A Bayesian Approach for Asynchronous Parallel Sparse Recovery

Asynchronous parallel algorithms are often studied for separable optimization problems where the component objective functions are sparse, or act on only a few components of the variable $x \in \mathbb{R}^{N}$. One challenge to developing asynchronous approaches for sparse recovery is that the optimization formulation of this problem has dense component objective functions. However, the assumed sparsity of the signal may be exploited in an asynchronous parallel approach. Here we propose such an approach where multiple processors asynchronously infer hidden variables that estimate the support of x in a Bayesian manner. We include numerical simulations that demonstrate the potential benefits of this method.