Multi-Line Acquisition With Minimum Variance Beamforming in Medical Ultrasound Imaging

Transcription

1 IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, vol. 60, no. 12, Decemer Mult-Lne Acquston Wth Mnmum Varance Beamformng n Medcal Ultrasound Imagng Ad Ranovch, Zv Fredman, and Are Feuer, Fellow, IEEE Astract In recent years, multple-lne acquston (MLA) has een ntroduced to ncrease frame rate n cardac ultrasound medcal magng. owever, ths method nduces locklke artfacts n the mage. One approach suggested, synthetc transmt eamformng (STB), nvolves overlappng transmt eams whch are then nterpolated to remove the MLA lockng artfacts. Independently, the applcaton of mnmum varance (MV) eamformng has een suggested n the context of MLA. We demonstrate here that each approach s only a partal soluton and that comnng them provdes a etter result than applyng ether approach separately. Ths s demonstrated y usng oth smulated and real phantom data, as well as cardac data. We also show that the STB-compensated MV eamfomer outperforms sngle-lne acquston (SLA) delay-and-sum n terms of lateral resoluton. I. Introducton One of the major challenges n ultrasound today s that of ncreasng the frame rate. It s mportant for gettng hgh temporal resoluton for fast-movng ojects such as the heart n tradtonal 2-D magng and, more recently, s even more vtally mportant n 3-D ultrasound magng. The frame rate depends on the speed of sound n the medum, numer of transmt (Tx) lnes per frame, and depth of penetraton of the scanned feld of vew (FOV). A major constrant on the frame rate s the numer of transmttng lnes coverng the FOV. In standard ultrasound magng there, s a receve (Rx) lne created for each Tx lne. Together, they gve the Tx-Rx or 2-way eam profle, whch s the multplcaton of the Tx y the Rx eam profles. Ths mproves SNR y a square factor. Because the eam profles are the Fourer transforms at the far feld (or focal pont) of a fnte aperture, ther profles have a man loe and sde loes and are symmetrc when the aperture shadng s real. Ths means that the overall Tx-Rx profle also has ths symmetrc form wth a man loe and sde loes. Potentally, one can attempt to produce several Rx lnes from a wder transmt profle coverng the same lateral FOV as several Rx lnes. Ths s called mult-lne acquston (MLA), or parallel receve eamformng (PRB), and was orgnally proposed n [1] and [2]. Manuscrpt receved July 10, 2013; accepted August 7, A. Ranovch and A. Feuer are wth the Department of Electrcal Engneerng, Technon, Israel Insttute of Technology, afa, Israel (e-mal: feuer@ee.technon.ac.l). Z. Fredman s wth GE ealthcare, Tel-Avv, Israel. DOI There are several nherent prolems wth ths method. One prolem s the shftng of the peak locaton of the Tx-Rx eam profle s man loe. It happens ecause the Tx and Rx eam profles are no longer algned, hence the Tx-Rx peak wll le etween the peaks of the Tx and Rx profles. Ths s called warpng. Another prolem stems from the fact that the Tx-Rx eam profle s no longer symmetrc ths s called skewng. A thrd prolem s the gan loss ecause the energy s not concentrated at the center of the Tx-Rx profle, ut rather spread out more; hence, the peak of the Tx-Rx eam profle s lower when usng sngle-lne acquston (SLA) mode. All these effects are descred n detal n [3]. owever, the strongest effect notceale when usng MLA s the decorrelaton of the Rx lnes n the transton regon etween adjacent MLA group lnes. It creates a lateral lock-lke appearance n the mage that ntensfes as the numer of Rx lnes per Tx lne ncreases. There s also much loss of lateral resoluton n an MLA group regon ecause strong reflectors tend to smear out all over the lateral Tx regon. Ths happens ecause of the lack of focus n transmt. As the transmsson needs to cover a wder area, strong reflectors wll appear all over the man loe of the wde Tx profle and wll not e reduced y the sde loes, as n standard SLA. To compensate for these artfacts, several approaches were proposed n the patent lterature, such as snc apodzaton on transmt [4], dynamc steerng [5], [6], or ncoherent nterpolaton after RF detecton [7], [8]. The most promnent approach that utlzes coherent nterpolaton efore eamformng was suggested n [3] and [9]. Ths approach, called synthetc transmt eamformng (STB), proposes generatng the Rx lnes y lnear nterpolaton of the delayed-and-summed (DAS) Rx lnes generated from adjacent overlappng Tx lnes. We wll descre the STB method n some detal n the followng. In [3], t s shown that the STB does reduce the artfacts of MLA eamformng, especally the lock-lke appearance, ecause t hghly correlates adjacent Rx lnes, even those elongng to dfferent Tx regons. owever, t seems to suffer from loss of resoluton and contrast ecause of the nterpolatons t nvolves. Synnevag et al. [10] suggest, as one of the enefts n usng mnmum varance (MV) eamformng, or the Capon eamformer [11], n ultrasound magng s ts applcaton to MLA (or PRB, as they refer to t). They have used 4 Rx lnes per transmsson to demonstrate that the performance of MV gves good results compared wth DAS wth /$ IEEE

