Extensions of semidefinite programming methods for atomic decomposition

We present an extension of recent semidefinite programming formulations for atomic decomposition over continuous dictionaries, with applications to continuous or `gridless' compressed sensing. The dictionary considered in this paper is defined in terms of a general matrix pencil and is parameterized by a complex variable that varies over a segment of a line or circle in the complex plane. The main result of the paper is the formulation as a convex semidefinite optimization problem, and a simple constructive proof of the equivalence. The techniques are illustrated with a direction of arrival estimation problem, and an example of low-rank structured matrix decomposition.