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We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of observations n, the ambient signal dimension p, and the signal sparsity k are all allowed to tend to infinity in a… (More)

—The problem of graphical model selection is to estimate the graph structure of an unknown Markov random field based on observed samples from the graphical model. For Gaussian Markov random fields, this problem is closely related to the problem of estimating the inverse covariance matrix of the underlying Gaussian distribution. This paper focuses on the… (More)

— We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of observations n, the ambient signal dimension p, and the signal sparsity k are all allowed to tend to infinity in a… (More)

Consider a large-scale wireless sensor network measuring compressible data, where n distributed data values can be well-approximated using only k « n coefficients of some known transform. We address the problem of recovering an approximation of the n data values by querying any L sensors, so that the reconstruction error is comparable to the optimal… (More)

We propose a distributed multiresolution representation of sensor network data so that large-scale summaries are readily available by querying a small fraction of sensor nodes, anywhere in the network, and small-scale details are available by querying a larger number of sensors, locally in the region of interest. A global querier (such as a mobile collector… (More)

We propose random distributed multiresolution representations of sensor network data, so that the most significant encoding coefficients are easily accessible by querying a few sensors, anywhere in the network. Less significant encoding coefficients are available by querying a larger number of sensors, local to the region of interest. Significance can be… (More)

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