Spatially unsupervised analysis of within-subject FMRI data using multiple extrapolations of 3D Ising field Partition Functions

In this paper, we present a fast numerical scheme to estimate Partition Functions (PF) of symmetric Ising fields. Our strategy is first validated on 2D Ising fields, and then applied to the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated regions and estimate the region-dependent hemodynamic filter. For any region, a specific 3D Ising field may embody spatial correlation over the hidden states of the voxels by modeling whether they are activated or not. To make spatial regularization adaptive, our approach is first based upon a classical path sampling method to approximate a small subset of reference PFs corresponding to prespecified regions. Then, we propose an extrapolation method that allows us to approximate the PFs associated to the Ising fields defined over the remaining brain regions. In comparison with preexisting approaches, our method is robust against grid inhomogeneities within the reference PFs and remains efficient irrespective of the topological configurations of the reference and test regions. Our contribution strongly alleviates the computational cost and makes spatially adaptive regularization of whole brain fMRI datasets feasible.