Fast online deconvolution of calcium imaging data

Fluorescent calcium indicators are a popular means for observing the spiking activity of large neuronal populations, but extracting the activity of each neuron from raw fluorescence calcium imaging data is a nontrivial problem. We present a fast online active set method to solve this sparse non-negative deconvolution problem. Importantly, the algorithm 3progresses through each time series sequentially from beginning to end, thus enabling real-time online estimation of neural activity during the imaging session. Our algorithm is a generalization of the pool adjacent violators algorithm (PAVA) for isotonic regression and inherits its linear-time computational complexity. We gain remarkable increases in processing speed: more than one order of magnitude compared to currently employed state of the art convex solvers relying on interior point methods. Unlike these approaches, our method can exploit warm starts; therefore optimizing model hyperparameters only requires a handful of passes through the data. A minor modification can further improve the quality of activity inference by imposing a constraint on the minimum spike size. The algorithm enables real-time simultaneous deconvolution of O(105) traces of whole-brain larval zebrafish imaging data on a laptop.Author summary: Calcium imaging methods enable simultaneous measurement of the activity of thousands of neighboring neurons, but come with major caveats: the slow decay of the fluorescence signal compared to the time course of the underlying neural activity, limitations in signal quality, and the large scale of the data all complicate the goal of efficiently extracting accurate estimates of neural activity from the observed video data. Further, current activity extraction methods are typically applied to imaging data after the experiment is complete. However, in many cases we would prefer to run closed-loop experiments—analyzing data on-the-fly to guide the next experimental steps or to control feedback—and this requires new methods for accurate real-time processing. Here we present a fast activity extraction algorithm addressing both issues. Our approach follows previous work in casting the activity extraction problem as a sparse nonnegative deconvolution problem. To solve this optimization problem, we introduce a new algorithm that is an order of magnitude faster than previous methods, and progresses through the data sequentially from beginning to end, thus enabling, in principle, real-time online estimation of neural activity during the imaging session. This computational advance thus opens the door to new closed-loop experiments.