A computationally efficient filter for reducing shot noise in low S/N data

Functional multineuron calcium imaging (fMCI) provides a useful experimental platform to simultaneously capture the spatiotemporal patterns of neuronal activity from a large cell population in situ. However, fMCI often suffers from low signal-to-noise ratios (S/N). The main factor that causes the low S/N is shot noise that arises from photon detectors. Here, we propose a new denoising procedure, termed the Okada filter, which is designed to reduce shot noise under low S/N conditions, such as fMCI. The core idea of the Okada filter is to replace the fluorescence intensity value of a given frame time with the average of two values at the preceding and following frames unless the focused value is the median among these three values. This process is iterated serially throughout a time-series vector. In fMCI data of hippocampal neurons, the Okada filter rapidly reduces background noise and significantly improves the S/N. The Okada filter is also applicable for reducing shot noise in electrophysiological data and photographs. Finally, the Okada filter can be described using a single continuous differentiable equation based on the logistic function and is thus mathematically tractable.