  Non-invasive methods to measure brain activity are important to understand
cognitive processes in the human brain. A prominent example is functional
magnetic resonance imaging (fMRI), which is a noisy measurement of a delayed
signal that depends non-linearly on the neuronal activity through the
neurovascular coupling. These characteristics make the inference of neuronal
activity from fMRI a difficult but important step in fMRI studies that require
information at the neuronal level. In this article, we address this inference
problem using a Bayesian approach where we model the latent neural activity as
a stochastic process and assume that the observed BOLD signal results from a
realistic physiological (Balloon) model. We apply a recently developed
smoothing method called APIS to efficiently sample the posterior given single
event fMRI time series. To infer neuronal signals with high likelihood for
multiple time series efficiently, a modification of the original algorithm is
introduced. We demonstrate that our adaptive procedure is able to compensate
the lacking of inputs in the model to infer the neuronal activity and that it
outperforms dramatically the standard bootstrap particle filter-smoother in
this setting. This makes the proposed procedure especially attractive to
deconvolve resting state fMRI data. To validate the method, we evaluate the
quality of the signals inferred using the timing information contained in them.
APIS obtains reliable event timing estimates based on fMRI data gathered during
a reaction time experiment with short stimuli. Hence, we show for the first
time that one can obtain accurate absolute timing of neuronal activity by
reconstructing the latent neural signal.
