Large scale Lasso with windowed active set for convolutional spike sorting

Spike sorting is a fundamental preprocessing step in neuroscience that is central to access simultaneous but distinct neuronal activities and therefore to better understand the animal or even human brain. But numerical complexity limits studies that require processing large scale datasets in terms of number of electrodes, neurons, spikes and length of the recorded signals. We propose in this work a novel active set algorithm aimed at solving the Lasso for a classical convolutional model. Our algorithm can be implemented efficiently on parallel architecture and has a linear complexity w.r.t. the temporal dimensionality which ensures scaling and will open the door to online spike sorting. We provide theoretical results about the complexity of the algorithm and illustrate it in numerical experiments along with results about the accuracy of the spike recovery and robustness to the regularization parameter.