Direct computation of harmonic moments for tomographic reconstruction

Abstract

A novel algorithm to compute harmonic moments of a density function from its projections is presented for tomographic reconstruction. For projection p(r, θ), we define harmonic moments of projection by ∫π0∫∞−∞p(r,θ)(reiθ)ndrdθ and show that it coincides with the harmonic moments of the density function except a constant. Furthermore, we show that the harmonic moment of projection of order ncan be exactly computed by using n+ 1 projection directions, which leads to an efficient algorithm to reconstruct the vertices of a polygon from projections.