2 2522 IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, vol. 60, no. 12, Decemer 2013 SLA. owever, they worked n a smulated envronment of Feld II [12], whch does not emphasze the MLA-nduced artfacts n ther somewhat smplfed examples. In real ultrasound data, and especally n organs such as the heart where strong reflectons are present near weak or nonreflectng meda, these effects are much more severe. Ths can e oserved n the orgnal STB work [3], n whch the lock-lke artfacts are not seen n a smulated medum wth 2MLA (see [3, Fg. 8]), whereas n the susequent work [13], the results clearly show that real data dsplays these artfacts (see [13, Fg. 2], for example). Therefore, we feel that there s no evdence n the lterature that applyng MV n the context of MLA removes the lockng artfacts. On the contrary, to challenge ths, we have appled MV eamformng on cardac data and show that these artfacts stll reman. On the one hand, STB reduces the MLA artfacts at the prce of lateral resoluton and contrast loss; on the other, MV cannot allevate the MLA artfacts, ut has een shown to mprove resoluton and contrast (see e.g., [14] [19]). Ths realzaton prompted us to comne the two, and that s what we descre n ths paper. To demonstrate the enefts of ths comnaton over the use of each separately, we have used oth smulated Feld II data and data from real phantoms, as well as data from real cardac ultrasound magng. We wll show that MV n an MLA settng does not remove the decorrelaton lock-lke artfacts when the Rx lnes are generated from a sngle Tx. We wll demonstrate that the STB method does compensate for these artfacts, ut when comned wth MV can produce etter results than STB wth fxed apodzaton alone, and that applyng STB wth MV can produce etter results than applyng MV n an MLA settng wthout STB. In our next secton, we descre refly the known theory ehnd the STB approach and MV adaptve eamformng. Secton III provdes the detals of our smulatons, the real data set-up, and the wde Tx profle smulaton. In Secton IV, we present and dscuss the results of our experments, and Secton V contans the conclusons drawn from ths work. II. Theory A. Synthetc Transmt Beamformng (STB) The full ackground and motvaton for usng the STB technque s gven n [3]. A ref dscusson s provded here for the eneft of the reader. Ths method creates synthetc transmt eams etween the real transmtted eams. Let d, a, and λ e the Tx focal depth, aperture wdth, and central wavelength, respectvely. Then, assumng that the transmt eams sample the scanned FOV at no more than the Nyqust samplng crteron of d/aλ, y nterpolatng the sampled data on each aperture element, one can construct data as f receved from a synthetc transmt eam n any ntermedary drecton. The nterpolated data can n turn e steered and focused n the drecton of the synthetc eam. In ths way, we get a (synthetc) transmt eam algned wth the receved eam and all of the geometrc dstortons mentoned earler are allevated. More formally, assume an aperture of M elements transmts B eams transmtted nto the FOV of the ultrasound mage. For eam 1 < < B, the aperture wll e focused at pont x, wth a radal depth of d = ct 0 /2, where c s the speed of sound n the medum and t 0 s the tme of flght requred to reach depth d. Let S m (x, n) denote the sampled sgnal receved at element m after focusng at pont x, and {S m (x, n)} 1<<B,1<m<M s the set of collected sgnals. Usng samplng theory and the Nyqust assumpton, the sgnal orgnatng from an ntermedate pont x and receved at element m can e found as S m( x, n)= hx (, S ) m( x, n), (1) where h(x, ) s the nterpolaton flter. Then, the receved sgnal eamformed n the x drecton can e found y S ( x n S, ) = m( x, n τ m( x)) (2) m = hx (, S ) ( x, n τ ( x )) (3) m m m = hx (, ) S ( x, n τ ( x )) (4) m m m = hx (, S ) ( x, n), (5) where {τ m (x )} 1<m<M are the tme delays correspondng to x. The nterchange from (3) to (4) can e done f we assume that the flter h(x, ) s lnear, shft nvarant, and ndependent of m. It s nterestng to oserve that the sgnals S (x, n) are the results of transmttng n the x drecton and focusng n the x drecton n the receve mode. Clearly, for these sgnals to e non-neglgle, there must e a suffcent overlap n the transmt eams ecause only those overlappng are ncluded n the summaton over. In practce, each x s contaned n two correspondng values of and the choce for h(x, ) s [1 w, w] where w s the relatve dstance (see [3] for more detals). Ths overlap and nterpolaton s an essental factor n the cure for the lockng artfacts typcal n MLA ut, as we ponted out earler, t s also the cause of the loss of resoluton and contrast. We note that n (2), one can add a fxed apodzaton vector g = [g 1,,g M ] and the sum over m n (4) wll e modfed accordngly. B. Correlaton Analyss Although the geometrc dstorton artfacts n the transton etween MLA groups may e vsle n the mage,

3 ranovch et al.: mult-lne acquston n medcal ultrasound magng 2523 a quanttatve measure s needed to assess ts sgnfcance, and that of a measurale reducton n the artfacts after applyng STB compensaton. To assess the decorrelaton of adjacent scan lnes stemmng from MLA n the results secton, we have used the quanttatve measure ntroduced n [13]. When the two-way profles are sampled rregularly, such as wthout STB-compensated MLA, where two adjacent Rx lnes are generated from dfferent Tx eams, the correlaton wll e low. When the profles elong to the same Tx eam (same MLA group) t wll e hgher. When STB compensaton s used, the correlaton should e approxmately the same regardless of the two-way profles par examned. Usng the notaton n 1 ˆ = 1 yry [] j[] r, d (6) R j r= n d for the correlaton estmate etween adjacent Rx scan lnes, and j, wth denotng estmaton, and where y [n] s the delayed and eam-summed complex (IQ) sgnal along scan lne and depth sample n, a correlaton coeffcent can e defned n the form of C c = 2 Real( R ˆ ) Rˆ + Rˆ. C c can e calculated for the whole length of the measured sgnal (all samples) or a certan suset of length d around the Tx focal regon, for example. A C c plot of adjacent Rx lnes can e used to vew oth the correlaton wthn MLA groups and at the transton regons etween MLA groups. In addton, an ndcator of fractonal correlaton coeffcent, D c was defned n [13] as D c 1 1 j jj (7) C C X c j W Y j T c = 100, (8) 1 C X j W where j are a par of scan lnes, the set W contans all pars wthn MLA groups, the set T contans all pars n the transton regons etween MLA groups, and X and Y are the set szes, accordngly. D c s 0 when no dfference n correlaton etween MLA groups and transton regons s present, and 100 when there s full correlaton wthn the MLA groups and no correlaton etween the groups. A negatve value appears when there s more correlaton on average n the transton regons than wthn MLA groups. C. Mnmum Varance Beamformng (MV) Wth STB c The MV eamformer fnds the