A propagation-backpropagation method for ultrasound tomography

Ultrasound tomography is modelled by the inverse problem of a 2D Helmholtz equation at fixed frequency with plane-wave irradiation. It is assumed that the field is measured outside the support of the unknown potential f for finitely many incident waves. Starting out from an initial guess f⁰ for f we propagate the measured field through the object f⁰ to yield a computed held whose difference to the measurements is in turn backpropagated. The backpropagated field is used to update f⁰. The propagation as well as the backpropagation are done by a finite difference marching scheme. The whole process is carried out in a single-step fashion, i.e. the updating is done immediately after backpropagating a single wave. It is very similar to the well known ART method in X-ray tomography, with the projection and backprojection step replaced by propagation and backpropagation.