RAFNI: Robust Analysis of Functional NeuroImages with Non-normal α-Stable Error

Functional Magnetic Resonance Imaging (fMRI) is a non-inasive neuro-imaging method that is widely used in cognitive neuroscience. It relies on the measurement of changes in the blood oxygenation level resulting from neural activity. The technique is widely used in cognitive neuroscience. fMRI is known to be contaminated by artifacts. Artifacts are known to have fat tails and are often skewed therefore modeling the error using a Gaussian distribution is a not enough. In this paper, we introduce RAFNI, an extention of AFNI, which is an fMRI open source software for the Analysis of Functional NeuroImages. We are modeling the error introduced by artifacts using α-stable distribution. We demonstrate the applicability and efficiency of stable distributions on real fMRI. We show that the α-stable estimator gives better results than the OLS-based estimators.

[1]  F. Gregory Ashby,et al.  Statistical Analysis of fMRI Data , 2011 .

[2]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[3]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[4]  R W Cox,et al.  AFNI: software for analysis and visualization of functional magnetic resonance neuroimages. , 1996, Computers and biomedical research, an international journal.

[5]  Rainer Goebel,et al.  Analysis of functional image analysis contest (FIAC) data with brainvoyager QX: From single‐subject to cortically aligned group general linear model analysis and self‐organizing group independent component analysis , 2006, Human brain mapping.

[6]  Richard L. Hudson,et al.  The Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward , 2004 .

[7]  R. Weron.  Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime , 2001, cond-mat/0103256.

[8]  N. Logothetis.  The neural basis of the blood-oxygen-level-dependent functional magnetic resonance imaging signal. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[9]  Mark W. Woolrich,et al.  Bayesian analysis of neuroimaging data in FSL , 2009, NeuroImage.

[10]  Mark W. Woolrich,et al.  Advances in functional and structural MR image analysis and implementation as FSL , 2004, NeuroImage.

[11]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[12]  S. Janson.  Stable distributions , 2011, 1112.0220.

[13]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[14]  D. Heeger,et al.  In this issue , 2002, Nature Reviews Drug Discovery.

[15]  R. H. Rimmer,et al.  Stable Distributions in Mathematica , 2005 .

[16]  S. Rachev,et al.  Stable Paretian Models in Finance , 2000 .