apodzaton weghts at each eamformed pont x so that the varance of the eamformed sgnal s mnmzed whle forcng a gan one n the x drecton. An n-depth descrpton and analyss of MV eamformer can e found n [16] and [17] and references theren. We wll refly descre t here and show how t s modfed to e appled wth STB. Consder the eamformed sgnal as n (2) wth apodzaton where M S ( x, n) = w ( x, ns ) ( x, n τ ( x )) m m 1 = w ( x, n)( S x, n), w( x, n) = [ w ( x, n),..., w ( x, n) ], 1 M m m (9) S * ( x, n) = S 1( x, n τ 1( x ) ),..., S (, ( ) ) M x n τ M x, denotes the complex conjugate and denotes the conjugate transpose (ermtan). Then, the varance of ths sgnal can e wrtten as E{ Sx (, n ) 2 } = w ( x, n) R( x, n) w( x, n), (10) where E{ } denotes the expectaton and R(x, n) = E{ S ( x, n)( S x, n) } s the spatal covarance matrx. The weght vector mnmzng ths varance can e found as the soluton of w( x, n) = argmn w R( x, n) w such that w 1 = 1, (11) w where 1 = [1,,1] T, as the sgnals across the aperture are pre-steered. The constrant guarantees a gan of 1 n the steered drecton. The soluton to ths prolem s known to e R 1 w( x n ( x, n), ) = T 1 R( x, n) 1. (12) The MV eamformer adapts to the recorded data, placng nulls n drectons where strong nterferences appear, large sde loes at low-energy lateral regons, and forcng unt gan at the drecton of arrval (DOA), whch s the steerng angle. The covarance matrx, R(x, n) s not gven and must e estmated from the data. There are several methods to do ths for the SLA set up, ut the most common one used n [16] s spatal averagng. Spatal averagng s needed ecause the sgnals nvolved are nonstatonary, and ecause sgnals from dfferent scatterers can e correlated, whch may lead to sgnal cancellaton. Ths may e avoded usng su-array averagng, as descred n [20] and [21]. In addton, to acheve speckle statstcs smlar to DAS, as descred n [22], temporal or depth averagng s also needed. The estmate of the covarance matrx wth su-array length L, and 2K + 1 temporal wndow wll e

4 2524 IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, vol. 60, no. 12, Decemer 2013 where K M L+ 1 S ( xn k) S ( x n k) Rˆ( x n ) k= K =1 l, l, l, =, (2K + 1)( M L + 1) S l (13) ( x, n) = [ Sl( x, n τl( x)),, Sl+ L 1( x, n τl+ L 1( x))]. (14) We note that the optmzaton prolem s reduced n dmenson from M to L and the steered sgnal ecomes S ( x, n)= M L+ l=1 1 w ( x, n ) Sl ( x, n ), M L + 1 (15) whch gves more weght to the central elements and causes a taperng of the full length aperture and reduces the lateral resoluton. Because the MV eamformer s senstve to steerng errors, the optmzaton n (11) can e modfed to requre that w[ n] ([ an] + d[ n]) = 1 d ε. (16) Ths means that the covarance matrx, R ˆ( x, n) s replaced y R ˆ( x, n) + εi n (12), where I s the dentty matrx, the same sze as R ˆ( x, n). We took ε, as suggested n [16] and [17], to e proportonal to the power of the oservatons, ε = tr { R ˆ ( x, n) }, (17) where tr { } s the trace operator and Δ s usually a small gan on the order of 1/100L. Because we apply the MV eamformng wth STB, we note that { S l ( xn, )} are not avalale and must e generated usng (1). Namely, ts entres are gven y S ( x, n τ ( x ))= h( x, S ) ( x, n τ ( x ). ) (18) m l m l Ths means that efore applyng the estmaton and weghtng schemes for the MV eamformng as detaled prevously, the sgnals along Rx scan lnes (dentfed y x ) should e nterpolated from adjacent measured sgnals along eams of a certan nterpolaton order. III. Methods As mentoned earler, we have conducted extensve experments usng smulated data, real phantom data, and real cardac data. In the followng, we descre n some detal the setup and nformaton pertanng to these experments. In all our experments, we have appled SLA and 4MLA. For the use of STB compensaton we have, for each transmtted eam, 8 receve eams enumerated as = 4 + l, l {±1, ±2, ±3, ±4} four of whch are common to two consecutve transmt eams. The nterpolaton flter we used s then gven y [ ] for = [ ] for = + [( hx,), h( x, + 1)] = 4 2 [ ] for = [ ] for = (19) A. Smulaton Setup and Selectng Aperture Wdth For our experment wth smulated data we used a setup smlar to the one used n the experments descred n [10] for 4MLA. Namely, an 18.5-mm aperture wth 96 elements was used, and a Gaussan pulse at the central frequency of 3.5 Mz and 85% fractonal andwdth was smulated. The transmsson was focused at 70 mm depth and no apodzaton was appled on transmsson. The returned sgnals were sampled usng 20 Mz samplng frequency. The IQ envelope of the sgnal was extracted and sampled usng lnear nterpolaton at the approprate dynamc delays. Three optons were appled wth dynamc receve eamformng: No apodzaton (rectangular wndow), ammng apodzaton, and MV adaptve apodzaton. A 20 sector was spanned wth 32 Tx lnes n SLA mode and 8 Tx lnes n 4MLA mode. The numer of Rx lnes was the same n oth cases, 32 lnes wth lne densty. An mportant pont to consder when smulatng the MLA settng s the transmsson eam pattern. To acheve effcent lateral coverage n MLA mode, a wder eam pattern s needed, as descred n [3]. It s even more mportant when usng STB compensaton, ecause the transmsson wdth should span at least twce the lateral spacng of uncompensated MLA to uphold the Nyqust crteron. In [10], the authors have used 0.25 of the aperture to generate a wder eam. We have analyzed the eam profles for ths settng and show that ths generates a eam wder than necessary to hold the Nyqust crteron n [3], and we nstead used 0.5 of the actve aperture. Although usng a wde profle on transmt helps to reduce MLA-nduced artfacts, t also causes a poorer lateral resoluton n the process; hence, usng a larger aperture helps preserve lateral resoluton. We have compared the Tx profles for the 0.25 and 0.5 apertures. Usng a wder aperture narrows the eam profle as known through the relaton F DF = λ, (20) a where a s the aperture length, F s the depth dstance to the focal spot, and D F s the profle wdth at the focus.

