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arXiv · 1407.3064

Distributed Compressed Sensing off the Grid

Zhenqi Lu·Rendong Ying·Sumxin Jiang·Peilin Liu·Wenxian Yu
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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.

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Zhenqi Lu, Rendong Ying, Sumxin Jiang, Peilin Liu, Wenxian Yu. 2014-08-13. Distributed Compressed Sensing off the Grid. https://doi.org/10.1109/lsp.2014.2349904

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