A Fourier-based formalism for 3D ultrafast imaging with diverging waves

Ultrafast imaging based on diverging wave is an active area of research in ultrasound sectorial acquisition because of its capacity of reaching high frame rate. The current state-of-the-art technique in 3D sectorial ultrafast imaging is based on diverging wave transmission and a reconstruction strategy using delay and sum (DAS). Recently, we have introduced a Fourier-based technique for the reconstruction of 2D images for sectorial acquisition. In this study, we extend our previous formalism to 3D acquisition. We demonstrate that the flexibility of the proposed formalism allows a direct use of compounding in order to improve image quality from a set of diverging waves with different virtual source positions. Simulation results show that the proposed approach provides competitive results in terms of image quality compared to the state-of-the-art DAS technique, but with a much lower computational complexity.