Improvement of Range Resolution of FDMAS Beamforming in

Ultrasound Imaging

Ryoya Kozai, Jing Zhu, Kan Okubo and Norio Tagawa

Graduate School of System Design, Tokyo Metropolitan University, Hino, Tokyo 191-0065, Japan

Keywords:

Reception Beamforming, Super-resolution, Transmission With Frequency Sweep, MUSIC Algorithm.

Abstract:

Ultrasound imaging is applied to various ﬁelds because it is noninvasive and real-time imaging i s possible.

However, in diagnosis applications, ultrasound imaging is inferior in resolution to other modalities, so resear-

ches for improving resolution have been actively conducted. Recently, researches on beamforming methods

have been advanced for the purpose of i mproving lateral resolution. In order to form a narrower beam, adap-

tive beamformers such as the MV (minimum variance) beamformer that adaptively changes the beamforming

weights have been proposed, but these methods increase the computational complexity. Therefore, in recent

years, the FDMAS (Filtered-Delay Multiply And Sum) beamformer which can realize high resolution and

high contrast without using complicated calculation attracts attention. On the other hand, we proposed a met-

hod called the SCM (Super resolution FM-Chirp correlation Method) that improves range resolution based on

frequency sweep. In addition, we proposed a new DAS (Delay And Sum) beam former which improves range

resolution by multiplying the echo signal by the result of the SCM before DA S processing. This method is

constructed in the usual RF (Radio Frequency) band. In this study, we ﬁrst reconstruct the FDMAS as a base-

band processing in order to improve the SNR, and apply the SCM result to the FDMAS in order to improve

both range and lateral resolution.

1 INTRODUCTION

Ultrasound imaging is effectively used for medical

diagnosis (Amy et al., 2015) and non-destructive in-

spection. (Ylitalo, 1996) In p articular, real-time ima-

ging is a major ad vantage of ultrasonic imaging, and

it has been extend e d to applications such as an auto-

mobile obstacle detection system (Shoval and Boren-

stein, 2001) and an indoor po sitioning system. (Ha-

zas and Hopper, 2006) Currently, researches aimed at

improving the pe rformance of ultrasonic imaging are

actively condu c te d, and further improvements are also

expected in the future.

Recent researches on the ultrasonic beamforming

methods have been particularly advanced in the la-

teral resolution. The beamforming method serves as

the basis of array signal processing using a transducer

array composed of a plurality of transducer elements

and is a techniq ue to improve the lateral resolution

by fo rming directivity. The most basic beamforming

method is the DAS (Delay and Sum) (Thome nius,

1996) that compensates for the delay of received sig-

nals between transducer elements of the sensor array

and adds them. However, this technique strongly re-

ﬂects the limitation o f the beam width determined by

the aperture width of the transducer array. In order

to form a narrower beam, adaptive beamformers such

as the MV (Minimum Variance) beamformer (Wang

et al., 2005 ; Vignon and Burcher, 2 008; Holm et al.,

2009) th at adaptively changes the beamforming weig-

hts have been pr oposed, but these me thods incre ase

the computational com plexity. Recently the FDMAS

(Filtered-Delay Multip ly and Sum) beamformer (Ma-

trone et al., 201 5) which can realize high resolu tion

and contrast without complicated calculatio n by using

approximate calculation of correlation between recei-

ved signals of each tra nsducer element attracts atten-

tion. Various extensions of the FDMAS have been

proposed in (Matron e et al., 2017; Matrone et al.,

2018; Su et al., 2018). On the other hand, we pr opo-

sed me thods called the SCM (Super-resolution FM-

Chirp correlation M ethod) (Fujiwara et al., 2009) and

the SA-SCM (Synthetic Ap erture-SCM) (Wada et al.,

2015; Tagawa et al., 2018) to improve the range re-

solution. These methods rea lize super reso lution in

the range direc tion by using the phase inf ormation of

the carrier wave by transmitting and receiving a plu-

rality of pulses with different carrier frequencies. The

SCM utilizes focused pulse tra nsmission and the SA-

SCM is an extension of the SCM to utilized divergent

198

Kozai, R., Zhu, J., Okubo, K. and Tagawa, N.

