Efficient Bandwidth Estimation in Two-dimensional Filtered Backprojection Reconstruction
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A method to efficiently estimate the bandwidth of the reconstruction filter in two-dimensional Filtered Backprojection is presented. The approach uses matrix notation to write the reconstruction equation in 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 experiments simulated emission tomography settings are promising. The superior performance holds at both low and high total expected counts, pointing to the method's applicability even in the case of weaker signal-noise 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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