MMSE denoising of sparse Lévy processes via message passing

Many recent algorithms for sparse signal recovery can be interpreted as maximum-a-posteriori (MAP) estimators rely-ing on some specific priors. From this Bayesian perspective, state-of-the-art methods based on discrete-gradient regulariz-ers, such as total-variation (TV) minimization, implicitly as-sume the signals to be sampled instances of Lévy processes with independent Laplace-distributed increments. By extend-ing the concept to more general Lévy processes, we propose an efficient minimum-mean-squared error (MMSE) estima-tion method based on message-passing algorithms on factor graphs. The resulting algorithm can be used to benchmark the performance of the existing or design new algorithms for the recovery of sparse signals. Index Terms — signal denoising, sparse estimation, TV denoisin