Improvement of Range Resolution of FDMAS Beamforming in Ultrasound Imaging.

DOI: 10.5220/0007583601980205

In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 198-205

ISBN: 978-989-758-354-4

pulse transmission for th e purpose of inc reasing the

frame rate. The SA-SCM transmits divergent pulses

and applies the SA processing (Jensen et al., 2006),

for example the DAS, as a reception beamformer to

echoes received by all transducer elements. After cal-

culating each line signal, resolution is improved by

applying the SCM. Since the SCM is a processing for

each imag e line, discontinuities tend to occu r in the

lateral direction. In order to solve this problem, we

ﬁrst applied the SCM to the received echo of each ele-

ment, and multiply the received echo by th e result to

generate the echo signal with high range resolution.

After that, by applying the DAS to th e obtain e d high-

resolution echoes, we constructed a beam former cal-

led the SCM-weighted SA, in which lateral discon-

tinuities do not occur. (Zhu and Tagawa, 2018)

In this study, we aim to improve the lateral resolu-

tion based o n the FDMAS. First, by reconstructing the

FDMAS as baseban d processing, it is possible to use

not only the frequency band of twice the transmission

frequency used in the FDMAS but also the tran smis-

sion frequency band. SNR (Signal-to-Noise Ratio) is

expected to be improved by using this baseband FD-

MAS. Since the SCM is exe c uted in baseband, the

result of the SCM can be efﬁciently incorporated into

the baseband FDMAS. By this new beam former, in

which the SCM results are used as the same way of

the SCM-weighted SA. we simultane ously impr ove

both range and lateral resolution.

2 METHOD

2.1 Super-Resolution FM-Chirp

Correlation Method

In this section, we explain the principle of the SCM.

We transmit a FM-chirp pulse s(t) = Re[x(t)e

jω

]

with a center frequency of ω

, and r e ceive the echo

signal y(t) in RF-band from D point scatterers, which

is mathematically expressed as

y(t) =

∞

−∞

h(τ)s(t − τ)dτ, (1)

h(t) =

∑

i=1

δ(t − τ

), (2)

where h

is the set of the amplitudes of reﬂections in

all the scatterers, τ

is set of pro pagation delay time s

of echoes of all scatterers, and δ(·) is the Dira c delta

function. The received FM-chirped echo is expressed

as a baseband analytic signal v(t), and a compressed

Figure 1: Example of FM-chirp pulse compression: (a)

transmitted signal s(t) with 8 MHz bandwidth and wit h

Hanning window apodization; (b) absolute value of com-

pressed signal r(t).

signal is formulated as z(t), which are

v(t) =

∑

i=1

x(t − τ

− jω

+ n(t), (3)

z(t) =

∑

i=1

r(t − τ

− jω

+ m(t), (4)

where r(t) is the autocorrelation function of x(t) in

the baseband th at takes complex values, and hence,

z(t) is the complex valued delay proﬁle. The observa-

tion noise n(t) is assumed to be Gaussian white noise

restricted to baseband with variance σ

, and hence,

m(t) is the complex value cross-correlation of x(t) and

n(t). An example of FM-chirp pulse compression is

shown in Fig. 1.

Equation 4 shows that the echo from each scatte-

rer has a phase that depends on the carrier frequency

and the scatterer position. Therefore, by receiving

echoes of different carrier frequencies, it is possible

to separate scatterers based on phase information. Fi-

gure 2 shows an example of the phase informa tion

obtained by different frequency transmission.

