One of the most common problems in machine learning and statistics consists of estimating the mean response Az from a vector of observations y assuming y=Az+epsilon where A is known, z is a vector of parameters of interest and epsilon a vector of stochastic errors. We are particularly interested here in the case where the dimension K of z is much higher than the dimension of y. We propose some flexible Bayesian models which can yield sparse estimates of z. We show that as K tends to infinity, these models are closely related to a class of Levy processes. Simulations demonstrate that our models outperform significantly a range of popular alternatives.