Distributed Compressed Sensing off the Grid

Abstract

This letter 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 $\left[0,1\right]$. 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. Numerical experiments are performed to illustrate the effectiveness of the proposed approach and its advantage over separate recovery.

5 pages, 2 figures

References in corpus (2)

• Reducing Basis Mismatch in Harmonic Signal Recovery via Alternating Convex Search
• Super-resolution Line Spectrum Estimation with Block Priors