Reconstruction from truncated projections using mixed extrapolations of exponential and quadratic functions

Abstract

In computer tomography (CT), truncated projections are produced due to scanning large objects with a detector that is limited in width. Applying filtered back-projection(FBP) method directly to truncated projections, the reconstructed image will contain truncation artifacts – bright rings on the boundary of region of interest (ROI). Extrapolation algorithms can be used to reduce the truncation artifacts; however extrapolations are usually double the length of the projection data; resulting in an increased calculation time. This paper introduces mixed extrapolation, which is a combination of exponential and quadratic extrapolation. It is proven that doubling the length of the projection data for the mixed extrapolation can be avoided. The projections were extrapolated according to the boundary values and their derivatives. The algorithm achieves equivalence to the extrapolation approach with negligible increased calculation time. Supplementary functions are introduced in order to simplify the calculations. These functions can be calculated prior to extrapolation process, hence the calculation time is significantly reduced. The calculation times are compared between fast extrapolation introduced in this paper and normal extrapolation with doubling the length of projection data.