Generalized Sidelobe Canceller for Ultrasound Imaging ...

ISSN 1063-7710, Acoustical Physics, 2019, Vol. 65, No. 1, pp. 123–131. © Pleiades Publishing, Ltd., 2019.

ACOUSTICS OF LIVING SYSTEMS.BIOMEDICAL ACOUSTICS

Generalized Sidelobe Canceller for Ultrasound Imagingbased on Eigenvalue Decomposition1

Ping Wanga, *, Yizhe Shia, Jinyang Jianga, Lu Konga, and Zhihui Gonga

aState Key Lab. of Power Transmission Equip. and System Security and New Tech., Chongqing University, Chongqing, 400044 China*e-mail: [email protected]

Received November 30, 2017; Revised May 21, 2018; Accepted August 28, 2018

Abstract—The improved generalized sidelobe canceller (GSC) based on eigenvalue decomposition beam-forming technique for ultrasound imaging is proposed. Firstly, the signal subspace is obtained by performingeigenvalue decomposition on the covariance matrix of received data. Secondly, the weighting vector of GSCis divided into adaptive and non-adaptive two parts. Then the non-adaptive part is projected into the signalsubspace to obtain a new steer vector. Subsequently, based on the orthogonal complementary space of thenew steer vector, the blocking matrix is constructed. Finally, the weighting vector is updated by projecting thefinal weighting vector into the signal subspace. In order to verify the proposed algorithm, the simulations ofthe point targets and the cyst phantom were conducted in Field II. The experimental results indicate that theproposed method has better resolution and contrast ratio than the conventional algorithms. In addition, thealgorithm is robust to noises. Furthermore, combining with coherence factor, the contrast ratio of the pro-posed algorithm can be further improved in comparison with a conventional GSC with coherence factor.

Keywords: generalized sidelobe canceller, eigenvalue decomposition, resolution, contrast ratio, robustnessDOI: 10.1134/S1063771019010159

1. INTRODUCTIONUltrasound is widely used in medical and industrial

inspection field due to its safety and low cost. Thetransducer array transmits a focused beam to the targetand receives the pulse-echo dynamically to form a B-mode image. The conventional delay-and-sum (DAS)beamforming is the most widely used and the simplestmethod in ultrasound imaging, but it has many draw-backs, such as low resolution, serious artifacts andgrating sidelobes. The adaptive beamforming tech-niques can overcome some of these defects. J.F. Syn-nevag [1] adopted the minimum variance (MV) adap-tive beamforming method, which was first proposedby Capon in 1969, in medical ultrasound imaging fieldand achieved a better image quality than DAS.Although the MV method can achieve a better resolu-tion, its robustness is not better than the conventionalDAS [2]. J. Li [3] used the diagonal loading method toimprove the beamformer’s robustness and provided aguidance to define the amount of diagonal loading.K.W. Hollman first put forward the conception ofcoherence factor (CF) which can effectively compressthe sidelobes to improve the contrast ratio of imaging[4], and this method is adopted in many adaptive algo-rithms to correct the phase distortion resulted from thefocusing error [5–7]. Besides, Li et al. proposed a gen-eralized coherence factor (GCF) as an adaptive

weighting coefficient for imaging algorithms, which iswidely used in practice [8, 9]. Many scholars seekother ways to improve the lateral resolution and SNRexcept the MV-based methods. In [10], the authorimproved the image quality via using the phase infor-mation, phase coherence factor (PCF) and signcoherence factor (SCF). Apart from the conventionalDAS imaging algorithm, almost all of improved meth-ods will increase the computational complexity. Asland Mahloojifar suggested that the computationalcomplexity of matrix inversion can be reduced by con-structing the covariance matrix into a Toeplitz matrix[11]. Some scholars also proposed the QR decomposi-tion method to realize the fast inversion calculation ofthe covariance matrix [12]. Other MV-based compu-tation reduction methods can be found in [13, 14]. Thegeneralized sidelobe canceller (GSC) algorithm, asthe equivalent structure of MV, is divided into theupper and lower channels. The upper channel is anon-adaptive channel and the lower channel is theadaptive part; the desired signal can be blocked by theblocking matrix [15–17]. At last, the undesired signalis eliminated and the quality of ultrasound imaging isimproved through overlaying.

This paper proposes an improved generalized side-lobe canceller beamforming (IGSC) differing from[18]. The proposed method concerns more about theimprovement of resolution and contrast ratio (CR).Based on IGSC, the IGSC-CF algorithm is also pro-1 The article is published in the original.

