Estimation performance at low SNR: predictions of the Barankin bound

Stefan P. Mueller; Marie Foley Kijewski; Christian Kappeler; Stephen C. Moore

doi:10.1117/12.208333

8 May 1995 Estimation performance at low SNR: predictions of the Barankin bound

Stefan P. Mueller, Marie Foley Kijewski, Christian Kappeler, Stephen C. Moore

Author Affiliations +

Proceedings Volume 2432, Medical Imaging 1995: Physics of Medical Imaging; (1995) https://doi.org/10.1117/12.208333
Event: Medical Imaging 1995, 1995, San Diego, CA, United States

Abstract

Nonlinear quantitation tasks can be viewed as parameter estimation problems, and task performance quantified by the variance of parameter estimates. At high signal-to-noise ratio (SNR), the Cramer-Rao bound (CRB), an absolute lower limit on the variance of any unbiased estimator, is a valid predictor of the variance. At low SNR, however, the CRB may not be achievable, i.e., the realizable parameter variances may exceed the CRB. The determination of this SNR threshold, below which efficient estimation is no longer possible, is of great importance for the optimization of quantitative imaging systems. One approach to this problem is calculating the Barankin bound (BB), which at low SNR predicts larger parameter variances than does the CRB. The computation of the BB, which requires selection of a set of test points in parameter space, presents numerical difficulties. Choosing the test points based on (Chi) ²-confidence regions mitigates the numerical problems and renders the BB calculation practical using very high precision calculations in a computer algebra system. Simulations of a nonlinear two-parameter quantitation task demonstrated that the BB can be used to determine the SNR threshold region were ML-estimation performance no longer achieves the CRB. The BB, however, does not converge at low SNR. Therefore, it cannot be used as an absolute standard of achievable performance, and detailed simulations are necessary to investigate optimized strategies for data acquisition and analysis at very low SNR.

Citation Download Citation

Stefan P. Mueller, Marie Foley Kijewski, Christian Kappeler, and Stephen C. Moore "Estimation performance at low SNR: predictions of the Barankin bound", Proc. SPIE 2432, Medical Imaging 1995: Physics of Medical Imaging, (8 May 1995); https://doi.org/10.1117/12.208333

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