Iowa State University - Department of Statistics
The problem of bandwidth estimation for smoothed least squares (SLS) image reconstruction - such as filtered backprojection (FBP) in Positron Emission Tomography (PET) - has been extensively studied in the statistics literature. Here, I extend the generalized cross-validation (GCV) strategy for ridge regression (Golub et al, 1979) and develop it to determine the optimal smoothing parameter in FBP reconstruction. Results on eigendecomposition of symmetric one- and two-dimensional circulant matrices are derived. Computational implications of the above in making reconstruction bandwidth estimation a simple extension of standard FBP are studied, and methodology developed. The suggested approach is evaluated using numerical simulations on a class of idealized one-dimensional generalized deconvolution problems and two-dimensional PET phantom experiments. In each case, performance measures are excellent and bandwidth selection is in real-time, proving the potential viability of this approach in a practical setting.
This research is supported in part by the National Science Foundation (NSF) CAREER DMS #0437555 and the National Institutes of Health (NIH) DC006740.