# Type I and Type II Bayesian Methods for Sparse Signal Recovery using Scale Mixtures

17 Jul 2015  ·  , ·

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 $\ell_1$ and Reweighted $\ell_2$ 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 $\ell_1$ method. Extensive empirical results are provided and they show that the Type II methods exhibit better support recovery than the corresponding Type I methods.

PDF Abstract

## Code Add Remove Mark official

No code implementations yet. Submit your code now

## Datasets

Add Datasets introduced or used in this paper

## Results from the Paper Edit

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

## Methods Add Remove

No methods listed for this paper. Add relevant methods here