Statistics and Its Interface

Volume 8 (2015)

Number 3

Group analysis of fMRI data using $L_1$ and $L_2$ regularization

Pages: 379 – 390



Rosanna Overholser

Ronghui Xu (Department of Mathematics, University of California at San Diego)


In clinical studies using functional magnetic resonance imaging (fMRI), it is of interest to compare multiple subjects from different groups. We investigate the analysis of such data using random effects and non-parametric estimation of mean activation curves. The random effects modeling replaces the existing approach in fMRI literature where each curve is ‘normalized’ by a percent change. For the mean curves we consider smoothing via splines using $L_1$ or $L_2$ regularization. Our general framework allows analysis of fMRI curves that are correlated, and with correlated within curve errors. We describe a unified algorithm that uses existing software to carry out the estimation. The different regularization approaches are compared using simulation.We apply the method to an fMRI study about the effects of caffeine on the motor cortex of the brain, and discuss the limitation on currently available computing resources for carrying out such analysis on very large data sets.


correlated curves, correlated errors, functional linear model, penalized splines, semiparametric mixed-effects model, voxel level analysis

2010 Mathematics Subject Classification


Published 17 April 2015