Simulation-based methods for blind maximum-likelihood filter identification
Signal Processing - Special issue on blind source separation and multichannel deconvolution
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
IEEE Transactions on Signal Processing
Unsupervised deconvolution of sparse spike trains using stochasticapproximation
IEEE Transactions on Signal Processing
Improved maximum-likelihood detection and estimation of Bernoulli - Gaussian processes (Corresp.)
IEEE Transactions on Information Theory
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This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework is usually adopted, and the chosen sampling scheme is most often the Gibbs sampler. However, such a sampling scheme fails to explore the state space efficiently. Our first alternative, the K-tuple Gibbs sampler, is simply a grouped Gibbs sampler. The second one, called partially marginalized sampler, is obtained by integrating the Gaussian amplitudes out of the target distribution. While the mathematical validity of the first scheme is obvious as a particular instance of the Gibbs sampler, a more detailed analysis is provided to prove the validity of the second scheme. For both methods, optimized implementations are proposed in terms of computation and storage cost. Finally, simulation results validate both schemes as more efficient in terms of convergence time compared with the plain Gibbs sampler. Benchmark sequence simulations show that the partially marginalized sampler takes fewer iterations to converge than the K-tuple Gibbs sampler. However, its computation load per iteration grows almost quadratically with respect to the data length, while it only grows linearly for the K-tuple Gibbs sampler.