  Two-photon imaging of calcium indicators allows simultaneous recording of responses of hundreds of neurons over hours and even days, but provides a relatively indirect measure of their spiking activity. Existing deconvolution algorithms attempt to recover spikes from observed imaging data, which are then commonly subjected to the same analyses that are applied to electrophysiologically recorded spikes (e.g., estimation of average firing rates, or tuning curves). Here we show, however, that in the presence of noise this approach is often heavily biased. We propose an alternative analysis that aims to estimate the underlying rate directly, by integrating over the unobserved spikes instead of committing to a single estimate of the spike train. This approach can be used to estimate average firing rates or tuning curves directly from the imaging data, and is sufficiently flexible to incorporate prior knowledge about tuning structure. We show that directly estimated rates are more accurate than those obtained from averaging of spikes estimated through deconvolution, both on simulated data and on imaging data acquired in mouse visual cortex. 
Direct Estimation of Firing Rates from Calcium Imaging Data