An information-theoretic criterion for intrasubject alignment of FMRI time series: motion corrected independent component analysis

A three-dimensional image registration method for motion correction of functional magnetic resonance imaging (fMRI) time-series, based on independent component analysis (ICA), is described. We argue that movement during fMRI data acquisition results in a simultaneous increase in the joint entropy of the observed time-series and a decrease in the joint entropy of a nonlinear function of the derived spatially independent components calculated by ICA. We propose this entropy difference as a reliable criterion for motion correction and refer to a method that maximizes this as motion-corrected ICA (MCICA). Specifically, a given motion-corrupted volume may be corrected by determining the linear combination of spatial transformations of the motion-corrupted volume that maximizes the proposed criterion. In essence, MCICA consists of designing an adaptive spatial resampling filter which maintains maximum temporal independence among the recovered components. In contrast with conventional registration methods, MCICA does not require registration of motion-corrupted volumes to a single reference volume which can introduce artifacts because corrections are applied without accounting for variability due to the task-related activation. Simulations demonstrate that MCICA is robust to activation level, additive noise, random motion in the reference volumes and the exact number of independent components extracted. When the method was applied to real data with minimal estimated motion, the method had little effect and, hence, did not introduce spurious changes in the data. However, in a data series from a motor fMRI experiment with larger motion, preprocessing the data with the proposed method resulted in the emergence of activation in primary motor and supplementary motor cortices. Although mutual information (MI) was not explicitly optimized, the MI between all subsequent volumes and the first one was consistently increased for all volumes after preprocessing the data with MCICA. We suggest MCICA represents a robust and reliable method for preprocessing of fMRI time-series corrupted with motion.