5 ranovch et al.: mult-lne acquston n medcal ultrasound magng 2525 Fg. 1 shows the Tx pressure felds at the focal depth of 70 mm for 0.25 and 0.5 actve apertures at the central steerng angle of 0. It s mportant to note that the transton regon from near feld to far feld for 0.25 actve aperture wth a wdth of mm s R C = a 2 /λ = a 2 f c /c = ((4.625 mm) 2 (3.5e 6 /s))/(1540e 3 mm/s) = 48.6 mm, whch s smaller than the desred focus of 70 mm. That s why the cross secton of the pressure feld at 70 mm does not show a sngle man loe for 0.25 actve aperture. At the same tme, the transton regon of 0.5 actve aperture wth a wdth of 9.25 mm s R C = mm, whch s larger than the 70 mm depth, and hence the 70 mm focus s possle and the pressure feld has a clear man loe. When lookng at the magnfed profles (see same fgure) t s clearly oserved that 0.5 actve aperture can e used to span 4 adjacent Rx lnes wth pressure no less than 3 db, and 0.25 actve aperture spans 8 adjacent Rx lnes approxmately aove 3 db whch s needed for lnear nterpolaton wth STB, meanng that the Tx profle for 0.25 actve aperture s approxmately twce as wde aove 3 db than that of 0.5 actve aperture, as expected. Usng these results, we have used 0.5 actve aperture for MLA smulatons wthout STB, and 0.25 actve aperture for STB-compensated MLA smulatons, whch s needed to mantan the Nyqust crteron for angular samplng so that the Rx data can e nterpolated from adjacent transmssons. B. Expermental Data Setup For the expermental data analyss, we have used a GE expermental readoard ultrasound system, courtesy of GE ealthcare, Israel. The system was appled to an acrylc phantom and a healthy heart of a human suject. The same transducer was used for oth trals, ut wth dfferent lne densty and receve settngs. An mm proe wth 64 elements was used. Its central frequency was 2.5 Mz, and t transmtted 1.5 perods of Gaussan pulse at 1.71 Mz frequency wth 60% andwdth. On receve, the second harmonc of 3.42 Mz was used for eamformng. Tx focus was 14 cm. The RF sgnals for each channel were sampled at 20 Mz. Afterward, the sgnals were re-sampled accordng to the calculated delays for dynamc receve usng lnear nterpolaton, ther n-phase and quadrature (IQ) components were extracted usng the lert functon, and the approprate apodzaton was appled accordng to the selected method. The delays, quadrature extracton, and apodzatons were mplemented separately usng Matla (The MathWorks Inc., Natck, MA). The FOV of the scan covered 75 wth 76 lnes, whch gave a lne densty. The maxmum depth was 16 cm. For the cardac data, the proe, ts transmtted pulse, and Tx focus were the same as those used for scannng the phantom. The RF sgnals for each channel were sampled at 50 Mz frequency, and then were demodulated, shftng them 3.42 Mz. The resultng sgnals were re-sampled at 4 Mz frequency and ther IQ components were extracted. Afterward, the IQ sgnals were re-sampled accordng to the calculated delays for dynamc receve usng lnear nterpolaton, and the approprate apodzaton was appled accordng to the selected method. The delays and apodzatons were mplemented separately usng Matla. The FOV of the scan covered 75 wth 120 lnes, whch gave a lne densty. The maxmum depth was 16 cm. For ths part of the analyss, we chose to compare the MV eamformer mages to DAS wth rectangular wndow only, ecause ths s a commonly used wndow for comparson; t preserves resoluton at the expense of contrast compared wth wndows wth taperng at the edges of the aperture, such as ammng or annng wndows. C. Smulatng a Wder Transmt Pulse for Expermental Data The RF data for the phantom and the cardac IQ data were oth otaned usng standard SLA mode, where the transmtted pulse spans a sngle receve lne laterally, as ths s what the system allowed at the tme. We had to smulate a wder transmt pulse from ths data. To smu- Fg. 1. Tx pressure felds at 0 steerng angle and 70 mm depth focus used for the smulaton. Sold lnes represent the locatons of the adjacent Rx lnes n the same MLA group, dashed lnes represent the Rx lnes also used n STB. (a) Comparson of the Tx profles at the focal depth. () Magnfcaton of the regon spanned y 8 Rx lnes used n STB mode.