123

124 PING WANG et al.

Fig. 1. Generalized sidelobe canceller.

x[k]

y[k]–+

wq

waB

posed in order to further compress sidelobes andimprove the contrast ratio of imaging. The main fea-ture of the proposed method is to modify the blockingmatrix, instead of defining it fixed beforehand. Thenthe non-adaptive weighting vector is projected into thesignal space to acquire a new steer vector, and theimproved blocking matrix is constructed based on itsorthogonal complementary space adaptively. At last,the final weighting vector is projected into the signalspace to get a new vector to further improve the perfor-mance of the algorithm. The proposed algorithm inthis paper can be applied to synthetic, plane wave andother acquisition sequences.

This paper is organized as follows: the IGSCmethod is presented in section 2 in detail. The proce-dures of acquiring the covariance matrix are describedin section 3. Experimental results and the discussionof the resolution, CR and robustness are presented insection 4, which includes the comparison between theproposed IGSC, IGSC-CF, and DAS, MV, GSC,GSC-CF as well. All experiments use the linear arrayfor the transmission and reception of ultrasound sig-nals. Conclusion is drawn in section 5.

2. METHOD

2.1. Generalized Sidelobe Canceller

The MV is the most commonly-adopted adaptivebeamforming technique. Supposing a linear arraywhich consists of equal space elements, its beam-forming output can be written as

(1)

where is the k-th signal sample received by i-thelement after a certain time delay, is the weightingvector for each element and

The main task is to obtain the . A criterion is pro-vided in MV, which the weights are acquired by mini-mizing the output power of the beamformer subjecting

N

[ ] ( ) [ ] [ ]=

= =1

1 1 ,N

Hi i

i

y k w x k k kN N

w x

[ ]ix kw

[ ] [ ] [ ] [ ]( )= 1 2, ...... .HHNk w k w k w kw

w

to a constraint condition, it can be expressed as fol-lows:

(2)

where is the abbreviation of “subject to”, meaningconstrained, is the output power,

is the covariance matrix of thereceived data, is the steering vector of the desired sig-nal. The solution to the optimization problem (2) canbe obtained by using Lagrangian method, and thesolution is:

(3)

The GSC is the equivalent structure of the MValgorithm. Unlike MV, the GSC algorithm transformsits constraint optimization problem into uncon-strained optimization problem through the upper andlower branches, and its structure is illustrated in Fig. 1.

In GSC, the weighting vector is divided into non-adaptive and adaptive parts, the first one lies in theconstraint subspace and the latter belongs to the sub-space, which is orthogonal to the former. The weight-ing vector can be expressed as

(4)

where is a fixed vector and B is a blocking matrix, which blocks the desired signal intothe lower path. Since the is fixed, the previous con-straint problem (2) turns into an unconstrained opti-mization problem to solve the adaptive vector . Theoptimal solution is [19]:

(5)

Here denoting is the out-put after the received data passes through theupper branch and the blocking matrix respectively.The adaptive weighting vector can be expressed as:

(6)

where , is the covari-ance matrix of and is the correlation vector of and . In fact, the optimal solution (5) is the Wienersolution that minimizes the mean square errorbetween the upper and lower paths.

2.2 Eigenvalue DecompositionAccording to the echo signals, the covariance

matrix can be obtained:

(7)

[ ] [ ]{ } [ ] [ ]{ } =

= =

2

arg min . 1,

H

H H

p k E y k E k k

s t

w x x w

w w Rw w a

H=

.s t[ ]p k

[ ] [ ]{ }= HE k kR x xa

[ ] [ ][ ]

−

−=1

1 .H

nn

n

R aw

a R a

= − =. 0,Hq a qs tw w Bw B w

qw ×1N × −( 1)N N

qw

aw

( )−=

1.H H

a qw B RB B Rw

[ ] [ ]= =,q

H Hcy k kw x B xz

[ ]x ki

B

−= 1 ,a z zw R p

= =,H Hz z qR B RB p B Rw zR

z zp cyz

= ε( ) { ( ) ( ) },Hk k kR x x

ACOUSTICAL PHYSICS Vol. 65 No. 1 2019

GENERALIZED SIDELOBE CANCELLER FOR ULTRASOUND IMAGING 125

where represents the expected value,, is the number of

array elements, represents the k-th sampling pointand is the echo data of the k-th sampling pointreceived by all array elements.

