Fourier Beamforming of Ultrasound Signals From Chirp Transmits Using the Chirp Scaling Algorithm

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.