Bias-Variance Tradeoffs Analysis Using Uniform CR Bound For a SPECT System

Abstract

The authors quantify fundamental bias-variance tradeoffs for the image reconstruction problem in radio-pharmaceutical tomography using Cramer-Rao (CR) bound analysis. The image reconstruction problem is very often biased and the classical or the unbiased CR bound on the mean square error performance of the estimator can not be used. The authors use a recently developed “uniform” CR bound which applies to biased estimators whose bias gradient satisfies a user specified length constraint. The authors demonstrate the use of the “uniform” CR bound for a simple SPECT system using several different examples.