An Asynchronous Parallel Approach to Sparse Recovery

Abstract

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 _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 xR^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 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.

Tasks

Reproductions