In practical applications, the covariance matrix isusually unknown. Therefore, spatial smoothing is gen-erally used to estimate the covariance matrix withautocorrelation sampling matrix, to effectively reducethe matrix dimension and eliminate the correlationbetween echo signals:

(8)

In equation (8), is the number of array elements, is the number of array elements in the sub-array, allarray elements can be divided into sub-arrays altogether. The average of the echo data of eachsub-array can be used to estimate the covariancematrix.

After obtaining the signal covariance matrix , thespace is obtained by using eigenvalue decomposi-tion, which includes both the desired signal and thenoise signal space. Then, rearranging its eigenvalues in descending order, if the ratio of adjacent eigenvalue

exceeds a preset threshold value, a new spaceis constituted:

(9)

where is the corresponding eigenvector and Us is thesignal space.

In order to increase the robustness of the algo-rithm, the diagonal loading technique is used to pro-

cess the matrix, is used instead of the origi-

nal autocorrelation matrix , where is the unitmatrix and the diagonal loading coefficient is

, δ is a constant satisfying . In

this paper .

2.3. Improved Generalized Sidelobe Canceller

The GSC can work properly whether z contains alittle desired signal or not. Once the desired signalexceeds its limitation, which means the desired signalsleak much to the lower path, thus the imaging qualitywill degrade a lot. Here the IGSC is introduced bymodifying the blocking matrix B and the final weight-ing vector is projected into the signal space to improvethe GSC ability to block the undesired signal. Asdescribed in (4), the blocking matrix B is orthogonalto the non-adaptive weighting vector . In the pro-

ε ⋅{}

−= 0 1 1( ) [ ( ), ( ),..., ( )]HNk x k x k x kx N

k( )kx

− +∧

==

− + 1

1

1( ) ( ) ( ) .1

N Ll l Hn n

l

k x k x kN L

R

N L

− +( 1)N L

RU

λi

+λ λ 1/i i

[ ]= 1 2, ...... ,s iU u u u

iu

∧+ ε( )kR I

∧( )kR I

∧ε = δtrace( ( ))kR δ ≤ 1

Lδ = 1

100L

qw


posed IGSC, the new adaptive vector is obtainedby projecting the non-adaptive vector into the sig-nal space , and the improved blocking matrix isorthogonal to the adaptive vector . The specificdescription is shown in (10), through these operations,the blocking matrix changes from a non-adaptivematrix into an adaptive matrix, which improves theability to block the desired signal.

The new steer vector is acquired by projecting thenon-adaptive weighting vector into the signal space:

(10)

The renewed blocking matrix Bp is then established onthe basis of the orthogonal complementary space ofwp. Thus the weighting vector can be expressed as

(11)

where

In general, is a fixed vector and the block-ing matrix is orthogonal to vector , so is usuallya fixed matrix. In this paper, we project into the sig-nal space and then construct the blocking matrix adaptively.

Here the blocking matrix is established in a novelway, and then the final weighting vector is obtainedthat can be projected into the signal space to furtherimprove the resolution and contrast ratio. So, the finalweighting vector can be expressed as:

(12)

After obtaining the covariance matrix and theresult from (12), the IGSC beamforming output canbe determined as:

(13)

By emphasizing the in-phase signals and reducingthe out-of-phase ones, CF can be weighted to improvethe contrast ratio, enhance the ability of sidelobe sup-pression. The definition of CF is the ratio of coherentenergy to total energy, the expression is as follows:

(14)

In order to make an overall comparison with [18],the proposed method integrates with CF too, the out-put of combining IGSC with CF is

(15)

pw

qw

sU pB

pw

p ps.t= = 0.H Hp s s qU U w B ww

− ,pq p aw w B w=

( )−=

1.p H

a p p p qw B RB B Rw

qw ×1NB qw B

qwB

=opt .Hs sw E E w

[ ] [ ] [ ]− +

==

− + 1

opt,1

1 .1

N LH

i ii

y k w k x kN L

− +

=− +

=

=− +

21

11

2

1

( )[ ] .

