Conference paper
Adaptive regularization of noisy linear inverse problems
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.
| Language: | English |
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| Publisher: | IEEE |
| Year: | 2006 |
| Pages: | 1-5 |
| Proceedings: | 2006 14th European Signal Processing Conference |
| ISSN: | 22195491 |
| Types: | Conference paper |
| ORCIDs: | Hansen, Lars Kai and Madsen, Kristoffer Hougaard |
Abstracts Bayesian modeling framework Biomedical imaging Brain models Heating Neuroimaging Three-dimensional displays adaptive regularization exponential distribution fMRI neuroimaging functional magnetic resonance imaging learning (artificial intelligence) noisy linear inverse problem optimal hyper-parameter posterior distribution prior distribution regression analysis regularization function regularization strength