The MUSIC (MUltiple SIgnal Classiﬁcation) al-

gorithm (Schmidt, 1986; Zhou et al., 2008) is used

for super-resolution processing of the SCM. As a d is-

crete representation, we deﬁne a compressed echo

vector z

z ≡ [z(t

),z(t

),··· ,z(t

)]

⊤

, a steering vec-

tor r

≡ [r(t

− τ

),r(t

− τ

),··· ,r(t

− τ

)]

⊤

indica-

ting the compressed echo of the i th scatterer, and a

noise vector m

m ≡ [m(t

),m(t

),··· ,m(t

)]

⊤

with M

the number of time sampling. Using an array ma-

nifold matrix Γ

Γ ≡ [r

,· ·· ,r

]

⊤

and a gain vector

g ≡ [h

− jω

,· ·· ,h

− jω

]

⊤

, z

z and its

variance covariance matrix R

R can be formulated as

z = Γ

Γg

g + m

m, (5)

Improvement of Range Resolution of FDMAS Beamforming in Ultrasound Imaging

199

Figure 2: Phase information obtained by transmitting multi-

ple pulses having different frequencies: (a) example of com-

pressed FM-chirp echo; (b) I (In-phase) and Q (Quadrature-

phase) components of z corresponding to (a); (c) I and Q

components for different frequency transmission.

R = Γ

ΓG

GΓ

⊤

+ R

, (6)

G ≡ E

], (7)

≡ E

] = σ

, (8)

where E

[·] and E

[·] indicate the expectation opera-

tors with respect to ω

and E

[·] and with respect to

n(t) respectively by assuming that echoes and obser-

vation noise are statistically independen t. The Her-

mitian matrix R

consists of r(t), a nd the (k,l)th ele-

ment is r(t

− t

). The superscript H mea ns complex

conjuga te transpo se. In the SCM proce ssing, it is ne-

cessary to solve the generalized eigenvalue problem

of the following equation to ob tain eige nvalues λ

and

eigenvectors e

= λ

, i = 1, 2,· ·· , M. (9)

When M > D, the column vectors of Γ

Γ are linearly in-

dependent, and hence, the ra nk of R

R − R

= Γ

ΓG

GΓ

D. Therefore, R

R has D g e neralized eigenval ues grea-

ter than σ

and M − D generalized eig envalues equal

to σ

. The set of D eigenvectors {e

}

i=1

correspo n-

ding to the largest D eigenvalues spans the signal sub-

space. The remaining M − D eigenvectors {e

}

i=D+1

span the noise subspace that does not contain signals.

The noise subspace is orth ogonal to the steering vec-

tor corresponding to the true delay time of the echo.

In order to estimate the arrival time of the reﬂected

wave from the scatterer, the orthogonality between the

steering vector and the noise subspace is evaluated by

changin g the delay time of the steering vector as a

super-resolution dela y proﬁle S(t

) deﬁned as

S(t

) ≡

−1

∑

j=D+1

. (10)

If t

matches the actual position of the scatterer, the

correspo nding r

is orthogonal to {e

}

j=D+1

, and

hence, the d e nominato r of Eq. 10 becomes small.

In this scheme, D must be the number of scatte-

rers, and in practical applications, for example, the

Akaike’s I nformation Criteria (AIC) or the Minimum

Description Length (MDL) criteria are used to deter-

mine D.

In this study, in order to avoid artifacts through

periodicity, we randomly changed the transmission

wave frequency. With K transmissions having a rand-

omly shifted freq uency band, we estimate R

R as an en-

semble average of

R = (

∑

k=1

)/K.

