shown by eqn (7).
Figure 8 (a–c) shows the reconstructed B-mode
images of the simulated point-scatterers from thereceiving beams, ZP-LPF signals and the modulated
receiving beams, respectively. The images are reconstructed from 157 transmissions and a lateral distance.30 mm to visualize the grating-lobe artifacts of thepoint-scatterers, which are pronounced at the top edgeof the image in Figure 8a. For reconstruction of thesteered receiving beams, boxcar apodization was used.
In Figure 8b, the artifacts are reduced but at the expenseof loss in spatial resolution because of the LPF. In
Figure 8c, the artifacts are suppressed without a loss inspatial resolution.
Figure 9a shows the lateral profile at a depth of 14mm. Figure 9 (b, c) shows the depth profile along thepoint-scatterers of the central column and the positionsof the scatterers. As can be seen in Figures 8 and 9a,
the lateral profiles of the point-scatterers in the ZP-LPF
image are wider, whereas those using the proposed technique are still comparable to the image from the original
receiving beams. In addition, the lateral side-lobes(Fig. 9a) and the depth side-lobes (Fig. 9b) are significantly reduced. The depth side-lobes are caused by theSuppression of grating lobe artifacts in ultrasound images d A. PONNLE et al.

687

Table 2. Half-maximum width and relative change in half-maximum width of image of the point-scatterer at a depth of 14 mmalong the central column of scatterers
Half-maximum width (mm)Relative change in half-maximum width, X (%)

Receiving beams ZP-LPF signals Modulated receiving beams Receiving beams: ZP-LPF signals Receiving beams: mod-receiving beams
Lateral
Axial

0.212
0.295

0.238
0.365

212.2
223.7

0.225
0.267

26.1
9.5

ZP-LPF 5 zero-phase low-pass filter.

trailing pulses, which propagate after the main pulses of
the wavefronts of the diverging transmitting beam(Ponnle et al. 2011). The main pulses are the effective
pulses for imaging.
Suppression of grating lobe artifacts
Considering the lateral profile plots of Figure 9a, thelateral region considered for evaluation of the suppression of grating lobe artifacts is shown enclosed by thebroken purple line. Within these regions, the averagelevel of the image signal for each case is indicated by
the horizontal line of corresponding color running acrossthe regions. The image signals within these regions are
the result of the combined effect of side-lobes andgrating-lobe artifacts of the scatterers. The average levelsof image signals are 243.7, 256.2 and 283.3 dB for theimage from receiving beams, ZP-LPF signals and modulated receiving beams, respectively. Regarding the image
from the receiving beams, these values indicate a reduction of 12.5 dB by the ZP-LPF signals and a reductionof 40 dB by the modulated receiving beams.
Half-maximum width of image of point scatterer andresolution
The effect on image point spread (resolution) is evaluated as:
X5

a2b
a

(8)

where a is the half-maximum width of the image point
spread from receiving beams, b is the half-maximum
width of the image point spread from other cases (ZPLPF and modulated receiving beams) and X indicates
relative change in the image point spread. The halfmaximum widths with corresponding values of X (inpercentage) were evaluated for the point scatterer at 14mm in depth in the central column from Figure 9, assummarized in Table 2. A positive value for X indicates
improvement, whereas a negative value for X indicatesotherwise.
For the diverging beam scanning, there is a significant loss in both axial and lateral resolution by the ZPLPF signals. This loss is not unexpected because in theimage formation from the diverging beam scanning,several steered receiving beams are spatially combined,
and filtering is performed in the direction of steering of
the receiving beams. Therefore, this would degrade theresolution both laterally and axially.
However, using the modulated receiving beams,
a slight loss of lateral resolution is noticed in Table 2,
but there is an improvement in resolution along the depth
by suppression of the depth side-lobes. The loss in lateral
resolution is marginal and does not have much effect on
the B-mode image. It should be noted that these analyses
are from images produced by simulations.
Phantom
Figure 10 (a–c) shows the reconstructed B-mode
images obtained from the scanning of the siliconerubber tube phantom in water from the receiving beams,
ZP-LPF signals and the modulated receiving beams,
respectively. The images are reconstructed from 157
transmissions and over a lateral distance .30 mm toobserve the grating lobe artifacts due to the wall of thephantom, which is conspicuous at the edges of the image
in Figure 10a. As is the case in the simulation, grating
lobe artifacts are suppressed in Figure 10b, but the spatial
resolution is degraded because of the LPF. Using the
proposed modulation method, grating lobe artifacts are
significantly reduced in Figure 10c without a loss inspatial resolution.
Figure 10d shows the axial (depth) profile along thecenter of the tube for the B-mode image from receiving
beams, ZP-LPF signals and the modulated receiving
beams, respectively. As shown in the figure, the level ofdepth side-lobes in the image from the ZP-LPF signals
and the modulated receiving beams are more reduced
than in the image from the receiving beams. In addition,in the depth profile, there is a loss in spatial resolution of
the image from the ZP-LPF signals (the thickness of thetube’s wall is wider for the ZP-LPF signals), but no significant loss in spatial resolution for the modulated receiving
beams (same thickness of tube’s wall as that of thereceiving beams).
As stated earlier, the grating lobe artifacts caused by
the wall of the tube are more pronounced (and the
suppression resulting from the proposed technique ismore observed) toward the edges of the image in688

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Fig. 10. Reconstructed B-mode images of the silicone-rubber tube phantom in the transverse cross-sectional plane from(a) receiving beams, (b) ZP-LPF signals and (c) modulated receiving beams (images in 60 dB range).(d) Depth profile
along the center of the tube in the B-mode image in (a), (b) and (c).

