Extension of ultrasound Fourier slice Imaging theory to sectorial acquisition

Ultrasound image reconstruction from the echoes received by an ultrasound probe after the transmission of diverging waves is an active area of research because of its capacity to insonify at ultra-high frame rate with large regions of interest using small phased arrays as the ones used in echocardiography. Current state-of-the-art techniques are based on the emission of diverging waves and the use of delay and sum strategies applied on the received signals to reconstruct the desired image (DW/DAS). Recently, we have introduced the concept of Ultrasound Fourier Slice Imaging (UFSI) theory for the reconstruction of ultrafast imaging for linear acquisition. In this study, we extend this theory to sectorial acquisition thanks to the introduction of an explicit and invertible spatial transform. Starting from a diverging wave, we show that the direct use of UFSI theory along with the application of the proposed spatial transform allows reconstructing the insonified medium in the conventional Cartesian space. Simulations and experiments reveal the capacity of this new approach in obtaining competitive quality of ultrafast imaging when compared with the current reference method.