2.2 Synthetic Aperture-SCM

The SCM performs super-resolution processing for

each imag ing line. For that purpose, it is necessary

to transmit multiple FM chirp pu lses having different

frequency bands in each direc tion corresponding to

each imaging line; see Fig. 3 (a). If the image con-

sists of N lines and K times of transmissions are per-

formed in each direction, N × K transmissions must

be ma de to generate the whole image. This extremely

decreases the frame rate when super-resolution is per-

formed on the entire imaging area. In order to solve

the problem, the SA-SCM is realized by incorpora-

ting the SAI (Synthetic Aperture Imaging ) into the

SCM. In the SAI, unfocused pulses are transmitted

in a wide ran ge from sub-aperture elements [Fig. 3

(b)], and for each tr ansmission, echoes from the en-

tire imaging area are received simultaneously by all

the elements and rec eive beam forming is applied. By

randomly changing the frequency band of each trans-

mitted FM-chirp pulse in the SAI, the total number of

the transmissions is reduced. The above-men tioned

N × K times of transmission in the SCM is realized

by only K transmissions in the SA-SCM. Multiple

line signals with different frequencies for each line

are input to the SCM process. To avoid fr equency de-

viation re la te d to the position of the sub-aperture for

transmission, a freque ncy band is randomly assigned

to the position of the sub-apertu re.

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

200

Figure 3: Transmission procedure: (a) SCM; (b) SA-SCM.

2.3 SCM-Weighted SA

Since the SCM is executed for each image line, dis-

continuities tend to occur in the lateral direction. In

order to solve the problem, w e proposed a new DAS

incorporating th e SCM re sults. In this method, the

SCM is ﬁrstly applied to the echoes received by each

element before the DAS processing. Although it is

possible to apply the DAS to the SCM result, i.e., S(t)

deﬁned by E q. 10, sin c e S(t) does no t include phase

informa tion, suppression of unwanted signals using

phase mismatch is not done. By multiplying the re-

ceived RF echo o f each e le ment by S(t), we improve

the range resolution of echo before the DAS b eamfor-

ming and gene rate an image by the DAS. We call this

method the SCM-weigh te d SA. The refore, an image

can be obtain ed for each freque ncy of the transm is-

sion pulse, and it can be used as multispectral infor-

mation, or by integrating all of them, an image with

high SNR can be obtained while avoiding gratin g lo-

bes.

In this m ethod, unlike the SA-SCM, it is necessary

to ﬁx transmission positions of plural transmissions to

the same one in the array transducer. If the transmis-

sion of d ifferent freq uencies is perform ed from dif -

ferent positions, the time position of the correspon-

ding reﬂected wave will deviate between the echoes

used for the SCM processing, and hence, the SCM

processing can not be executed correctly. This limi-

tation is not a problem for phased array tran sducers.

However, in linear arrays and convex arrays, this li-

mitation is not desirable in order to proper ly measure

the information o f the e ntire imaged area . In order

to avoid this problem, it is sufﬁcient to execute the

SCM-weighted SA for some tran smission positions,

and to do so, apply a method based on the concept of

compressive sensing in (L iu et al., 2018) to reduce the

transmission position is effective.

2.4 High Range-Resolution FDMAS

In this section, we propose the FDMAS in baseband

and a new beamformer with improved its range reso-

lution. In the SCM-weighted SA, the ﬁrst SCM pro-

cessing uses the pulse-com pressed IQ (In-phase a nd

Quadrature-phase) echoes, whereas the subsequent

DAS beamforming is applied to the pulse-compressed

RF echo, and ﬁnally in order to generate the B-mod e

image. Namely, the beamforme d RF signal is conver-

ted to the IQ signal again. Since this series of pro-

cedures is inefﬁcient, the FDMAS should be realized

in baseband when incorporating the SCM results into

the FDMAS.

In the baseband FDMAS, ﬁrst, time delay of the

pulse-com pressed IQ echo is corrected instead of the

RF echo. In addition, it is necessary to compensate

the phase deviation of th e IQ signal, which is caused

by the time delay correction. The correction amount

is calculated by the following equ ation.

