Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite optimization problems and in related convex optimization problems involving sparse positive semidefinite matrices. Chordal graph properties are also fundamental to several classical results in combinatorial optimization, linear algebra, statistics, signal processing, machine learning, and nonlinear op...

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector consistent with the measurements and reformulate it as a group-sparse optimization problem with linear constraints. Then, we analyze the convex relaxation of ...

In this paper we revisit one of the classical problems of compressed sensing. Namely, we consider linear under-determined systems with sparse solutions. A substantial success in mathematical characterization of an l1 optimization technique typically used for solving such systems has been achieved during the last decade. Seminal works [4, 18] showed that the l1 can recover a so-called linear spa...

A set of vectors (or signals) are jointly sparse if all their nonzero entries are found on a small number of rows (or columns). Consider a network of agents that collaboratively recover a set of jointly sparse vectors from their linear measurements . Assume that every agent collects its own measurement and aims to recover its own vector taking advantages of the joint sparsity structure. This pa...