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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:
 35R30 Inverse problems for PDE 92C55 Biomedical imaging and signal processing, tomography