MATHEMATICAL QUESTIONS OF EMISSION TOMOGRAPHY OF INHOMOGENEOUS MEDIA - THEORY AND NUMERICAL METHODS

摘要

The following problem of emission tomography with scattering is considered. There is a source distribution for particles (or radiation) in a bounded domain M. The particles move in M according to a Hamiltonian. A medium is contained in M which can absorb and scatter the particles. It is assumed that the energy of a particle does not change in scatterings; in other words the scattering is elastic and media atoms are unmoving and much more harder than the particles. The Hamiltonian, absorption and scattering diagram are known. One has to recover the source distribution from the emitting flow through the boundary of M. The uniqueness theorem and stability estimate are obtained under some assumptions on the Hamiltonian, absorption and scattering diagram. The main assumption is formulated in terms of some connection that is constructed according to the Hamiltonian. Some numerical method is offered.