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NMR object boundaries: B-spline modeling and estimator performance

We give estimation error bounds and specify optimal estimators for continuous, closed boundary curves in an NMR image. The boundary is parameterized using periodic B-splines. A Cramer-Rao lower bound on mean-square-estimate error in the presence of system smoothing and Gaussian noise is derived, and the performance of maximum likelihood and penalized maximum likelihood estimators is compared to this bound. Finally, we comment on the usefulness of estimates of the boundary for providing anatomical side information in the reconstruction of functional tomographic images like those of a PET or SPECT system.