Distributed Compressed Sensing Off The Grid

This paper investigates the joint recovery of a frequency-sparse signal ensemble sharing a common frequency-sparse component from the collection of their compressed measurements. Unlike conventional arts in compressed sensing, the frequencies follow an off-the-grid formulation and are continuously valued in [0, 1], rather than constrained to a pre-determined grid. As an extension of atomic norm, the concatenated atomic norm minimization approach is proposed to handle the exact recovery of signals, which is reformulated as a computationally tractable semidefinite program.The optimality of the proposed approach is characterized using a dual certificate. The strict complementarity between the primal semidefinite program and dual semidefi-nite program is checked to ensure the effectiveness of commonly used path-tracking convex optimization solvers. A prototype of dual polynomial ensemble construction is proposed, and its correctness is checked via the invertibility of the resulting linear system. Numerical experiments are performed to illustrate the effectiveness of the proposed approach and its advantage over separate recovery.