Efficient Bandwidth Estimation in Two-dimensional Filtered Backprojection PET Reconstruction
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A method to efficiently estimate the bandwidth of the reconstruction filter in two-dimensional Positron Emission Tomography is presented. The approach uses matrix notation to recast the convolution Filtered Backprojection equation into its equivalent Backprojected Filtering form. Results on eigendecomposition of symmetric two-dimensional circulant matrices are derived and their computational implications in making reconstruction bandwidth estimation a simple extension of standard backprojected filtering investigated to provide a computationally efficient generalized cross-validation estimator. Performance evaluations on a wide range of simulation experiments are promising. The superior performance holds at both low and high total expected emissions, pointing to the method's applicability in a wide range of radio-tracer dosage situations. The approach is easily applied 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.
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