6 2526 IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, vol. 60, no. 12, Decemer 2013 Fg. 2. Smulated Tx pressure felds at 0 steerng angle and 140 mm depth focus used for MLA pulse smulaton of real data. Sold lnes represent the locatons of the adjacent Rx lnes n the same MLA group, dashed lnes represent the Rx lnes also used n STB. (a) Comparson of the Tx profles at the focal depth. () Magnfcaton of the regon spanned y 8 Rx lnes used n STB mode. late an MLA scan settng, the receved sgnals of adjacent scan lnes were averaged. For an uncompensated 4MLA settng, the sgnals from groups of 4 adjacent SLA scan lnes were averaged for each element. For the STB-compensated settng, the sgnals from groups of 8 adjacent SLA scan lnes were averaged wth overlaps of 4 lnes, whch would e expected of an overlappng wde transmsson for STB acquston. Fg. 2 shows the pressure felds cross sectons at the focal depth of 14 cm, and magnfed vew on the regon of 8 adjacent Rx lnes. It can e seen that to get proper lateral coverage for STB, the data from 8 adjacent scan lnes should e averaged, ecause the profle n the regon spannng 8 scan lnes s n the range of 4 db, whereas f averagng only 4 lnes, the furthest lnes have 15 db ampltude compared wth the peak at the center of transmsson, whch may ncur alasng for 2-way profles unless the Rx profle s wde enough to compensate for t. It s suffcent to average 4 adjacent scan lnes when non-compensated MLA s used, ecause then t needs to span only 4 Rx lnes. It s mportant to note that n a real scenaro, the actual Tx profle would e wder, whch wll reduce SNR. In the oserved results n susectons IV-B and IV-c, the SNR s mproved as a result of the use of the smulated wde Tx profle, whch s narrower than real Tx profle n 4MLA eamformng. IV. Results and Dscusson As mentoned earler, we have used Feld II smulatons as well as expermental data of a phantom and heart. We wll show that oth the smulatons and real data expermental results support our clam that comnng the STB wth the MV gves superor performance to ether separately used MLA settng. A. Smulated Phantom Results We have nvestgated the effects of MLA n an envronment smlar to the heart, where strong reflectons n the heart wall are adjacent to weak reflectons of lood nsde the chamer, and ntermedate reflectons of tssue outsde the heart. For that purpose, we have smulated an ellptc rng centered along the man axs, at 0, at a depth of 69 mm. The outer permeter of the rng s defned y an ellpse wth man axs lengths 7 and 11 mm, such that x 2 /7 2 + z 2 /11 2 = 1. The nner permeter of the rng s defned y an ellpse wth man axes 5 and 9 mm, such that x 2 /5 2 + z 2 /9 2 = 1. The rng s cylndrcal, and has the same shape for all ptch (y) values. The maged regon spanned from 9 to 9 mm n azmuth (x), 5 to 5 mm n ptch, and 56 to 84 mm n depth (z). The densty of all scatterers nsde the chamer, n the rng, and outsde the rng was set to e 10 scatterers per resoluton cell of sze λ 3, where λ = c/f c s the central wavelength that matches the central frequency, f c, as suggested n [23]. The dfference n reflectance was accordng to the standard devaton (STD) of the Gaussan drawn ampltudes nsde the dfferent regons. The mean values of the Gaussan was 0 for all regons. Outsde the rng, ts STD was set to 1, nsde the nner ellpse to 0.1, and nsde the rng to 10. Between the rng and the nner ellpse (chamer) there was a dfference of 2 orders of magntude (n terms of STD). In addton, 2 pars of strong reflectors were smulated deeper than the rng for lateral resoluton measurements. The azmuthal dstance etween the reflectors was 3 mm. The frst par was at a depth of 81 mm and the second at the depth of 83 mm. The fxed ampltude of the strong reflectors was set to 500. The smulated chamer was processed usng standard SLA DAS eamformng wth rectangular and ammng wndows and MV eamformng. In addton, t was processed usng 4MLA settng wthout and wth STB compensaton. In oth cases, 0.5 of the aperture was actve n transmt. The MV eamformng was done usng a suarray of length L = 48 (half of the aperture), Δ = 1/100L, and K = 5 (11 samples, whch corresponds to 0.42 mm and 0.96 wavelengths). Fg. 3 shows a comparson of the results for the 3 eamformers usng SLA and STB-compensated and uncompensated 4MLA. The mages have a dsplay range of 60 db. Below each mage, there s a plot of the C c values, whch represent the correlaton of adjacent scan lnes as defned n (7). Grey ars represent the correlaton etween Rx lnes n the same MLA group; lack lnes represent the correlaton etween Rx lnes of dfferent MLA groups. The whole dsplayed depth was used for correlaton measurements. Notce the sharp transton seen nsde the chamer etween the rghter reflectons and the darker, weak reflectons, when no STB compensaton s appled. Ths artfact stems from the sde loes of the rng projected laterally nto the chamer. Wthout STB compensaton ths sharp transton s caused y the skewng and warpng effects of MLA. Ths s notceale even wth MV eamformng whch potentally can reduce nterference for the rng s sde loes; ecause they are too strong, t s manfested nsde the chamer as seen y the straght lnes followng the transtons etween adjacent MLA groups centered nsde

