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A propagation-backpropagation method for ultrasound tomography. (English) Zbl 0839.35146
Summary: 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 f 0 for f we propagate the measured field through the object f 0 to yield a computed field whose difference to the measurements is in turn backpropagated. The backpropagated field is used to update f 0 . 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.

MSC:
35R30Inverse problems for PDE
92C55Biomedical imaging and signal processing, tomography