( 1) ( )

N L

ii

N L

ii

x k

CF k

N L x k

[ ] [ ] [ ] [ ]− +

==

− + 1

opt,1

.1

N LH

i ii

CF ky k w k x k

N L


Table 1. Initial values for the experiment

Parameter Value

Central frequency f0 3.5 MHzSampling frequency fs 50 MHzArray type LinearlyTransducer number N 64Subarray length L 32Bandwidth B 0.6 mmElement width 0.2 mmElement height 5 mmElement spacing 0.48 mmFocal depth (points) 60 mmFocal depth (cyst) 25 mm

4. EXPERIMENTAL RESULTS

This section tested the performance of DAS andother adaptive algorithms, as well as the proposedmethods IGSC and IGSC-CF based on Field II [20,21]. We conducted the experiment with two kinds ofdetection objects, the first one consists of 18 point tar-gets uniformly distributed between 30 to 70 mm in twocolumns, and the second is a circular cyst in a specklemedium. The basic parameters setting for these exper-iments are displayed in Table 1. It should be noted thatall the methods have used the spatial smoothing and

Fig. 2. 18-point targets images o

30

DAS

Dep

th, m

m

35

40

45

50

55

60

65

70

–4 0 4

30

MV

35

40

45

50

55

60

65

70

–4 0 4

30

GSC

35

40

45

50

55

60

65

70

–4 0 4Lateral

diagonal loading technique. Besides, a Gaussian whitenoise with a certain signal-to-noise ratio has beenadded to each simulation experiment [22]. The simu-lation of this paper adopts the linear array transducerto transmit ultrasound signals and the dynamic rangeof all images is 80 dB.

4.1. Point Targets Experiment

The point targets are distanced 4 mm in the lateraland 5 mm in the axial directions, images through dif-ferent methods are displayed in Fig. 2. It can be seenthat the IGSC-CF has the best performance and alladaptive methods have better performance than DAS.GSC performs nearly the same as MV. After combin-ing with CF, some artifacts in images are removed.The proposed IGSC achieves similar results in the fur-ther scanning depth, while it performs slightly worsethan the GSC-CF within the 45 mm, but better thanthe GSC. This is because CF weighting can improvethe contrast ratio and resolution by emphasizing thein-phase signals and reducing the out-of-phase ones.

After combining the IGSC with CF, both the neararea and the farther depth can acquire better resolu-tion than other methods. This improvement can befurther verified by Figs. 3a and 3b depicting the lateralvariation at depth of 40 and 60 mm respectively.

It can be seen from Fig. 3a that DAS image has thegreatest sidelobe level, GSC and MV improve slightly,however the imaging effect has a significant improve-


btained using different methods.

30

GSC-CF

35

40

45

50

55

60

65

70

–4 0 4

30

IGSC

35

40

45

50

55

60

65

70

–4 0 4

30

IGSC-CF

35

40

45

50

55

60

65

70

–4 0 4distance, mm


Fig. 3. (a) Lateral variation at depth of 40 mm, (b) lateral variation at depth of 60 mm.

–200

–50

–100

–150

0(а) (b)

5–4 –3 –2 –1 0 1 2 3 4–5Lateral distance, mm Lateral distance, mm

DASMVGSCGSC-CFIGSCIGSC-CF

Pow

er, d

B

Pow

er, d

B

–120

–20

–40

–60

–80

–100

0

5–4 –3 –2 –1 0 1 2 3 4–5


Table 2. Numerical results of mainlobe width for differentmethods in 40 mm

MethodMainlobe width First sidelobe peak,

dB–6 dB –20 dB

DAS 2.18 3.85 –3.02MV 0.56 2.06 –18.54GSC 0.56 2.06 –18.54GSC-CF 0.50 1.09 –57.18IGSC 0.61 1.69 –28.60IGSC-CF 0.52 1.14 –84.07

Table 3. Numerical results of mainlobe width for differentmethods in 60 mm


dB–6 dB –20 dB


ment with the help of CF, IGSC has a little improve-ment on the basis of GSC and has significantimprovement after combining with CF. Besides,IGSC-CF performs better than GSC-CF. Here we use−6 and –20 dB mainlobe width as indications of reso-lution and use the first sidelobe peak to represent thecontrast ratio. As it can be seen from Table 2, theIGSC performs slightly better than GSC at –20 dBmainlobe width, while it behaves 0.37 mm over GSC.IGSC-CF has similar results at –6 and –20 dB main-lobe width comparing with GSC-CF, but it is moreadvantageous at lower dB values than GSC-CF. Thelast column shows the contrast ratio of the differentmethods, and lower quantities represent better imagequality. The proposed IGSC performs better than MVand GSC, but worse than GSC-CF, the reason is thatCF has great ability in suppressing the sidelobes. So,the image quality of IGSC-CF is far superior to othermethods.

