An Asynchronous Parallel Approach to Sparse Recovery
  Asynchronous parallel computing and sparse recovery are two areas that have
received recent interest. Asynchronous algorithms are often studied to solve
optimization problems where the cost function takes the form $\sum_{i=1}^M
f_i(x)$, with a common assumption that each $f_i$ is sparse; that is, each
$f_i$ acts only on a small number of components of $x\in\mathbb{R}^n$. Sparse
recovery problems, such as compressed sensing, can be formulated as
optimization problems, however, the cost functions $f_i$ are dense with respect
to the components of $x$, and instead the signal $x$ is assumed to be sparse,
meaning that it has only $s$ non-zeros where $s\ll n$. Here we address how one
may use an asynchronous parallel architecture when the cost functions $f_i$ are
not sparse in $x$, but rather the signal $x$ is sparse. We propose an
asynchronous parallel approach to sparse recovery via a stochastic greedy
algorithm, where multiple processors asynchronously update a vector in shared
memory containing information on the estimated signal support. We include
numerical simulations that illustrate the potential benefits of our proposed
asynchronous method.
