Exact Continuous Spiking Rate Inference

Many cognitive functions involve multiple brain areas that simultaneously process, distribute, and share information. Adequately capturing such distributed brain-wide activity can be achieved through wide-field imaging techniques, which enable the simultaneous recording of brain activity from a wide field of view at a high rate. However, the wide field of view imposes limitations on the spatial resolution. As a result, each fluorescence trace captured by each camera pixel in this wide-field setup reflects the combined calcium-generated fluorescence of many neurons activities. Additionally, calcium indicators, which convert neural activity into light emissions, distort the neural activity by their dynamics. The inherent noise in recordings, combined with the low spatial resolution and the distorted dynamics by the calcium indicators, makes it a particularly challenging mathematical problem to infer underlying neural activity from recorded fluorescence in wide-field imaging. To date, there has not been a rigorously studied analytic solution for this inference problem in the wide-field setting. In this work, we phrase the inference problem that arises from wide-field recordings as an optimization problem and provide an analytic solution to it. To ensure the robustness of our findings and establish a solid foundation for application, we rigorously verify our solution using real data. Furthermore, we propose a novel approach for the optimization problem parameter-tuning. Beyond recovering the neural dynamics, our inference method will enable future studies to conduct more accurate, correlation-based analyses of brain-wide activity.