Coprime Sampling and Arrays in One and Multiple Dimensions

Vaidyanathan, P.P.; Pal, Piya

doi:10.1007/978-1-4614-4145-8_5

Cited by 2 publications

(1 citation statement)

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“…This type of sparse array has been studied extensively in the literature [52], [53], [54], [55], [56], [57], [58]. Let N 1 < N 2 be co-prime integers, i.e., their greatest common divisor (gcd) is 1.…”

Section: B Co-prime Arraymentioning

confidence: 99%

Sparse Doppler Sensing Based on Nested Arrays

Cohen

Eldar

2018

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Spectral Doppler ultrasound imaging allows visualizing blood flow by estimating its velocity distribution over time. Duplex ultrasound is a modality in which an ultrasound system is used for displaying simultaneously both B-mode images and spectral Doppler data. In B-mode imaging short wide-band pulses are used to achieve sufficient spatial resolution in the images. In contrast, for Doppler imaging, narrow-band pulses are preferred in order to attain increased spectral resolution. Thus, the acquisition time must be shared between the two sequences. In this work, we propose a non-uniform slow-time transmission scheme for spectral Doppler, based on nested arrays, which reduces the number of pulses needed for accurate spectrum recovery. We derive the minimal number of Doppler emissions needed, using this approach, for perfect reconstruction of the blood spectrum in a noise-free environment. Next, we provide two spectrum recovery techniques which achieve this minimal number. The first method performs efficient recovery based on the fast Fourier transform. The second allows for continuous recovery of the Doppler frequencies, thus avoiding off-grid error leakage, at the expense of increased complexity. The performance of the techniques is evaluated using realistic Field II simulations as well as in vivo measurements, producing accurate spectrograms of the blood velocities using a significant reduced number of transmissions. The time gained, where no Doppler pulses are sent, can be used to enable the display of both blood velocities and high quality B-mode images at a high frame rate.

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