Using Few Radon Projections to Recover 3-D NMR Spectrum

Abstract

Given a regular binary function f on R² with compact support D, we use translation to form a new binary function g from f so that the image representation of g (x, y) is made up of non-overlapping copies of D. Thus, g is made up of discrete entities that are surrounded by regions of space. We devise a procedure that can determine the translation parameters using a minimum number of Radon projections  g of g . This model is a mathematical abstraction of an application of the Radon transform in Spectroscopy.
Keywords: Radon transforms, transformation of an image, Back projection.