Comparison of angular interpolation approaches in few-view tomography using statistical hypothesis testing

Abstract

In this work we examine the accuracy of four periodic interpolation methods--circular sampling theorem interpolation, zero-padding interpolation, periodic spline interpolation, and linear interpolation with periodic boundary conditions--for the task of interpolating additional projections in a few-view sinogram. We generated 100 different realizations each of two types of numerical phantom--Shepp-Logan and breast--by randomly choosing the parameters that specify their constituent ellipses. Corresponding sinograms of 128 bins X 1024 angles were computed analytically and subsampled to 16, 32, 64, 128, 256, and 512 views. Each subsampled sinogram was interpolated to 1024 views by each of the methods under consideration and the normalized root-mean-square-error (NRMSE) with respect to the true 1024-view sinogram computed. In addition, images were reconstructed from the interpolated sinograms by FBP and the NRMSE with respect to the true phantom computed. The non-parametric signed rank test was then used to assess the statistical significance of the pairwise differences in mean NRMSE among the interpolation methods for the various conditions: phantom family (Shepp-logan or breast), number of measured views (16, 32, 64, 128, 256, or 512), and endpoint (sinogram or image). Periodic spline interpolation was found to be superior to the others in a statistically significant way for virtually every condition.