E(n) = exp(iβn

), (11)

where β satisﬁes the relation β = πd

/(λR

), d is the

pitch between transducer elements, R

is the shortest

distance from the transducer arr ay to the targeted ima-

ging point and n is a number correspo nding to each

element of the tr ansducer. The value of n at the shor-

test distance from the imaging point is set to 0. The

phase is cor rected by multiplying the analytic repre-

sentation of the delay-corrected received echoes by

Eq. 11. Figure 4 shows an example of the real part

of Eq. 11 c orresponding to the certain position in the

image. For the setting of Fig. 4, d is set to 0.14 mm, λ

is set to 0.3 mm, R

is set to 15 mm and the center ele-

ment of the sensor array holds n = 0. This phase cor-

rection corresponds to Doppler compression p roces-

sing in synthetic aperture r adar and β is called Dop-

pler constant. In the DAS, delay-corrected received

echoes received by all elements are added up, but in

the FDMA S, corrected received echoes are multiplied

by a combination of all pairs and added. Assumin g

that the number of elements used for beam forming is

N, the number of all combinations of the pairs is





− N

. (12)

Physical d imension is cha nged by multiplication, and

therefore processing to restore the dimension is per-

formed. That is

ˆs

i j

(t) = sign (s

(t)s

(t))

(t)s

(t)|, (13)

where s

indicates the IQ signal ( complex number) of

the ith element and sign(x) represents a unit complex

number corresp onding to x. The co rrelation of two

complex signals is generally computed as a complex

conjuga te produ ct, that indicates s

(t)

(t) in this

case. However, it was experimentally conﬁrmed that

it is d ifﬁcult to detect the phase d ifference between

Improvement of Range Resolution of FDMAS Beamforming in Ultrasound Imaging

201

Figure 4: Example of real pert of Equation 1 at the certain

position in image.

two signals with little time lag when using s

(t)

(t).

On the other hand, if s

(t) and s

(t) are target sig-

nals without time lag, the product s

(t)s

(t) becomes a

complex number of the same argument in all element

pairs, and a large signal ca n be obtained by add ing

them together. For pairs with time lag s, we found that

the difference in argument is emphasized, espec ia lly

for irregular signals such as spec kle, the rand omness

of the argument is strongly generated, and cancella-

tion occurs by adding them together. Therefore, in

our method, we adopt s

(t)s

(t) for multiplying pro-

cessing. It is noted that |s

(t)s

(t)| = |s

(t)

(t)|.

In the original FDMAS, s

(t) in Eq. 13 is a real

number (RF signal), and Eq. 13 in this study is a com-

plex version of the original eq uation o f the FDMAS.

From these equations, the signal a fter the ad dition is

∗

DMAS

(t) =

N−1

∑

i=1

∑

j=i+1

ˆs

i j

(t) =

−N)/2

∑

n=1

ˆs

(t). (14)

The B-mode image can be generated by computing

the amplitude of the complex value y

∗

DMAS

(t). In th e

FDMAS in RF band, it is ne c essary to extract th e band

correspo nding to the freq uency twice the fr equency

band of the transmission wave by using the band pass

ﬁlter. On the other hand, in the FDMA S in baseband,

the low pass ﬁlter is adopted instead of the band pass

ﬁlter, since both fundamental a nd 2nd harmonic co m-

ponen ts of the result of Eq. 14 appear around a DC

component. This means that the fundamental and the

2nd harmonic components are simultaneously extrac-

ted a nd used for imaging, wh a t is expected to improve

the SNR.

In order to improve the ra nge re solution of the

original FDM AS, we adopt the same method in the

SCM-weighted SA to incorporate the SCM result into

the FDMAS. Namely, before the processing of Eq. 14,

(t) is multiplied by the corre sponding S(t) obtai-

ned by a pplying the SCM to the echoes before be-

amform ing. We call this new beamformer HRR-

FDMAS (High Range-Resolution FDMAS). The re-

striction o f pulse transmission position exists simi-

larly to the SCM-weighted SA, and its improvement

strategy is the same as the SCM-weighted SA, an d it

will be a future task.

Figure 5: Experiment setting using metal wire with vinyl

coating.