Figure 10a; therefore, few observed grating lobe artifacts
are present at the center of the image, where the depth
profile is taken.
In vivo imaging
For scanning of the carotid artery, Figure 11 (a–c)
shows the reconstructed B-mode images obtained fromthe receiving beams, ZP-LPF signals and the modulated
receiving beams, respectively. Comparing the three
in vivo images, the images in Figure 11 (b, c) are clearer
than in Figure 11a. In Figure 11b, although receivegrating lobe artifacts are reduced, there is a degradationof spatial resolution. In Figure 11c, receive-grating lobe
artifacts are significantly suppressed without degradationof the spatial resolution. Some image features blurred byreceive-grating lobe artifacts in Figure 11a can be seenclearly in Figure 11c. In addition, image contrast isenhanced.
For the scanning of the carotid artery of the other two
subjects, Figures 12 (a–c) and 13 (a–c) show reconstructed
B-mode images obtained from the receiving beams,
ZP-LPF signals and the modulated receiving beams.
DISCUSSION
Aperture apodization can reduce side-lobes andgrating lobes to some extent, but it also widens themain lobe, which reduces the spatial resolution. In thisFig. 11. Reconstructed B-mode images of the carotid artery of the first subject in the transverse cross-sectional plane from(a) receiving beams, (b) ZP-LPF signals and (c) modulated receiving beams (images in 60 dB range).

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689

Fig. 12. Reconstructed B-mode images of the carotid artery of the second subject in transverse cross-sectional plane from(a) receiving beams, (b) ZP-LPF signals and (c) modulated receiving beams (images in 60 dB range).

work, boxcar aperture apodization was used in the creation of the steered receiving beams to have a narrow
main receiving lobe.
Spatial combination of steered receiving beams
from multiple transmissions also reduces grating-lobe
artifacts because the grating lobe components in each
receiving beam that are spatially combined at an image
point will not be coherent. If there is a sufficient numberof steered receiving beams (positive-angled and negativeangled receiving beams) that are combined at an image
point, grating lobe artifacts are reduced significantly.
However, in parts of the image region where there isconsiderable imbalance in the number of the positiveangled and negative-angled receiving beams that are
spatially combined, the incoherent grating lobe components in each receiving beam might not be completely
cancelled out by the combination; therefore, artifacts
will appear in such regions in the image. These regions
will be close to the edge of images corresponding to theregions of transmitting beams of the few initial transmissions and regions of transmitting beams of the few final
transmissions in a frame (assuming linear sequential
scanning).

Using the method proposed herein, this phenomenon
will no longer have an effect, because in every steered
receiving beam that is spatially combined, the amplitudesof the grating lobe components have already been
reduced. For single-angle conventional scanning andimages, grating lobe artifacts are stretched more for lower
frequencies than for higher frequencies (Hansen et al.
2009). In this method, the grating lobe artifacts resulting
from each steered receiving beam are stretched beyond
the surface of the transducer by the filtering operation
before combination.
By modulating the receiving beam signals using the
proposed technique described in this article, the proposed
method can not only compensate for some loss in spatial
resolution, but it can also further suppress grating lobe
artifacts as can be observed in images from the simulation, tube scanning and the in vivo scanning. Grating
lobe generating signals are not only suppressed, but so
are some non-grating lobe-generating signals that might
carry useful clinical information. Nevertheless, theproposed modulation technique (which is to prevent
loss in spatial resolution) involves only operations withsignal envelopes; therefore, ZP filtering is required to690

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Fig. 13. Reconstructed B-mode images of the carotid artery of the third subject in the transverse cross-sectional planefrom (a) receiving beams, (b) ZP-LPF signals and (c) modulated receiving beams (images in 60 dB range).

prevent relative time shifts between the original receiving
beams and the LPF signals.
CONCLUSION
In ultrasonic imaging using diverging transmitting
beams and steered receiving beams, although the spatial
combination of steered receiving beams from multiple
transmissions reduces the problem of receive grating
lobes, the proposed method in this study further suppressed receive grating-lobe artifacts. Reduction of 40
dB in the level of grating-lobe artifacts was achieved insimulations.
The modulating technique used in this work is effective for keeping the phases of the steered receiving beams
unaffected and for preserving the spatial resolution of thereconstructed image.
Although the image produced from diverging beamscanning seems to be more prone to grating-lobe artifacts,
diverging beam scanning has the advantage of obtaining
images that are better than those of conventional linear
scanning in terms of angular features that become moreclearly visible at frame rates still comparable to conven-tional linear scanning. The diverging beam, as used in thiswork, requires no steering of transmitting beams but thesteering was performed in reception. Diverging beamscanning is more suitable for imaging of the transverse
cross section of circular structures.
Acknowledgments—This study was partly supported by a Grant-in-Aid
for Research from Japan Society for the Promotion of Science (20112013, No. 23360177).The study was approved by the Ethics Committeeon Clinical Investigation, Graduate School of Engineering, Tohoku
University, and was performed in accordance with the policy of theWorld Medical Association Declaration of Helsinki Ethical Principles
for Medical Research involving Human Subjects. All subjects gave
informed consent.

