Efficient Bandwidth Estimation in Two-dimensional Filtered Backprojection Reconstruction

TL;DR

This paper introduces a computationally efficient method for estimating the optimal bandwidth of filters in 2D Filtered Backprojection reconstruction, improving performance especially in low signal-noise scenarios.

Contribution

It presents a generalized cross-validation approach leveraging eigendecomposition of circulant matrices to estimate filter bandwidth efficiently in 2D FBP reconstruction.

Findings

Effective in low and high count scenarios

Outperforms true optimal radially symmetric filters in some cases

Applicable to elliptically symmetric filters

Abstract

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in two-dimensional Filtered Backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form, derives results on eigendecomposition of symmetric two-dimensional circulant matrices and applies them to make bandwidth estimation a computationally efficient operation within the context of standard backprojected filtering reconstruction. Performance evaluations on a wide range of simulated emission tomography experiments give promising results. The superior performance holds at both low and high total expected counts, pointing to the method's applicability even in weaker signal-noise situations. The approach also applies to the more general class of elliptically symmetric filters, with reconstruction performance often better than even that obtained with the true optimal radially symmetric filter.