X2 isocontours: predictors of performance in nonlinear estimation tasks at low SNR

Stefan P. Mueller; Frank J. Rybicki; Craig K. Abbey; Stephen C. Moore; Marie Foley Kijewski

doi:10.1117/12.274107

25 April 1997 X2 isocontours: predictors of performance in nonlinear estimation tasks at low SNR

Stefan P. Mueller, Frank J. Rybicki, Craig K. Abbey, Stephen C. Moore, Marie Foley Kijewski

Author Affiliations +

Proceedings Volume 3034, Medical Imaging 1997: Image Processing; (1997) https://doi.org/10.1117/12.274107
Event: Medical Imaging 1997, 1997, Newport Beach, CA, United States

Abstract

Maximum-likelihood (ML) estimation is an established paradigm for the assessment of imaging system performance in nonlinear quantitation tasks. At high signal-to-noise ratio (SNR), maximum likelihood estimates are asymptotically normally distributed, unbiased, and efficient, thereby attaining the Cramer-Rao bound (CRB). Therefore, at high SNR the CRB is useful as a predictor of estimation performance. At low SNR, however, the achievable parameter variances are substantially larger than the CRB and the estimates are no longer Gaussian distributed. This implies that intervals derived from the CRB or other tighter symmetric variance bounds do not contain the appropriate fraction of the estimates expected from the normal distribution. We have derived the mathematical relationship between (chi) ² and the expected probability density of the ML-estimates, and have justified the use of (chi) ²-isocontours to describe the estimates. We validates this approach by simulation of spherical objects imaged with a Gaussian PSF. The parameters, activity concentration and size, were estimated simultaneously by ML, and variances and covariances calculated over 1000 replications per condition. At low SNR, where the CRB is no longer achieved, (chi) ²-isocontours provide a robust predictor of the distribution of the ML- estimates. At high SNR, the (chi) ²-isocontours approach asymptotically the contour derived from the Fisher information matrix.

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Stefan P. Mueller, Frank J. Rybicki, Craig K. Abbey, Stephen C. Moore, and Marie Foley Kijewski "X2 isocontours: predictors of performance in nonlinear estimation tasks at low SNR", Proc. SPIE 3034, Medical Imaging 1997: Image Processing, (25 April 1997); https://doi.org/10.1117/12.274107

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