An alternative derivation and description of Smith's data sufficiency condition for exact cone-beam reconstruction

Abstract

In this paper, we present an alternative derivation and description of Smith's data sufficiency condition for exact cone-beam reconstruction. Different from Smith's condition, our condition with new description can be considered as a bridge between the approximate and exact cone-beam reconstruction. When the data sufficiency condition is satisfied, a set of parallel-beam projections can be obtained for exact 3-D reconstruction. When it is not satisfied, some directional parallel-beam projections will be missed, and only approximate reconstruction is achieved. Although our data sufficiency condition is theoretically proved to be equivalent to Smith's condition, its derivation is totally different.