Bias-resolution-variance tradeoffs for single pixel estimationtasks using the uniform Cramer-Rao bound
Kragh, T.J.; Hero, A.O., III
Nuclear Science Symposium Conference Record, 2000 IEEE
Volume 2, Issue , 2000 Page(s):15/296 - 15/298 vol.2
Digital Object Identifier 10.1109/NSSMIC.2000.950124
Summary:Previously the authors introduced the Uniform Cramer-Rao (CR)
Bound as a lower bound on the variance of biased estimators, along with
the concept of the delta-sigma tradeoff curve. For an estimator whose
variance lies an this curve, lower variance can only be achieved at the
price of increased estimator bias gradient norm, and vice versa.
However, for single pixel estimation, one can specify a variety of
different estimator point response functions that have identical
bias-gradient norm but with widely different resolution properties. This
has lead to some counter-intuitive results and interpretation
difficulties when using the Uniform CR Bound in performance studies of
imaging systems. The authors now extend this tradeoff concept by
introducing the 2nd-moment of the paint response function as a measure
of resolution for single-pixel estimation tasks. They derive an
expression for the delta-gamma-sigma tradeoff surface. This surface
specifies an “unachievable region” of estimator variance.
For estimators that lie on this surface, lower variance can only be
achieved at the price of increased bias gradient norm and/or decreased
estimator resolution. The authors present a method for computing this
surface for linear gaussian inverse problems
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