GraFT: Graph Filtered Temporal Dictionary Learning for Functional Neural Imaging
Optical imaging of calcium signals in the brain has enabled researchers to observe the activity of hundreds-to-thousands of individual neurons simultaneously. Current methods predominantly focus on matrix factorization and aim at detecting neurons in the imaged field-of-view, and then inferring the corresponding time-traces. The explicit locality constraints on the cell shapes additionally limits the applicability to optical imaging at different scales (i.e., dendritic or widefield data). Here we present a new method that frames the problem of isolating independent fluorescing components as a dictionary learning problem. Specifically, we focus on the time-traces, which are the main quantity used in scientific discovery, and learn the dictionary of time traces with the spatial maps acting as the presence coefficients encoding which pixels the time traces are active in. Furthermore, we present a novel graph filtering model which redefines connectivity between pixels in terms of their shared temporal activity, rather than spatial proximity. This model greatly eases the ability of our method to handle data with complex non-local spatial structure, such as dendritic imaging. We demonstrate important properties of our method, such as robustness to initialization, implicitly inferring number of neurons and simultaneously detecting different neuronal types, on both synthetic data and real data examples. Specifically, we demonstrate applications of our method to calcium imaging both at the dendritic, somatic, and widefield scales.