Inferring the Spiking Rate of a Population of Neurons from Wide Field Calcium Imaging

Wide-field calcium imaging techniques allow recordings of high resolution neuronal activity across one or multiple brain regions. However, since the recordings capture light emission generated by the fluorescence of the calcium indicator, the neural activity that drives the calcium changes is masked by the calcium indicator dynamics. Here we develop and test novel methods to deconvolve the calcium traces and reveal the underlying neural spiking rate. Our methods take into account both the noise existent in the recordings and the temporal dynamics of the calcium indicator response. Our first method retrieves firing rates that are constant over discrete time bins. The size of each time bin depends on the data and is determined dynamically. Our second method retrieves the rate as a continuous function and is meant for studies that look for slow rate fluctuations rather than abrupt changes. We compare our results with those of two alternative approaches: direct deconvolution using a 9first differences9 approach, and the 9Lucy-Richardson9 image recovery method, adapted to recover temporal dynamics. We show that our methods outperform competitors on synthetic data as well as on wide-field calcium recordings in which parallel spiking recording was performed.