Adaptive regularization of noisy linear inverse problems  Lars Kai Hansen, Kristoffer Hougaard Madsen, Tue LehnSchiĝler
 Abstract  In 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 hyperparameter, 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.  Keywords  Bayes, regularization, inverse problems, fMRI  Type  Conference paper [With referee]  Conference  Eusipco  Year  2006  Electronic version(s)  [pdf]  BibTeX data  [bibtex]  IMM Group(s)  Intelligent Signal Processing 
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