Fourier f-k migration for plane wave ultrasound imaging: Theoretical framework

Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wavefronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting spherical waves and creating a diffraction hyperbola. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. In order to perform efficient PWI migration while keeping high-quality images at high frame rates, we propose a migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode simultaneously and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We proved that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic signatures present in the radio-frequency data.