  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.