3 EXPERIMENT

3.1 Experiment Conditions

In the experiments, the transmission and re ception se-

quences were generated using an experimental plat-

form for medical ultrasound (RSYS0003, Microsonic

Inc., Japan) with a sampling rate of 31.25 M Hz. The

number of transducer elements used for both trans-

mission and reception is 64, while the element pitch

is 0.315 mm. Transmitted waves are restricted to se-

ven gradations. A linear array probe (T0-1 599, Nihon

Dempa Kogyo Co ., Ltd., Japa n) was also used. Th is

probes center frequency is 7.5 MHz and its speciﬁc

bandwidth is 70%. The signal processing required

was performed ofﬂine using MATLA B software.

3.2 Experiments Using Wire Target

Figure 5 shows the experiment setting. We performed

an experime nt using a vinyl coated metal wire with a

diameter of 1.5 mm that was placed in the water at a

distance of 10 mm from the transducer as an imaging

target. The divergent waves wer e transmitted using a

central sub-array composed of 8 eleme nts with a fo-

cal point of −0.63 mm with respect to the sub-array

width of 2.52 mm. Because the probe element spa-

cing is wider, it is likely that grating lobes will be

formed. The f requency band of th e FM chirp pulse

that is used in the experiment is set at a relatively nar-

row 2 MHz, as described in the Table 1. Although the

frequency band that is used is not the most effective

band for all the transmissions, it was conﬁrmed that

can be perform ed appropriately.

3.3 Performance Evaluation of

Baseband FDMAS

First, pe rformm ance compa rison be twe en the DAS

and the FDMAS were conducted. Figure 6 shows the

B-mode images of processing in baseband, and Fig. 7

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202

Table 1: Parameter settings of the transmitted FM-chirp

pulse.

Parameter Value

Frequency band width 2 MHz

Chirp pulse duration 5 µs

Variation range of center freq. 4 to 6 MHz

Number of transmission 15

Apodization Hanning window

Figure 6: B-mode images using 4.62 MHz: (a) baseband

DAS; (b) baseband FDMAS.

shows the intensity distribution proﬁles on a line cros-

sing the imaging target. Since the reception echoes of

a plurality of frequencies are obtained for the SCM

processing, it is possible to g enerate a B-mode image

using each frequency echo. I n this study, the lowest

frequency of 4.62 MHz was used for imaging to avoid

grating lobes as much as possible. In ord er to con-

ﬁrm that th e grating lobes increase by using the high

frequency echo for B-mode imaging, the baseband

FDMAS result using high frequency of 5.75 MHz is

shown in Fig. 8(a). In addition, the intensity distribu-

tion proﬁles in the lateral dir ection using 4.62 MHz

and 5.75 MHz are shown in Fig. 8(b). From Figs. 6

and 7, it c an b e conﬁrmed that the range resolution

almost unchange d, but the lateral resolution improves

when the FDMAS is applied.

Next, in order to evaluate the performance of the

baseband FDMAS, the SNR was compared with the

RF band FDMAS. Figure 9 shows the B-mode image

of the RF band FDMAS and Fig. 10 shows the inten-

sity distribution proﬁles on a line crossing the im a-

ging target. In the deﬁnition of the SNR, the peak

of the echo signal from the target was a dopted as the

signal inte nsity, and the no ise average was adopted as

the noise intensity in the range direction proﬁle of one

line where the target exists. The SNR was 32.63 dB

for RF band FDMAS and 37.12 dB for baseband FD-

MAS. From this result, it was conﬁrmed that the ba-

Figure 7: Intensity distribution proﬁles on a line crossing

imaging target using 4.62 MHz: (a) range direction; (b) la-

teral direction.

