@CONFERENCE\{IMM2006-04417, author = "L. K. Hansen and K. H. Madsen and T. Lehn-Schi{\o}ler", title = "Adaptive regularization of noisy linear inverse problems", year = "2006", keywords = "Bayes, regularization, inverse problems, fMRI", booktitle = "Eusipco", volume = "", series = "", editor = "", publisher = "", organization = "", address = "", url = "http://www2.compute.dtu.dk/pubdb/pubs/4417-full.html", 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 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." }