Optimal Pre-Filtering for Linear Interpolation in Computed Tomography

Image interpolation is ubiquitous for image reconstruction in computed tomography (CT). For instance, the backprojection step of reconstruction algorithms is traditionally implemented with the simple linear interpolation model. This model is approximate but offers a good trade-off between speed and accuracy. Furthermore the implementation is natural and available on hardware graphics processing units (GPU). Approximation theory says that the image blurring induced by the triangular interpolation kernel can be compensated by enhancing the image with an all-pole recursive filter before resampling. This paper shows that the experimentally optimal pole differs from the one derived by theoretical approaches and that optimal pre-filtering leads to significant image quality improvement in term of signal to noise ratio (SNR). In fact, optimal pre-filtered linear interpolation outperforms the higher order cubic B-spline interpolation for image reconstruction in CT.