Tomographic image reconstruction from incomplete projection data by the method of convex projections

Abstract

This paper proposes a method based on estimation principles for reconstructing images from their incomplete projection data. The problem of estimating missing line integrals is formulated. This method can treat general problems of reconstruction of images from incomplete projection data. It is possible to take into account a priori knowledge of an object which is represented by a nonlinear constraint. This method has lesser possibility of being affected by errors due to the digital processing and requires a lesser amount of computation since the calculation is simpler than conventional methods. This paper also proposed the use of a priori knowledge of the external shape and internal structure of an object so that the performance of the method is improved. Simulation experiments were carried out taking some cases where the projection angle is limited and an object contains an opaque part within it. The results show that the proposed method is superior to conventional methods in the quality of reconstructed images and the amount of computation required.