Tomography and the Radon transform over finite fields,   Eric Grinberg,   University of Massachusetts, Boston,  Mon, 9 May, 2011,   10:00 a.m. C-236


A basic model of computed tomography and other imaging modalities entails recovering a function from its integrals over lines or planes, or other varieties. This is usually done over the continuum of real numbers, but finite analogs may be of interest in both pure, applied and computational settings. We replace the real line by a finite field a consider the uniqueness problem (when is a function determined by a collection of integrals over lines or planes, etc.), the range characterization (when is a line function the integral of a point function), and especially the admissibility problem, which asks for a classification of minimal collections of lines, planes, etc., whose corresponding integrals suffice to determine functions. This problem, pioneered by I.M.Gelfand in the 1950s, overlaps several parts of mathematics.