7 ranovch et al.: mult-lne acquston n medcal ultrasound magng 2527 Fg. 4. Steered responses of target ponts for DAS (rectangular and ammng wndows) and 4MLA wth MV (wth and wthout STB compensaton). Fg. 3. Smulated ventrcle. (a) DAS rectangular wndow SLA, () DAS ammng wndow SLA, (c) MV SLA (L = 48, K = 5), (d) Rect 4MLA (uncompensated), (e) ammng 4MLA (uncompensated), (f) MV 4MLA (uncompensated), (g) Rect 4MLA STB, (h) ammng 4MLA STB, () MV 4MLA STB. Correspondng C c values of adjacent Rx lnes are elow each mage. the rng and the chamer accordngly. STB compensaton reduces ths phenomenon, creatng a gradual transton etween the rng and the chamer. Ths s true for all three methods of eamformng, and especally relevant for the ammng wndow, whch has a wde Rx profle that emphaszes the MLA artfacts. Notce also the well-defned shape and edges of the rng usng STB-compensated MV eamformng compared wth SLA rectangular DAS. It can e oserved that the C c values are lower for transton etween MLA groups than nsde the MLA groups for the uncompensated MLA case. Usng STB rngs them to approxmately the same level. Ths s most notceale for ammng wndow and less notceale for MV eamformng, where the transton artfact s sutle and can e seen only n transtons etween strong and weak reflectons etween MLA groups. Fg. 4 shows a steered response through the strong reflectors at 81 mm depth. Note the narrower man loe wdth for the strong reflectors when usng MV wth 4MLA compared wth the man loe wdth of rectangular wndow SLA. In addton, notce the lower sde loes the MV eamformer has compared wth SLA rectangular DAS. We have measured the man loe wdth at 3 db level and sde loe maxmum levels of the strong reflectors. The results are gven n Tale I. From these measurements, t can e seen that MV has narrower man loes, and hence mproved lateral resoluton wth non-compensated MLA over that of SLA DAS. In addton, MV s sde loes wthout STB compensaton are lower than SLA DAS. It s also mportant to notce that applyng STB n 4MLA mode ncreased the wdth of the man loe and the sde loes levels for all three eamformers over those of ther SLA counterparts ecause of the wde Tx eam profle needed to span two adjacent MLA groups n STB-compensated mode. SLA/MLA TABLE I. Man Loe Wdth and Sde Loe Levels for Pont Reflectors. Beamformng Man loe wdth [ ] Max sde loes level [db] DAS rect SLA DAS ammng MV DAS rect MLA no STB DAS ammng MV DAS rect MLA wth STB DAS ammng MV

8 2528 IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, vol. 60, no. 12, Decemer 2013 Fg. 6. Steered responses of wre target at 88 mm depth for rectangular wndow DAS SLA and STB-compensated 4MLA generated wth rectangular DAS and MV eamformers. Fg. 5. Phantom mages wth rectangular apodzaton (DAS) and MV eamformer: (a) DAS-SLA (76 lnes), () DAS non-compensated 4MLA (19 lnes) from averaged 4 scan lnes, (c) DAS STB-compensated 4MLA from 8 averaged scan lnes, (d) MV-SLA, (e) MV Non-compensated 4MLA, (f) MV STB-compensated 4MLA. The smulatons results show that one can acheve etter separaton and lateral resoluton usng MV eamformng n an uncompensated MLA settng than SLA DAS. In addton to that, a method such as STB s needed to compensate for MLA-nduced artfacts of lock-lke sharp transtons etween adjacent MLA groups n strong reflectng meda next to weak reflectng meda. B. Phantom Analyss An acrylc phantom (405GSX LE, Gammex Inc., Mddleton, WI) was used n the frst part of the trals for assessment of lateral resoluton mprovement. It contaned needle pont reflectors emedded n an acrylc medum, as well as small leson-mmckng nclusons. Fg. 5 shows 6 mages wth DAS rectangular wndow and MV eamformer, comparng SLA, non-compensated 4MLA and STB-compensated approaches. MV eamformng was appled usng the parameters L = 32, K = 5 (11 temporal samples, 0.42 mm, 0.96 wavelengths for the second harmonc), and Δ = 1/100L. The mages have a dsplay range of 60 db. Below each mage s a correlaton plot of ts adjacent Rx lnes measured from 32 to 160 mm depth. The lock-lke artfacts n the transton etween MLA groups are clearly seen wthout STB compensaton. Wth STB compensaton, the artfacts are clearly reduced. Ths phenomenon can also e seen n the correlaton patterns of adjacent Rx lnes. The lack ars n the correlaton plots represent the correlaton etween Rx lnes of dfferent MLA groups. Wthout STB compensaton, the correlaton s lower than the correlaton of Rx lnes n the same MLA group. As opposed to the Feld II smulatons, n whch no sgnfcant transton artfacts were oserved for non-compensated MLA wth MV eamformng, Fg. 5(e) shows clear straght lnes n the transton etween adjacent MLA groups. Ths phenomenon can e also oserved n the sharp correlaton drop etween Rx lnes from adjacent MLA groups, as demonstrated y the lack ars, whch are much lower than the gray ars (we recall agan that the gray ars represent the correlaton wthn MLA groups). As expected, STB compensaton removes these transton artfacts. Overall, the wre targets have a much sharper appearance wth MV eamformng compared wth SLA DAS, even wth a much wder Tx profle than the narrow Tx profle used for SLA DAS. The cyst s shape s less oscured y the strong reflectors aove and elow t wth the MV eamformer than the DAS mages. Fg. 6 dsplays the steered responses around a wre target at 88 mm depth for DAS SLA wthout STB, and DAS and MV wth STB-compensated 4MLA. We oserve a slght deteroraton of lateral resoluton when SLA and STB-compensated MLA are compared. owever, y comparng the man loes, we see a sgnfcant resoluton enhancement when MV s appled to the STB-compensated MLA, outperformng even the SLA. Ths s especally mpressve as we recall that n the STB-compensated MLA case the Tx eam s much wder.

