Sparse Blind Deconvolution Accounting for Time-Shift Ambiguity

Our contribution deals with blind deconvolution of sparse spike trains. More precisely, we examine the problem in the Markov chain Monte-Carlo (MCMC) framework, where the unknown spike train is modeled as a Bernoulli-Gaussian process. In this context, we point out that time-shift and scale ambiguities jeopardize the robustness of basic MCMC methods, in quite a similar manner to the label switching effect studied by Stephens (2000) in mixture model identification. Finally, we propose proper modifications of the MCMC approach, in the same spirit as Stephens´ contribution