Fast MCMC computations for the estimation of sparse processes from noisy observations

The paper presents a fast MCMC (Markov chain Monte Carlo) algorithm specially designed for high dimensional models with block structure. Such models are often met in Bayesian inference problems in signal processing, such as spectral estimation, harmonic analysis, blind deconvolution or signal classification. Our algorithm generates samples distributed according to a posterior distribution. We show that sampling the amplitudes together with the remaining model parameters leads to quicker computations than sampling from the marginal posterior, where amplitudes have been integrated out. Simulation results demonstrate the soundness of this approach for high dimensional models.