Similar patterns are shown in the case of the fartherscanning depth (Fig. 3b), while the advantages of theproposed methods appear. Similarly, the DAS per-forms the worst and the IGSC has similar mainlobewidth with MV and GSC, but when these methods arecombined with CF, the first sidelobe peak can begreatly reduced. On the other hand, the first sidelobepeak of IGSC is around 20 dB better than that of GSCand MV, which indicates that the proposed methodhas better ability to compress sidelobes. When com-bined with CF, the contrast ratio has significantimprovement on the basis of IGSC; moreover, theclutter signals have larger distance to the mainlobe inGSC-CF and IGSC-CF. More experimental resultsare shown in Table 3.

In order to test the robustness against noises of theproposed methods, a 10 dB white Gaussian noise isadded to the received data. Figure 4 displays the


images obtained by the abovementioned methods, andFig. 5 shows the corresponding resolution at depth of40 and 60 mm respectively. After adding the noises,the background white spots are obviously enhanced. Itcan be seen that GSC-CF degrades its robustnessagainst noises than DAS, MV and GSC. IGSC hasbetter robustness than other adaptive methods, since


Fig. 4. 18-point targets noise images obtained using different methods.

30

DAS

Dep

th, m

m

35

40

45

50

55

60

65

70

–4 0 4

30

MV

35

40

45

50

55

60

65

70

–4 0 4

30

GSC

35

40

45

50

55

60

65

70

–4 0 4

30

GSC-CF

35

40

45

50

55

60

65

70

–4 0 4

30

IGSC

35

40

45

50

55

60

65

70

–4 0 4

30

IGSC-CF

35

40

45

50

55

60

65

70

–4 0 4Lateral distance, mm

Fig. 5. (a) Lateral variation at depth of 40 mm with noise, (b) lateral variation at depth of 60 mm with noise.

–70

–10

–20

–30

–40

–50

–60

0(а) (b)

5–4 –3 –2 –1 0 1 2 3 4–5Lateral distance, mm Lateral distance, mm


Pow

er, d

B

Pow

er, d

B

–60

–10

–20

–30

–40

–50

0

5–4 –3 –2 –1 0 1 2 3 4–5


we add relatively strong noises to the echo signals, allmethods’ performance are degenerated to somedegree.

Figure 5a,b display the corresponding resolution atdepth of 40 and 60 mm respectively. Both for the 40and 60 mm, IGSC achieves better first sidelobe peakvalue than DAS, MV and GSC which shows inferior-ity to GSC-CF and IGSC-CF in the 40 mm. How-ever, it shows a little dominance over GSC-CF andIGSC-CF in the 60 mm, which illustrates that the

IGSC has better robustness than other adaptive algo-rithms. IGSC has some improvement in mainlobewidth after integrating with CF in both 40 and 60 mm.Besides, IGSC displays nearly the same –6 dB main-lobe width and the lower first sidelobe peak value thanGSC-CF and IGSC-CF in the farther scanning depthsituation. Meanwhile, the IGSC has a lower first sid-elobe peak value than DAS, MV and GSC both in thenear area and the farther scanning depth, which shows



Table 4. Numerical results of mainlobe width for differentmethods in 40 mm with noise


dB–6 dB –20 dB


Fig. 6. Cyst phantom images obtained using different methods.

DASD

epth

, mm

20

25

30

35

20

25

30

35

20

25

30

35

20

25

30

35

20

25

30

35

20

25

30

35–2–4 0 42 –2 2 –2 2 –2 2 –2 2 –2 2

MV

–4 0 4

GSC

–4 0 4

GSC-CF

–4 0 4

IGSC

–4 0 4

IGSC-CF


Table 5. Numerical results of mainlobe width for differentmethods in 60 mm with noise


dB–6 dB –20 dB


its robustness against noises. The detailed numericalresults are listed in Tables 4 and 5.

4.2. Cyst Phantom Experiment

The cyst phantom is set 5 mm radius located at thedepth of 25 mm in a speckle medium. The scatteramplitudes are Gaussian distributed. The spatialsmoothing and the diagonal loading technique areadopted as well. The specific experiment parametersare listed in Table 1. Images after processing by differ-ent methods are shown in Fig. 6. In the same way, a 10dB noise is added to the received echo signals, and theimage results are shown in Fig. 7.

