Pulse-echo ultrasound imaging combining compressed sensing and the fast multipole method

We introduced the fast multipole method (FMM) into our concept for plane wave pulse-echo ultrasound imaging (UI) to reduce the memory consumption and the computational costs associated with the numerical solution of the underlying regularized linear inverse scattering problem (ISP). For an example of typical size and in comparison to the conventional approach, we showed that the FMM requires less than 0.25% of the memory and less than 24% of the number of complex-valued multiplications. The FMM thus enables the numerical solution of the regularized (e.g. by compressed sensing) linear ISP on standard personal computers. It significantly improves the applicability of inverse scattering strategies in practical UI.