Deconvolution of sparse spike trains by iterated window maximization

A new algorithm for deconvolution of sparse spike trains is presented. To maximize a joint MAP criterion, an initial configuration is iteratively improved through a number of small changes. Computational savings are achieved by precomputing and storing two correlation functions and by employing a window strategy. The resulting formulas are simple, intuitive, and efficient. In addition, they allow much more complicated transitions than state-space solutions such as Kormylo and Mendel's (1982) single most likely replacement algorithm. This makes it possible to reduce significantly the probability that the algorithm terminates in a local maximum. Synthetic data examples are presented that support these claims.