Adaptive regularization of noisy linear inverse problems

Lars Kai Hansen, Kristoffer Hougaard Madsen, Tue Lehn-Schiĝler

AbstractIn the Bayesian modeling framework there is a close relation between regularization and the prior distribution over parameters. For prior distributions in the exponential family, we show that the optimal hyper-parameter, i.e., the optimal strength of regularization, satisfies a simple relation: The expectation
of the regularization function, i.e., takes the same value in the posterior and prior distribution. We present three examples: two simulations, and application in fMRI neuroimaging.
KeywordsBayes, regularization, inverse problems, fMRI
TypeConference paper [With referee]
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing

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