  This paper introduces a spatio-temporal resonator model and an inference
method for detection and estimation of nearly periodic temporal phenomena in
spatio-temporal data. The model is derived as a spatial extension of a
stochastic harmonic resonator model, which can be formulated in terms of a
stochastic differential equation (SDE). The spatial structure is included by
introducing linear operators, which affect both the oscillations and damping,
and by choosing the appropriate spatial covariance structure of the driving
time-white noise process. With the choice of the linear operators as partial
differential operators, the resonator model becomes a stochastic partial
differential equation (SPDE), which is compatible with infinite-dimensional
Kalman filtering. The resulting infinite-dimensional Kalman filtering problem
allows for a computationally efficient solution as the computational cost
scales linearly with measurements in the temporal dimension. This framework is
applied to weather prediction and to physiological noise elimination in fMRI
brain data.
