Limited-Angle Problem in Tomography and Some Related Mathematical Problems.

摘要

Consider the problem of recovering a compactly supported function f(x), x element of R/sup n/, from a collection of its one dimensional projections give by Pf(w,t) = integral of f from (x,w) = t w element of S/sup n-1/. Here S/sup n-1/ denotes the unit sphere in R/sup n/, and (x,w) denotes the usual inner product of R/sup n/. The most common applications call for n = 2 (X-ray tomography) or n = 3 (Nuclear Magnetic Resonance Imaging) and therefore we will occasionally specialize our considerations to these cases. One of the main concerns in this lecture is the effect that a limitation of the range over which the directions w can be chosen has on the quality of the reconstruction. (ERA citation 08:034962)