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On the stopping criterion for numerical methods for linear systems with additive Gaussian noise

Benoît Hamelin, Yves Goussard, Jean-Pierre Dussault

Technical Report (2009)

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Abstract

We consider the inversion of a linear operator with centered Gaussian white noise by MAPestimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationaritymeasure of this approximate solution to the mean square error of the exact solution. Thisrelation enables the formulation of a stopping test for the numerical method, met only by iterates that satisfy chosen statistical properties. We extend this development to Gibbs priorsusing a quadratic extrapolation of the log-likelihood maximized by the MAP estimator.
Subjects: 2500 Electrical and electronic engineering > 2500 Electrical and electronic engineering
2500 Electrical and electronic engineering > 2514 Digital signal processing
2950 Applied mathematics > 2960 Mathematical modelling
Department: Department of Electrical Engineering
PolyPublie URL: https://publications.polymtl.ca/2649/
Report number: EPM-RT-2009-10
Date Deposited: 06 Oct 2017 13:51
Last Modified: 11 Nov 2022 14:05
Cite in APA 7: Hamelin, B., Goussard, Y., & Dussault, J.-P. (2009). On the stopping criterion for numerical methods for linear systems with additive Gaussian noise (Technical Report n° EPM-RT-2009-10). https://publications.polymtl.ca/2649/

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