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Plane wave ultrasound beamforming using a nonuniform fast Fourier transform based on low rank approximation

Fourier domain beamforming of plane wave imaging (PWI) can provide fast and accurate image reconstruction. The frequency domain remapping from the uniform sampled grid to a nonuniform grid can be implemented through the nonuniform fast Fourier transform (NUFFT), which provides a fast solution for the nonuniform Fourier transform. However, the state-of-the-art NUFFTs are usually based on oversampling, discrete convolutions and fast Fourier transform (FFT) on an oversampled grid. In this paper we adopt an efficient NUFFT method based on low rank approximation. It does not require any oversampling and costs only several calculations of FFT. We study the performance of the low rank NUFFT beamforming method in PWI in terms of resolution, contrast-to-noise ratio (CNR) and computational cost. The low rank NUFFT offers an advantage in the computation speed, FWHM and CNR, comparing with the DAS and the conventional oversampling NUFFT beamforming strategies. With the low rank NUFFT Fourier domain beamforming method and its potential parallel characteristic, it is feasible to obtain high quality images with only 3 PWs in real-time.