Barankin bound: instability in certain estimation problems

Craig K. Abbey; John L. Denny

doi:10.1117/12.237815

11 April 1996 Barankin bound: instability in certain estimation problems

Craig K. Abbey, John L. Denny

Proceedings Volume 2708, Medical Imaging 1996: Physics of Medical Imaging; (1996) https://doi.org/10.1117/12.237815
Event: Medical Imaging 1996, 1996, Newport Beach, CA, United States

Abstract

Variance bounds are attractive for use in assessing quantitative system performance because they tell us how well a system can perform an estimation task without specifying a particular estimator. The most familiar of the variance bounds is the Cramer-Rao Bound also known as the Fisher-Information Bound. While suitable for many estimation problems, the Cramer-Rao Bound is often unachievable when applied to the very noisy data from imaging systems in nuclear medicine. This leads to overly optimistic estimates of system performance. As a result, some researchers have turned to the Barankin Bound as an alterative to the Cramer-Rao Bound. Our main result is that if no unbiased estimator exists, the Barankin Bound is infinite and computational methods for finding the Barankin Bound are unstable. This result is most conveniently seen in a simple 1D test problem we have developed here for demonstration purposes. The implications of this work are that caution must be used in applying the Barankin Bound to a given problem. In the absence of an unbiased estimator, this bound is misleading and other measures must be used.

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Craig K. Abbey and John L. Denny "Barankin bound: instability in certain estimation problems", Proc. SPIE 2708, Medical Imaging 1996: Physics of Medical Imaging, (11 April 1996); https://doi.org/10.1117/12.237815

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