1 research outputs found
Type I and Type II Bayesian Methods for Sparse Signal Recovery using Scale Mixtures
In this paper, we propose a generalized scale mixture family of
distributions, namely the Power Exponential Scale Mixture (PESM) family, to
model the sparsity inducing priors currently in use for sparse signal recovery
(SSR). We show that the successful and popular methods such as LASSO,
Reweighted and Reweighted methods can be formulated in an
unified manner in a maximum a posteriori (MAP) or Type I Bayesian framework
using an appropriate member of the PESM family as the sparsity inducing prior.
In addition, exploiting the natural hierarchical framework induced by the PESM
family, we utilize these priors in a Type II framework and develop the
corresponding EM based estimation algorithms. Some insight into the differences
between Type I and Type II methods is provided and of particular interest in
the algorithmic development is the Type II variant of the popular and
successful reweighted method. Extensive empirical results are provided
and they show that the Type II methods exhibit better support recovery than the
corresponding Type I methods.Comment: Under Revie