Synthetic aperture transmit sequences can be used in medical ultrasound to increase image resolution without sacrificing frame rate. However, beamforming the large amount of collected data from the sequence is computationally costly for traditional delay-and-sum (DAS) beamforming, and the sequence has low SNR and limited penetration depth. These problems are especially apparent for deeper targets, when more data is collected and the low SNR results in poor visibility. Transmitting a chirp coded excitation can greatly improve the SNR and penetration depth, at the cost of some computational efficiency during beamforming, although frequency-domain beamforming can reduce the computations required for image reconstruction. This paper presents the chirp scaling algorithm (CSA), a frequency-domain beamformer originally developed for radar, that avoids the computational costs of interpolation and can account inherently for chirp excitation pulse compression for chirp transmit sequences. First, theory is presented to derive the beamforming steps for ultrasound multistatic synthetic aperture data. Then, comparative imaging with DAS and the range-Doppler algorithm (RDA, a related frequency-domain beamformer) are shown via Field II simulations and in vitro with a CIRS phantom imaged using a Verasonics Vantage 256 system. The results demonstrate similar lateral sidelobe levels (averaging) within 6 dB and resolution within 0.1 mm for the three beamformers for all sources of data. However, CSA has consistently faster median baseline runtime (at least 2.6 times faster compared to DAS), and a significant 6.5-fold runtime decrease from via precomputation, which reduces its runtime below even that of RDA. Together, our results demonstrate the feasibility for CSA to generate high-quality ultrasound images, particularly for resource-constrained devices.
NielsenMBCantisaniVSidhuPSBadeaRBatkoTCarlsenJ, et al. The use of handheld ultrasound devices - an EFSUMB position paper. Ultraschall Med. 2019;40(1):30-9.
LeMTVoigtLNathansonRMawAMJohnsonGDancelR, et al. Comparison of four handheld point-of-care ultrasound devices by expert users. Ultrasound J. 2022;14(1):27.
NikolovSIKortbekJJensenJA.Practical applications of synthetic aperture imaging. In: Proceedings of 2010 IEEE International Ultrasonics Symposium (IUS), 2010, pp. 350-8.
6.
JakovljevicMMichaelidesRBiondiEHyunDZebkerHADahlJJ.Adaptation of range-doppler algorithm for efficient beamforming of monostatic and multistatic ultrasound signals. IEEE Trans Ultrason Ferroelectr Freq Control. 2022;69(11):3165-78.
7.
KortbekJJensenJAGammelmarkKL.P2B-1 synthetic aperture focusing applied to imaging using a rotating single element transducer. In Proc. 2007 IEEE Ultrason. Symp, 2007, pp. 1504-7.
8.
AndresenHNikolovSIJensenJA.Synthetic aperture focusing for a single-element transducer undergoing helical motion. IEEE Trans Ultrason Ferroelectr Freq Control. 2011;58(5):935-43.
9.
van den HeuvelTLAGrahamDJSmithKJde KorteCLNeashamJA.Development of a low-cost medical ultrasound scanner using a monostatic synthetic aperture. IEEE Trans Biomed Circuits Syst. 2017;11(4):849-57.
10.
XuKKimYBoctorEM, et al. Enabling low-cost point-of-care ultrasound imaging system using single element transducer and delta configuration actuator. In: FeiBLinteCA eds. Med. Imag. 2019: Imag.-Guided Proced., Rob. Interventions, and Model. San Diego, California, USA. Vol. 10951. International Society for Optics and Photonics, SPIE; 2019, p.109510W.
11.
ToffaliESpairaniERamalliA, et al. Improving the quality of monostatic synthetic-aperture ultrasound imaging through deep-learning-based beamforming. In: Proc. 2022 IEEE Int. Ultrason. Symp. (IUS), 2022, pp. 1-4.
GarciaDLe TarnecLMuthSMontagnonEPoréeJCloutierG.Stolt’s f-k migration for plane wave ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2013;60(9):1853-67.
14.
HunterAJDrinkwaterBWWilcoxPD.The wavenumber algorithm for full-matrix imaging using an ultrasonic array. IEEE Trans Ultrason Ferroelectr Freq Control. 2008;55(11):2450-62.
15.
MoghimiradEVillagomez HoyosCAMahloojifarAMohammadzadeh AslBJensenJA.Synthetic aperture ultrasound Fourier beamformation using virtual sources. IEEE Trans Ultrason Ferroelectr Freq Control. 2016;63(12):2018-30.
16.
VosHJvan NeerPLMJMotaMMVerweijMDvan der SteenAFWVolkerAWF. F– k domain imaging for synthetic aperture sequential beamforming. IEEE Trans Ultrason Ferroelectr Freq Control. 2016;63(1):60-71.
17.
AlvarezYRodriguez-VaqueiroYGonzalez-ValdesBMantzavinosSRappaportCMLas-HerasF, et al. Fourier-based imaging for multistatic radar systems. IEEE Trans Microw Theory Tech. 2014;62(8):1798-810.
18.
KangJKimPYoonCYooYSongTK.Efficient parallel-beamforming based on shared FIFO for ultra-compact ultrasound imaging systems. IEEE Access. 2020;8:80490-501.
19.
MisaridisTJensenJA.Use of modulated excitation signals in medical ultrasound. Part I: Basic concepts and expected benefits. IEEE Trans Ultrason Ferroelectr Freq Control. 2005;52(2):177-91.
20.
MisaridisTJensenJA.Use of modulated excitation signals in medical ultrasound. Part II: Design and performance for medical imaging applications. IEEE Trans Ultrason Ferroelectr Freq Control. 2005;52(2):192-207.
21.
ZhuangLLDahlJZebkerHJakovljevicM.Rapid beamforming of ultrasound chirp signals in frequency domain using the chirp scaling algorithm. J Acoust Soc Am. 2023;153(3_supplement):A242.
