Distributed Compressed Sensing off the Grid

TL;DR

This paper introduces a novel off-the-grid joint recovery method for frequency-sparse signals using an extended atomic norm approach, formulated as a semidefinite program, demonstrating improved performance over separate recovery methods.

Contribution

It extends atomic norm minimization to off-the-grid frequency-sparse signals and proposes a computationally tractable joint recovery method with theoretical optimality guarantees.

Findings

Effective joint recovery of off-the-grid frequency-sparse signals.

The proposed method outperforms separate recovery in experiments.

Reformulation as a semidefinite program enables practical implementation.

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 $\left\lbrack 0,1 \right\rbrack$. 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.