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Entropy 2015, 17(5), 2573-2589; doi:10.3390/e17052573

Source Localization by Entropic Inference and Backward Renormalization Group Priors

Departamento de Física Geral, Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo-SP, Brazil
Academic Editor: Raúl Alcaraz Martínez
Received: 3 February 2015 / Revised: 13 April 2015 / Accepted: 16 April 2015 / Published: 23 April 2015
(This article belongs to the Section Information Theory)
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Abstract

A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG) transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG) priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI) experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible. View Full-Text
Keywords: inverse problems; maximum entropy; prior distribution; renormalization group; fMRI; EEG inverse problems; maximum entropy; prior distribution; renormalization group; fMRI; EEG
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Caticha, N. Source Localization by Entropic Inference and Backward Renormalization Group Priors. Entropy 2015, 17, 2573-2589.

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