Exact Continuous Spiking Rate Inference

Many cognitive functions involve multiple brain areas simultaneously processing, distributing, and sharing information. The wide-field imaging technique can record such brain-wide activity since it offers a unique combination of simultaneous recordings from a wide field of view at a high rate. This unique combination is achieved by using a single-photon camera, which is set to capture, from a large area, neural activity-driven light emission generated by calcium indicators. Adequately analyzing this captured data requires inferring the underlying neural activity from the recorded fluorescence, a challenging mathematical problem. The challenge arises from the calcium indicator dynamics, which distort the neural dynamics as it transforms the neural activity into light emission and from the presence of noise. The wide-field setting adds a distinctive challenge. Its wide field of view recordings at a high rate constrains the spatial resolution to be limited. As a result, each fluorescence trace captured by each camera’s pixel originates from many neuron activities and not a single neuron as typical of other recording techniques. No previous, rigorously studied analytic solution exists for inferring neural activity from recorded fluorescence in the wide-field setting. Here, we phrase the inference problem arising from wide-field recordings as an optimization problem and solve it exactly. To ensure the robustness of our solution and provide a solid foundation for its application, we rigorously verify it using real data. We further suggest a novel approach for the optimization problem parameter-tuning. Beyond recovering the neural dynamics, our inference will allow future studies to retrieve accurate, correlation-based analyses of brain-wide activity.