For the purpose of stating the superiority of theproposed methods, we calculated the contrast ratioand contrast-to-noise ratio (CNR). CR is the differ-ence between the value in background and value in cir-cle cyst region, CNR is calculated by CR divided bythe standard deviation of image intensity in back-ground region. The standard deviation is the index ofrobustness of the algorithm [23, 24]. Table 6 illustratesthe CR and CNR without noises, and Table 7describes the indexes under noise occasions.

As can be seen from Table 6, the MV and GSC per-form almost the same without noise, and the proposedIGSC performs better than MV, GSC and GSC-CF.With the help of CF, both GSC and IGSC have signif-icant improvement in CR. From the view of robust-ness, the DAS performs the best and the proposedIGSC-CF sacrifices the robustness to some extent.For CR, IGSC-CF do the best, which means the pro-posed IGSC-CF performs better than GSC-CF over-all, and the IGSC also performs better than GSC andMV overall. From Table 7 we can see that the CR andCNR of all algorithms have reduced significantlyunder the circumstance of relatively strong noises,which shows that noise has a greater impact on theimaging results of adaptive algorithms. Besides, boththe mean value in cyst region and the mean value inbackground region have a certain degree of increasingdue to noises. The proposed IGSC has higher CR thanother methods except DAS, which means that it has a


stronger ability to suppress noises than the othermethods and has the best robustness compared withother adaptive algorithms. GSC-CF shows the lowestCR, this is because CF raises the standard deviation ofthe background region and the robustness of the algo-rithm is reduced. At last, the DAS behaves the best inCR, which shows that it has the best robustness mainlydue to the simplest operation of this method. In con-trast, the adaptive algorithms are more susceptible tonoises due to the more complex matrix operationsthan the DAS, so the robustness of the algorithm isalso reduced. For standard deviation, the proposedIGSC is more robust than other adaptive algorithms


Fig. 7. Cyst phantom noise images obtained using different methods.

DASD

epth

, mm

20

25

30

35–2–4 0 42 –2 2 –2 2 –2 2 –2 2 –2 2

MV

–4 0 4

GSC

–4 0 4

GSC-CF

–4 0 4

IGSC

–4 0 4

IGSC-CF


Table 6. CR and CNR of the cyst phantom through different methods

Method Mean value in cyst region, dB

Mean value in background region, dB Standard deviation CR CNR

DAS –37.16 –17.68 6.81 19.48 2.86MV –47.21 –26.79 12.84 20.42 1.59GSC –47.21 –26.79 12.84 20.42 1.59GSC-CF –57.24 –35.35 16.42 21.89 1.33IGSC –46.21 –16.90 13.24 29.31 2.21IGSC-CF –55.89 –25.94 17.16 29.95 1.75

Table 7. CR and CNR of the cyst phantom through different methods with noise

Method Mean value in cyst region, dB

Mean value in background region, dB Standard deviation CR CNR

DAS –24.35 –14.09 6.39 10.26 1.61MV –32.58 –24.46 8.05 8.12 1.01GSC –32.35 –24.28 8.06 8.07 1.00GSC-CF –36.49 –30.31 8.68 6.18 0.71IGSC –25.41 –15.29 6.84 10.12 1.48IGSC-CF –29.74 –21.82 8.49 7.92 0.93

and the proposed IGSC-CF is more stable than theGSC-CF.

5. CONCLUSIONS

This paper proposes an improved generalized side-lobe canceller (IGSC) in ultrasound imaging system,which constructs the blocking matrix in a novel wayand projects the final weighting vector into signalspace. This method gets an adaptive blocking matrixthat increases the ability of the adaptive part to blockthe desired signal. The experimental results of thepoint targets image and the cyst phantom image showthat the main feature of the proposed method canenhance the mainlobe width, first sidelobe peak andCR compared with DAS, MV and GSC. Seeing fromstandard deviation of cyst phantom experiment, theIGSC has stronger robustness compared with other

adaptive algorithms. When IGSC is integrated withCF, not only the resolution, but also the CR areimproved as well. On the other hand, when exposed innoises occasions, the proposed IGSC has betterrobustness than MV, GSC, GSC-CF and IGSC-CF,and DAS has the best robustness compared to adaptivealgorithms because of its minimal complexity.Although the robustness of IGSC is degenerated tosome degree after combining with CF, it still performsbetter than GSC-CF, which further validates theeffectiveness and practicability of the proposedmethod.

ACKNOWLEDGMENTS

This study was supported by NSFC Grantno. 51677010.



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