Bounds on the Reconstruction of Sparse Signal Ensembles from Distributed Measurements

Details Bounds on the Reconstruction of Sparse Signal Ensembles from Distributed Measurements Bounds on the Reconstruction of Sparse Signal Ensembles from Distributed Measurements

2011-02-14

arxiv.org/abs/1102.2677v1

Computer Science

Information Theory

19 pages, 2 figures

Scientific paper

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce an ensemble sparsity model for capturing the intra- and inter-signal correlations within a collection of sparse signals. For strictly sparse signals obeying an ensemble sparsity model, we characterize the fundamental number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable. Our analysis is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal.

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