9 ranovch et al.: mult-lne acquston n medcal ultrasound magng 2529 SLA/MLA TABLE II. Phantom Data Man Loe Wdth and D c Values for Rectangular DAS and MV Beamformers. Beamformng Man loe ( 3 db) [ ] SLA DAS rect MV MLA no STB DAS rect MV MLA wth STB DAS rect MV D c [%] Tale II summarzes the comparson of lateral resoluton and D c values for the phantom. The D c value s a measurement for the overall relatve decorrelaton (0 to 100%) that exsts n the mage as descred n (8). It s nterestng to note that the man loe for DAS s wder when applyng STB, ecause t requres a wder Tx profle, whereas the man loe for MV s narrower after applyng STB. It s even narrower than the man loe wdth of SLA wth MV eamformng. Ths can e explaned y the fact that the wre target les n the transton etween the MLA groups, and thus t s slghtly suppressed y the Tx profles of the adjacent transmsson. When the targets le n the center of the MLA group, as n the smulaton results n susecton IV-A, the man loe wll e wder ecause of the wder Tx eam profle appled n STBcompensated MLA eamformng. Lookng at the D c values, the mprovement n terms of scan lne correlaton s seen wth STB compensaton. There s a sharp drop n D c value for DAS after STB compensaton compared wth non-compensated MLA. It s also notceale for the MV eamformer, as the D c value of 68.8 shows a very hgh decorrelaton etween MLA groups. STB compensaton rngs the D c value to the same level as SLA MV. C. Cardac Data Analyss In the second part of the trals wth real data, a healthy heart of a human suject was maged. The chosen frame shows a cross secton of the left ventrcle. Fg. 7 shows 6 mages wth DAS rectangular wndow and MV eamformer comparng SLA, non-compensated 4MLA, and STB-compensated 4MLA. MV eamformng was appled usng the parameters L = 32, K = 1 (3 temporal samples, 0.58 mm, 1.28 wavelengths for the second harmonc), and Δ = 1/100L. The mages have a dsplay range of 60 db. As can e seen from the mages, there are strong reflectons n the heart muscle next to weakly reflectng tssue and almost non-reflectng lood nsde the ventrcle and chamer. Ths causes sharp lnes etween MLA groups to appear n the transton etween the dfferent meda. The strong reflectors are smeared across the MLA group where they appear, whereas the MLA groups next to them are affected manly y the low reflectons. Ths property of the scanned medum enhances the MLA nduced artfacts, eecause now the data that s summed y the asymmetrc profles that tend toward the center of the MLA groups domnates the whole lateral range spanned y the MLA group. When comparng the MV mages to DAS, an mprovement n lateral resoluton can e seen n the form of sharper speckle appearance, although there s no contrast mprovement, and t even seems that there s a loss of contrast relatve to DAS. Ths stems from the fact that the strong reflectons n the heart wall have a smaller lateral sgnature wth MV eamformng, whereas some speckles n the lood are more emphaszed y the MV eamformer relatve to DAS ecause of the nterference cancellatons. Tale III shows the overall decorrelaton D c values for the mages n Fg. 7. The results for MV clearly show that the decorrelaton rse when usng non-compensated MLA compared wth SLA, and approxmately the same correlaton as SLA wth STB-compensated MLA. V. Conclusons In ths work, we have shown that an MV eamformer n a non-compensated MLA settng may have sharp transton artfacts, smlar to those seen n MLA settng wth fxed apodzaton eamformng. To our est knowledge, ths phenomenon of the MV eamformer was not encountered n the lterature efore and was not antcpated, ecause the MV eamformer outperforms fxed apodzaton eamformers n many cases n terms of mage qualty. Usng MV eamformng wth STB compensaton generated artfact-free mages. The scenaro that emphaszed these artfacts most was that of strong reflectons next to a weakly reflectng medum, such as the one that can e seen n the heart wall TABLE III. Cardac Data D c Values for Rectangular DAS and MV Beamformers. SLA/MLA Beamformng D c [%] SLA DAS rect 0.7 MV 1.0 MLA no STB DAS rect 42.8 MV 41.7 MLA wth STB DAS rect 1.3 MV 1.1

10 2530 IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, vol. 60, no. 12, Decemer 2013 Fg. 7. Cardac mages wth rectangular apodzaton (DAS) and MV eamformer: (a) DAS-SLA (120 lnes), () DAS non-compensated 4MLA (30 lnes), (c) DAS STB-compensated 4MLA, (d) MV-SLA (d) MV non-compensated 4MLA, (f) MV STB-compensated 4MLA. next to lood-flled chamer. It s vtally mportant to apply some sort of MLA compensaton to reduce these artfacts n a clncal settng, even wth a data-dependent eamformng such as the MV eamformer, ecause t cannot elmnate these artfacts on ts own. On the other hand, we have also demonstrated that STB compensaton n the MLA settng comes at the cost of resoluton and contrast loss. In concluson, we have shown that the MV eamformer wth STB compensaton can produce etter results than the MV eamformer wthout STB compensaton, etter than those of the STB-compensated DAS eamformer, and even etter than those of SLA DAS n terms of lateral resoluton n expermental settngs. Acknowledgments The authors thank GE ealthcare, Israel for access to ther expermental ultrasound system. References [1] D. P. Shattuck, M. D. Wenshenker, S. W. Smth, and O. T. von Ramm, Explososcan: A parallel processng technque for hgh speed ultrasound magng wth lnear phased arrays, J. Acoust. Soc. Am., vol. 