A method for approximating the density of maximum-likelihood and maximum a posteriori estimates under a Gaussian noise model

Craig K. Abbey; Eric Clarkson; Harrison H. Barrett; Stefan P. Müller; Frank J. Rybicki

doi:10.1016/S1361-8415(98)80019-4

A method for approximating the density of maximum-likelihood and maximum a posteriori estimates under a Gaussian noise model

Craig K. Abbey, Eric Clarkson, Harrison H. Barrett, Stefan P. Müller, Frank J. Rybicki

Medical Imaging

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.

Original language	English (US)
Pages (from-to)	395-403
Number of pages	9
Journal	Medical Image Analysis
Volume	2
Issue number	4
DOIs	https://doi.org/10.1016/S1361-8415(98)80019-4
State	Published - 1998

Keywords

Cramér-Rao bound
Maximum-likelihood estimation
Quantitation

ASJC Scopus subject areas

Radiological and Ultrasound Technology
Radiology Nuclear Medicine and imaging
Computer Vision and Pattern Recognition
Health Informatics
Computer Graphics and Computer-Aided Design

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10.1016/S1361-8415(98)80019-4

Cite this

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abstract = "The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cram{\'e}r-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.",

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AU - Abbey, Craig K.

AU - Clarkson, Eric

AU - Barrett, Harrison H.

AU - Müller, Stefan P.

AU - Rybicki, Frank J.

PY - 1998

Y1 - 1998

N2 - The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.

AB - The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.

KW - Cramér-Rao bound

KW - Maximum-likelihood estimation

KW - Quantitation

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JO - Medical Image Analysis

JF - Medical Image Analysis

IS - 4

ER -

A method for approximating the density of maximum-likelihood and maximum a posteriori estimates under a Gaussian noise model

Abstract

Keywords

ASJC Scopus subject areas

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