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This work is about the statistical restoration of hidden discrete signals. The problem we deal with is how to take into account, in recent pairwise and triplet Markov chain context, complex noises that can be non-Gaussian, correlated, and of class-varying nature. We propose to solve this modeling problem using Copulas. The interest of the new modeling is validated by experiments performed in supervised and unsupervised context. In the latter, all parameters are estimated from the only observed data by an original method.