22.
ZhuangLDahlJZebkerH, et al. Applying the chirp scaling algorithm for efficient beamforming of ultrasound images. In: Proc. 2022 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), 2022, pp. 3011-4.
23.
RaneyRKRungeHBamlerRCummingIGWongFH.Precision SAR processing using chirp scaling. IEEE Trans Geosci Remote Sens. 1994;32(4):786-99.
24.
CummingIBennettJ.Digital processing of Seasat SAR data. In: Proc. 1979 IEEE Int. Conf. Acoust., Speech, and Signal Process., 1979, volume 4. pp. 710-8.
25.
CummingIGWongFG.Digital Processing of Synthetic Aperture Radar. Artech House;2005.
26.
KungHT.Fast evaluation and interpolation. Pittsburgh, PA: Carnegie-Mellon University; 1973.
27.
CooleyJWTukeyJW.An algorithm for the machine calculation of complex Fourier series. Math Comput. 1965;19:297-301.
28.
JensenJA.Field: A program for simulating ultrasound systems. In: Med. and Biol. Eng. and Comput., Proc. 10th Nordic-Baltic Conf. Biomed. Imag., 1996, vol. 34, pp. 351-3.
29.
Rodriguez-MolaresARindalOMHD’hoogeJMasoySEAustengALediju BellMA, et al. The generalized contrast-to-noise ratio: A formal definition for lesion detectability. IEEE Trans Ultrason Ferroelectr Freq Control. 2020;67(4):745-59.
CruzHVéstiasMMonteiroJNetoHDuarteRP.A review of synthetic-aperture radar image formation algorithms and implementations: A computational perspective. Remote Sens. 2022;14(5):1258.
32.
DorauschEMGSwistDHerzogM, et al. Adoption and evaluation of a multistatic Fourier-based synthetic aperture radar method for ultrasound imaging. In: BoehmCBottenusN eds. Medical Imaging 2023: Ultrasonic Imaging and Tomography. San Diego, California, USA. Vol. 12470. International society for optics and photonics, SPIE; 2023, p.124700U.
33.
KimPKangJLeeJ, et al. A new nonlinear zone-based beamforming method for point-of-care ultrasound: algorithms and implementation. In: Proceedings of 2014 IEEE International Ultrasonics Symposium (IUS), 2014, pp. 2137-40.
34.
KimPKangJSongTK.A pseudo-dynamic delay calculation using optimal zone segmentation for ultra-compact ultrasound imaging systems. Electronics. 2019;8(2):242.
35.
MisaridisTJensenJA.Use of modulated excitation signals in medical ultrasound. Part III: High frame rate imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2005;52(2):208-19.
36.
ZauggECLongDG.Generalized frequency-domain SAR processing. IEEE Trans Geosci Remote Sens. 2009;47(11):3761-73.
37.
MoreiraAHuangY.Airborne SAR processing of highly squinted data using a chirp scaling approach with integrated motion compensation. IEEE Trans Geosci Remote Sens. 1994;32(5):1029-40.
38.
MoreiraAMittermayerJScheiberR.Extended chirp scaling algorithm for air- and spaceborne SAR data processing in stripmap and ScanSAR imaging modes. IEEE Trans Geosci Remote Sens. 1996;34(5):1123-36.
39.
DavidsonGWCummingIGItoMR.A chirp scaling approach for processing squint mode SAR data. IEEE Trans Aerosp Electron Syst. 1996;32(1):121-33.
40.
WangKLiuX.Quartic-phase algorithm for highly squinted SAR data processing. IEEE Geosci Remote Sens Lett. 2007;4(2):246-50.
41.
AmeinASSoraghanJJ.A new chirp scaling algorithm based on the fractional Fourier transform. IEEE Signal Process Lett. 2005;12(10):705-8.
42.
ChenXYiTHeFHeZDongZ.An improved generalized chirp scaling algorithm based on Lagrange inversion theorem for high-resolution low frequency synthetic aperture radar imaging. Remote Sens. 2019;11(16):1874.
43.
BilodeauMQuaegebeurNBerryAMassonP.Correlation-based ultrasound imaging of strong reflectors with phase coherence filtering. Ultrasonics. 2022;119:106631.
44.
AliRBrevettTHyunDBricksonLLDahlJJ.Distributed aberration correction techniques based on tomographic sound speed estimates. IEEE Trans Ultrason Ferroelectr Freq Control. 2022;69(5):1714-26.
45.
CummingIWongFRaneyK.A SAR processing algorithm with no interpolation. In: Proceedings of 1992 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), 1992, volume 1. pp. 376-9.
46.
RaneyR.A new and fundamental Fourier transform pair. In: Proceedings of 1992 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), 1992, volume 1, pp. 106-7.
47.
ChenCHansenHHGHendriksGAGMMenssenJLuJYde KorteCL.Point spread function formation in plane-wave imaging: A theoretical approximation in Fourier migration. IEEE Trans Ultrason Ferroelectr Freq Control. 2020;67(2):296-307.
48.
RungeHBamlerR.A novel high precision SAR focussing algorithm based on chirp scaling. In: Proceedings of 1992 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), 1992, volume 1, pp. 372-5.
49.
ChenKS.Principles of Synthetic Aperture Radar Imaging: A System Simulation Approach. CRC Press; 2015.
50.
HawkinsDW.Synthetic Aperture Imaging Algorithms: With application to wide bandwidth sonar. PhD Thesis, Univ. of Canterbury, Christchurch, New Zealand, 1996.
51.
HawkinsDGoughP.An accelerated chirp scaling algorithm for synthetic aperture imaging. In: Proceedings of 1997 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), 1997, volume 1, pp. 471-3.
