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This paper proposes and compares two new sampling schemes for sparsedeconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolutionproblem in a blind and unsupervised context, the Markov Chain Monte Carlo(MCMC) framework is usually adopted, and the chosen sampling scheme is mostoften the Gibbs sampler. However, such a sampling scheme fails to explore thestate space efficiently. Our first alternative, the $K$-tuple Gibbs sampler, issimply a grouped Gibbs sampler. The second one, called partially marginalizedsampler, is obtained by integrating the Gaussian amplitudes out of the targetdistribution. While the mathematical validity of the first scheme is obvious asa particular instance of the Gibbs sampler, a more detailed analysis isprovided to prove the validity of the second scheme.  For both methods, optimized implementations are proposed in terms ofcomputation and storage cost. Finally, simulation results validate both schemesas more efficient in terms of convergence time compared with the plain Gibbssampler. Benchmark sequence simulations show that the partially marginalizedsampler takes fewer iterations to converge than the $K$-tuple Gibbs sampler.However, its computation load per iteration grows almost quadratically withrespect to the data length, while it only grows linearly for the $K$-tupleGibbs sampler.

Enhanced sampling schemes for MCMC based blind Bernoulli-Gaussian deconvolution