Multi-Dimensional Acoustical Tomography by Incomplete Data

Abstract

The reconstruction problem of three-dimensional biological structures, as determined by the purposes of medical tomography, faces a number of basic and technical difficulties. The main difficulties are the following. Firstly, biological medium in real conditions appears to be inhomogeneous with regard to three components simultaneously (phase velocity c( r ), density ρ(r) and amplitude coefficient of absorption α(r, ω)). Each of these components should be reconstructed. Secondly, for the majority of problems the inhomogeneities of medium belong to a class of strong scatterers, i.e. they bring in an essential distortion to an internal field in comparison with an incident field. Thirdly, some spatial-geometrical positions of sources and receivers might be unavailable in experiment. Absence of these positions leads to incompleteness of the scattering data.