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

摘要

Abstract: In this work we examine the accuracy of four periodicinterpolation methods - circular sampling theoreminterpolation, zero-padding interpolation, periodicspline interpolation, and linear interpolation withperiodic boundary conditions - for the task ofinterpolating additional projections in a few-viewsinogram. We generated 100 different realizations eachof two types of numerical phantom -Shepp-Logan andbreast - by randomly choosing the parameters thatspecify their constituent ellipses. Correspondingsinograms of 128 bins $MUL 1024 angles were computedanalytically and subsampled to 16, 32, 64, 128, 256,and 512 views. Each subsampled sinogram wasinterpolated to 1024 views by each of the methods underconsideration and the normalized root-mean-square-error(NRMSE) with respect to the true 1024-view sinogramcomputed. In addition, images were reconstructed fromthe interpolated sinograms by FBP and the NRMSE withrespect to the true phantom computed. Thenon-parametric signed rank test was then used to assessthe statistical significance of the pairwisedifferences in mean NRMSE among the interpolationmethods for the various conditions: phantom family(Shepp-logan or breast), number of measured views (16,32, 64, 128, 256, or 512), and endpoint (sinogram orimage). Periodic spline interpolation was found to besuperior to the others in a statistically significantway for virtually every condition.!20