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Spatial-temporal plane-wave image formation with Sparse Uniform ReSampling

Ultrafast imaging based on coherent plane-wave compounding improves image quality and allows for much faster acquisition. This method, however, is limited by severe computational loads stemming from delay-and-sum beamforming (DAS BF) that creates a major bottleneck for real-time implementation. Spatial-temporal (ST) processing yields the entire frame without a need for DAS BF of each image line. First, the 2D Fourier transform (FT) of the non-delayed aperture data yields the nonuniform samples of 2D Fourier spectrum of the underlying image. The points of the non-uniform grid are defined by the relationship between the temporal frequency of the aperture data and the spatial frequencies of the image. The core step is then to remap the spectrum of the image to a uniform grid prior to applying an inverse 2D FT yielding the image in space. We propose implementing this interpolation step using the recently developed Sparse Uniform ReSampling (SPURS) algorithm which results in small approximation error and low computational cost.