Figure 8: Grating lobes increase using high frequency echo:

(a) B-mode i mage using 5.75 MHz; (b) intensity distribu-

tion proﬁles in lateral direction using diff erent frequencies.

seband FDMAS improves the SNR and the lateral re-

solution. In the RF band FDMAS, the range resolu-

tion is improved by extracting the double frequency

band using a band pass ﬁlter. On the other hand,

the baseband FDM A S processes the baseb a nd signal

in which both the transmission frequency component

and the doubled frequency component are conve rted,

so that the SNR can be improved. By using not only

the double freque ncy band but also th e transmission

frequency band, we were worried about lowering the

resolution compared to the FDMAS in the RF band.

However, due to the fact th a t th e double freq uency

band has sufﬁcient power, no reduc tion in range re-

solution was conﬁrmed. Improvemen t of lateral re-

solution is considered to be due to phase matching

of processing in baseband. However, pr ocessing with

baseband causes a rtifacts regardless of the beamfo r-

ming method. Since th is does not occur in processing

Improvement of Range Resolution of FDMAS Beamforming in Ultrasound Imaging

203

Figure 9: B-mode image of RF band FDMAS.

Figure 10: Intensity distribution proﬁles on a line crossing

imaging target of B-mode images in RF band and baseband

FDMAS: (a) range direction; (b) lateral direction.

with the RF band, we will investigate the cause in the

future.

3.4 Performance Evaluation of

HRR-FDMAS

Performance of HRR-FDMAS was evaluated. Fi-

gure 11 shows th e B-mode image s by the SCM-

weighted SA and by th e HRR-FDMAS, and Fig. 12

shows the intensity distribution proﬁles on a line cros-

sing the imaging target of all the methods described

in this p aper. In this experiment, the value of D in

SCM processing was set to 1 because there is only

one target. Figu re 13 shows the result of SCM when

changin g the value of D. As sh own in Fig. 13, arti-

facts m a y be gener a te d in the re sult of the SCM if D

setting is not a ppropriate. From this result, it can be

conﬁrmed that the HDD-FDMAS improves the lateral

resolution compared with the SCM-weighted SA.

4 CONCLUSION

We ﬁrst proposed the realization of FDMAS in ba-

seband, and experimentally conﬁrmed that SNR and

lateral resolution are grea tly improved c ompared with

Figure 11: B-mode images: (a) SCM-weighted SA; (b)

HRR-FDMAS.

Figure 12: Intensity distribution proﬁles on a line crossing

imaging target of al l methods described in this paper: (a)

range direction; (b) lateral direction.

Figure 13: Result of SCM when changing the value of D:

(a) D = 1; (b) D = 5.

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

204

FDMAS in RF band. Subsequently, we proposed a

new beamformer HRR-FDMAS in which the SCM

result is applied to the FDMAS in o rder to improve

range resolution. The improvement of the spatial re-

solution for the FDMAS in the conventional RF ban d

was clearly conﬁrmed by experiments. Evaluation

and veriﬁcation of a c tual performance of the HRR-

FDMAS fo r living organ isms is a task to be carr ie d

out as soon as possible in the f uture.

In the HRR-FDMAS, the SCM processing takes

much computational cost because the phase informa-

tion of the carrier is extracted by the MUSI C algo-

rithm that requires the e igenvalue analysis. Therefore,

we are considering improvin g the range resolution by

other methods that can use phase information with a

low cost procedure. The essence of the SCM is to

transmit and receive multiple times while ch anging

the carrier frequency irregularly, and we aim to pro-

pose an efﬁcient beamforming method that can take

advantage of this principle.

REFERENCES

Amy, D., Durante, E., and Tot, T. (2015). T he lobar appro-

ach to breast ultrasound i maging and surgery. Ultra-

sonics, 42(3):331–339.

Fujiwara, M., Okubo, K., and tagawa, N. (2009). A no-

vel technique for high resolution ultrasound imaging

using super resolution fm-chirp correlation method

(scm). In Proc. IEEE Int. Ultrason. Symp., pages

2390–2393.

Hazas, M. and Hopper, A. (2006). Broadband ultrasonic lo-

cation systems for improved indoor positioning. IEEE

Trans. Mobile Computing, 5(5):536–547.

