Compressed Fourier-Domain Convolutional Beamforming for Sub-Nyquist Ultrasound Imaging

Efficient ultrasound (US) systems that produce high-quality images can improve current clinical diagnosis capabilities by making the imaging process much more affordable and accessible to users. The most common technique for generating B-mode US images is delay-and-sum (DAS) beamforming, where an appropriate delay is introduced to signals sampled and processed at each transducer element. However, sampling rates that are much higher than the Nyquist rate of the signal are required for high-resolution DAS beamforming, leading to large amounts of data, making remote processing of channel data impractical. Moreover, the production of US images that exhibit high resolution and good image contrast requires a large set of transducer elements, which further increases the data size. Previous works suggest methods for reduction in sampling rate and in array size. In this work, we introduce compressed Fourier domain convolutional beamforming, combining Fourier domain beamforming (FDBF), sparse convolutional beamforming, and compressed sensing methods. This allows reducing both the number of array elements and the sampling rate in each element while achieving high-resolution images. Using in vivo data, we demonstrate that the proposed method can generate B-mode images using 142 times less data than DAS. Our results pave the way toward efficient US and demonstrate that high-resolution US images can be produced using sub-Nyquist sampling in time and space.