  We consider the challenges in extracting stimulus-related neural dynamics
from other intrinsic processes and noise in naturalistic functional magnetic
resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC)
of low-level regional activity and neglect varying responses in individuals. We
propose a novel, data-driven approach based on low-rank plus sparse (L+S)
decomposition to isolate stimulus-driven dynamic changes in brain functional
connectivity (FC) from the background noise, by exploiting shared network
structure among subjects receiving the same naturalistic stimuli. The
time-resolved multi-subject FC matrices are modeled as a sum of a low-rank
component of correlated FC patterns across subjects, and a sparse component of
subject-specific, idiosyncratic background activities. To recover the shared
low-rank subspace, we introduce a fused version of principal component pursuit
(PCP) by adding a fusion-type penalty on the differences between the rows of
the low-rank matrix. The method improves the detection of stimulus-induced
group-level homogeneity in the FC profile while capturing inter-subject
variability. We develop an efficient algorithm via a linearized alternating
direction method of multipliers to solve the fused-PCP. Simulations show
accurate recovery by the fused-PCP even when a large fraction of FC edges are
severely corrupted. When applied to natural fMRI data, our method reveals FC
changes that were time-locked to auditory processing during movie watching,
with dynamic engagement of sensorimotor systems for speech-in-noise. It also
provides a better mapping to auditory content in the movie than ISC.