Holm, S., Synnevdg, J. F., and Austeng, A. (2009). Capon

beamforming for active ultrasound imaging systems.

In Proc. IEEE 13th DSP Workshop, pages 60–65.

Jensen, J. A., Nikolov, S. I., Gammelmark, K. L., and Pe-

dersen, M. H. (2006). Synthetic aperture ultrasound

imaging. Ultrasonics, 44:e5–e15.

Liu, J., He, Q., and Luo, J. (2018). Compressed sensing

based synthetic transmit aperture imaging: Validation

in a convex array conﬁguration. IEEE trans. ultrason.

ferroelectr. freq. control, 65(3):300–315.

Matrone, G., Ramalli, A., Savoia, A . S., Tortoli , P., and Ma-

genes, G. (2017). High frame-rate, high resolution

ultrasound imaging with multi-line transmission and

ﬁltered-delay multiply and sum beamforming. IEEE

Trans. Med. Imag., 36(2):478–486.

Matrone, G., R amalli, A., Tortoli, P., and Magenes, G.

(2018). Experimental evaluation of ultrasound higher-

order harmonic imaging with ﬁltereddelay multiply

and sum (f-dmas) non-linear beamforming. Ultraso-

nics, 86:59–68.

Matrone, G., Savoia, A. S., Caliano, G., and Magenes, G.

(2015). The delay multiply and sum beamforming al-

gorithm in ultrasound b-mode medical imaging. IEEE

Trans. Med. Imag, 34(4):940–949.

Schmidt, R. O. (1986). Multiple emitter location and sig-

nal parameter estimation. IEEE Trans. Antennas and

Propagation, 34(3):276–280.

Shoval, S. and Borenstein, J. (2001). Using coded signals to

beneﬁt from ultrasonic sensor crosstalk in mobile ro-

bot obstacle avoidance. In Proc. IEEE Int. Conf. Ro-

botics and Automation, volume 3, pages 2879–2884.

Su, T. , Li, D., and Zhang, S. (2018). An efﬁcient subar-

ray average delay multiply and sum beamformer al-

gorithm in ultrasound imaging. Ultrasonics, 84:411–

420.

Tagawa, N., Zhu, J., and Okubo, K. (2018). Performance

analysis of high-frame rate and super-resolution ultra-

sound i maging based on f requency sweeping. submit-

ted to Applied Sciences.

Thomenius, K. E. (1996). Evolution of ult r asound beamfor-

mers. In Proc. IEEE Int. Ultrason. Symp., volume 2,

pages 1615–1622.

Vignon, F. and Burcher, M. R. (2008). Capon beamfor-

ming in medical ultrasound imaging with focused be-

ams. IEEE trans. ultrason. ferroelectr. freq. control,

24(10):1308–1322.

Wada, T., Ho, Y., Okubo, K., Tagawa, N., and Hirose, Y.

(2015). High frame r ate super resolution imaging ba-

sed on ultrasound synthetic aperture scheme. Physics

Procedia, 70:1216–1220.

Wang, Z., Li, J. , and Wu, R. (2005). Ti me-delay-

and time-reversal-based robust capon beamformers

for ultrasound imaging. IEEE Trans. Med. Imag.,

24(10):1308–1322.

Ylitalo, J. (1996). A fast ultrasonic synthetic aperture ima-

ging method: application to ndt. Ultrasonics, 34(2-

5):331–333.

Zhou, L., Zhao, Y. J., and Cui, H. (2008). High resolution

wideband doa estimation based on modiﬁed music al-

gorithm. In Proc. IEEE Int. Conf. Inf. Automat., pages

20–22.

Zhu, J. and Tagawa, N. (2018). Super-resolution ultrasound

imaging based on the phase of the carrier wave wit-

hout deterioration by grating lobes. In Proc. Int. Conf.

Pattern Recognition, pages 2791–2796.

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