75, no. 4, pp , [2] O. von Ramm, S. Smth, and J. Pavy, gh-speed ultrasound volumetrc magng system. II. Parallel processng and mage dsplay, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 38, no. 2, pp , Mar [3] T. ergum, T. Bjastad, K. Krstoffersen, and. Torp, Parallel eamformng usng synthetc transmt eams, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 2, pp , [4] L. J. Augustne, gh resoluton multlne ultrasonc eamformer, U.S. Patent , Fe. 24, [5] K. E. Thele and A. Brauch, Method and apparatus for dynamcally steerng ultrasonc phased arrays, U.S. Patent , Jun. 21, [6] T. J. unt, B. M. errck, K. K. Roertson, K. E. Thele, and M. J. Zel, Ultrasound magng system usng lne splcng and parallel receve eam formaton, U.S. Patent , Oct. 31, [7] G. L. olley and I. M. Guracar, Ultrasound mult-eam dstorton correcton system and method, U.S. Patent , Jul. 14, [8] D.-l. D. Lu, J. C. Lazeny, Z. Banjann, and B. A. Mcdermott, System and method for reducton of parallel eamformng artfacts, U.S. Patent , Sep. 10, [9] N. J. Wrght, S.. Maslak, D. J. Fnger, and A. Gee, Method and apparatus for coherent mage formaton, U.S. Patent , Aug. 11, [10] J.-F. Synnevag, A. Austeng, and S. olm, Benefts of mnmumvarance eamformng n medcal ultrasound magng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 9, pp , Sep [11] J. Capon, gh-resoluton frequency-wavenumer spectrum analyss, Proc. IEEE, vol. 57, no. 8, pp , Aug [12] J. A. Jensen, Feld: A program for smulatng ultrasound systems, Med. Bol. Eng. Comput., vol. 34, suppl. 1, pt. 1, pp , [13] T. Bjastad, S. Aase, and. Torp, The mpact of aerraton on hgh frame rate cardac B-mode magng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 1, pp , Jan [14] J. Mann and W. Walker, A constraned adaptve eamformer for medcal ultrasound: Intal results, n Proc. IEEE Ultrasoncs Symp., vol. 2, pp

11 ranovch et al.: mult-lne acquston n medcal ultrasound magng 2531 [15] M. Sasso and C. Cohen-Bacre, Medcal ultrasound magng usng the fully adaptve eamformer, n Proc. IEEE Int. Conf. Acoustcs, Speech, and Sgnal Processng, 2005, vol. 2, pp [16] J. Synnevag, A. Austeng, and S. olm, Mnmum varance adaptve eamformng appled to medcal ultrasound magng, n IEEE Ultrasoncs Symp., 2005, vol. 2, pp [17] J.-F. Synnevag, A. Austeng, and S. olm, Adaptve eamformng appled to medcal ultrasound magng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 8, pp , Aug [18] F. Vgnon and M. Burcher, Capon eamformng n medcal ultrasound magng wth focused eams, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 55, no. 3, pp , Mar [19] Z. Wang, J. L, and R. Wu, Tme-delay- and tme-reversal-ased roust capon eamformers for ultrasound magng, IEEE Trans. Med. Imagng, vol. 24, no. 10, pp , Oct [20] J. Evans, J. Johnson, and D. Sun, gh resoluton angular spectrum estmaton technques for terran scatterng analyss and angle of arrval estmaton, n Proc. 1st ASSP Workshop Spectral Estmaton, 1981, vol. 1, p. 1. [21] T.-J. Shan, M. Wax, and T. Kalath, On spatal smoothng for drecton-of-arrval estmaton of coherent sgnals, IEEE Trans. Acoust. Speech Sgnal Process., vol. 33, no. 4, pp , Aug [22] J.-F. Synnevag, C.-I. Nlsen, and S. olm, Speckle statstcs n adaptve eamformng, n Proc. IEEE Ultrasoncs Symp., 2007, pp [23] R. Wagner, M. Insana, and S. Smth, Fundamental correlaton lengths of coherent speckle n medcal ultrasonc mages, Ultrasoncs, Ferroelectrcs and Frequency Control, IEEE Transactons on, vol. 35, no. 1, pp , jan Zv Fredman receved the B.Sc. degree n physcs from the Technon-Israel Insttute of Technology, afa, n 1966, the M.Sc. degree from the Wezmann Insttute of Scence, Rehovot, n 1970, and the Ph.D. degree n sold-state physcs from the Tel Avv Unversty, Israel, n e joned the ultrasound dvson of Elscnt, afa, as a Senor Scentst n Snce 1998, ths dvson ecame part of the cardovascular actvty n GE ealthcare. s man areas of nterest nclude applcaton of advanced sgnal processng methods to ultrasonc magng n general and to eamformng n partcular. e s also workng on the development of advanced cardac applcatons. Are Feuer receved the B.Sc. and M.Sc. degrees n mechancal engneerng at the Technon-Israel Insttute of Technology, afa, Israel, n 1967 and 1973, respectvely, and the Ph.D. degree from Yale Unversty n CT n From 1967 to 1970, he was wth Technomatcs Inc., workng on the desgn of automatc machnes. From 1978 through 1983, he worked for Bell Las n network performance evaluaton. In 1983, he joned the faculty of Electrcal Engneerng at the Technon, where he s currently a professor emertus. Professor Feuer s a Fellow of the IEEE. s current research nterests nclude medcal ultrasound magng, resoluton enhancement of dgtal mages and vdeos, samplng and comned representatons of sgnals and mages, and adaptve systems n sgnal processng and control. Ad Ranovch receved hs B.Sc. degree from the Bomedcal Engneerng faculty at the Technon-Israel Insttute of Technology, afa, Israel n From 2011 to 2013, he was wth MedcVson, afa, Israel, where he was workng on the development and mprovement of computed tomography magng algorthms. e s currently pursung an M.Sc. degree n electrcal engneerng at the Technon, and workng as a senor developer at ImageGall, afa, Israel, on ultrasound magng qualty and performance mprovement. s research nterests nclude medcal sgnal and mage processng, computer vson n medcal magng, and fast mplementatons of medcal magng algorthms.