Sparse deconvolution: Comparison of statistical and deterministic approaches

Sparse spike train deconvolution is a classical inverse problem which gave rise to many deterministic and stochastic algorithms since the mid-80's. In the past decade, sparse approximation has been an intensive field of research, leading to the development of a number of algorithms including greedy strategies and convex relaxation methods. Spike train deconvolution can be seen as a specific sparse approximation problem, where the observation matrix contains highly correlated columns and where the focus is set on the exact recovery of the spike locations. The objective of this paper is to evaluate the performance of algorithms proposed in both fields in terms of detection statistics, with Monte-Carlo simulations of spike deconvolution problems.