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arXiv · 1108.0443

Sparse Recovery with Graph Constraints: Fundamental Limits and Measurement Construction

Meng Wang·Weiyu Xu·Enrique Mallada·Ao Tang
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Abstract

This paper addresses the problem of sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs. A general measurement construction algorithm is also proposed and evaluated. For any given graph $G$ with $n$ nodes, we derive order optimal upper bounds of the minimum number of measurements needed to recover any $k$-sparse vector over $G$ ($M^G_{k,n}$). Our study suggests that $M^G_{k,n}$ may serve as a graph connectivity metric.

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Meng Wang, Weiyu Xu, Enrique Mallada, Ao Tang. 2011-08-01. Sparse Recovery with Graph Constraints: Fundamental Limits and Measurement Construction. https://arxiv.org/abs/1108.0443

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