Spatial Regularization of Functional Connectivity Using High-Dimensional Markov Random Fields

In this paper we present a new method for spatial regularization of functional connectivity maps based on Markov Random Field (MRF) priors. The high level of noise in fMRI leads to errors in functional connectivity detection algorithms. A common approach to mitigate the effects of noise is to apply spatial Gaussian smoothing, which can lead to blurring of regions beyond their actual boundaries and the loss of small connectivity regions. Recent work has suggested MRFs as an alternative spatial regularization in detection of fMRI activation in task-based paradigms. We propose to apply MRF priors to the computation of functional connectivity in resting-state fMRI. Our Markov priors are in the space of pairwise voxel connections, rather than in the original image space, resulting in a MRF whose dimension is twice that of the original image. The high dimensionality of the MRF estimation problem leads to computational challenges. We present an efficient, highly parallelized algorithm on the Graphics Processing Unit (GPU). We validate our approach on a synthetically generated example as well as real data from a resting state fMRI study.