REFERENCES
Barthez PY, Leveille R, Scrivani PV. Sidelobes and grating lobe artifacts
in ultrasound images. Vet Radiol Ultrasound 1997;38:387–393.
De Jong N, Souquet J, Faber G, Bom N. Transducers in medical ultrasound: Part two. Vibration modes, matching layers and grating
lobes. Ultrasonics 1985;23:176–182.
Delannoy B, Torquet R, Bruneel C, Bridoux E, Rouvaen JM, Lasota H.
Acoustical image reconstruction in parallel processing analog electronic systems. J Appl Phys 1979;50:3153–3159.
Fink M, Sandrin L, Tanter M, Catheline S, Chaffai S, Bercoff J,
Gennisson JL. Ultra High Speed Imaging of Elasticity. Proc IEEE
UltrasonSymp 2002;2:1811–1820.

Suppression of grating lobe artifacts in ultrasound images d A. PONNLE et al.
Gammelmark K, Jensen JA. Multi-element synthetic transmit aperture
imaging using temporal encoding. IEEE Trans Med Imaging
2003;22:552–563.
Gustafsson F. Determining the initial states in forward-backward
filtering. IEEE Trans Signal Process 1996;44:988–992.
Hansen HHG, Lopata RGP, De Korte CL. Non-invasive carotid strain
imaging using angular compounding at large beam spread angles:
Validation in vessel phantoms. IEEE Trans Med Imaging 2009;28:
872–880.
Huang J, Que PW, Jim JH. A parametric study of beam steering for ultrasonic linear phased array transducer. Russ J Nondestr Test 2004;40:
254–259.
Jensen JA. Field: A program for simulating ultrasound systems. Med
Biol Eng Comput 1996;34:351–353.
Jensen JA, Nikolov SI, Gammelmark KL, Pedersen MH. Synthetic aperture ultrasound imaging. Ultrasonics 2006;44:e5–e15.
Karaman M, Li P, O’Donnell M. Synthetic aperture imaging for small
scale systems. IEEE Trans Ultrason Ferroelect Freq Contr 1995;
42:429–442.
Kremkau FW. Diagnostic ultrasound: Principles and instruments.
Philadelphia: Saunders Elsevier; 2006.
Kremkau FW, Taylor KJW. Artifacts in ultrasound imaging: A review.
J Ultrasound Med 1986;5:227–237.
Lockwood GR, Talman JR, Brunke SS. Real-time 3-D ultrasoundimaging using sparse synthetic aperture beamforming. IEEE TransUltrason Ferroelect Freq Contr 1998;45:980–988.
Nikolov SI, Gammelmark KL, Jensen JA. Recursive ultrasoundimaging. Proc IEEE Ultrason Symp 1999;2:1621–1625.

691

O’Donnell M. Efficient parallel receive beam forming for phased array
imaging using phase rotation. Proc IEEE Ultrason Symp 1990;3:1495–1498.
Ponnle A, Hasegawa H, Kanai H. Multi-element diverging beam froma linear array transducer for transverse cross-sectional imaging of
carotid artery: Simulations and phantom vessel validation. Jpn J
Appl Phys 2011;50:1–10.
Selesnick IW, Burrus CS. Generalized digital butterworth filter design.
Proc IEEE Inter Conf Acoust Speech Signal Proces 1996;3:
1688–1694.
Shattuck DP, Weinshenker MD, Smith SW, von Ram OT. Explososcan:
A parallel processing technique for high speed ultrasonic imaging
with linear phased arrays. J Acoust Soc Am 1984;75:1273–1282.
Shenoi BA. Introduction to digital signal processing and filter design.
Hoboken, NJ: Wiley; 2006.
Shenoi K, Agrawal B. On the design of recursive low-pass digital filters.
IEEE Trans Acoust Speech Signal Process 1980;28:79–84.
Smith SW. The scientist and engineer’s guide to digital signal processing. San Diego, USA: California Technical Publishing; 1997.
Thomson RN. Transverse and longitudinal resolution of the synthetic
aperture focusing technique. Ultrasonics 1984;22:9–15.
Wright JN, Christopher RC, Albert G, Hugh GL, Samuel HM. Method
and apparatus for adjustable frequency scanning in ultrasoundimaging. US Patent 5549111, 8/1996.
Yamaguchi K, Higashiizumi T, Shimazaki T, Sano S, Takeuchi Y. Azimuth adaptive phased array sonar. US Patent 4631710, 12/1986.