Continuous compressed sensing with a single or multiple measurement vectors

We consider the problem of recovering a single or multiple frequency-sparse signals, which share the same frequency components, from a subset of regularly spaced samples. The problem is referred to as continuous compressed sensing (CCS) in which the frequencies can take any values in the normalized domain [0, 1). In this pa-per, a link between CCS and low rank matrix completion (LRMC) is established based on an `0-pseudo-norm-like formulation, and theoretical guarantees for exact recovery are analyzed. Practically efficient algorithms are proposed based on the link and convex and nonconvex relaxations, and validated via numerical simulations. Index Terms — Continuous compressed sensing, multiple mea-surement vectors (MMV), atomic norm, DOA estimation. 1