Iterative algorithms for learning a linear gaussian observation model with an exponential power scale mixture prior

The authors study an iterative algorithm for learning a linear Gaussian observation model with an exponential power scale mixture prior (EPSM). This is a generalisation of previous study based on the Gaussian scale mixture prior. The authors use the principle of majorisation minimisation to derive the general iterative algorithm which is related to a reweighted lp-minimisation algorithm. The authors then show that the Gaussian and Laplacian scale mixtures are two special cases of the EPSM and the corresponding learning algorithms are related to the reweighted l₂-and l₁-minimisation algorithms, respectively. The authors also study a particular case of the EPSM which is a Pareto distribution and discuss Bayesian methods for parameter estimation.