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The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed. Just as the classical result provides a tradeoff between signal localization in time and frequency, this result provides a(More)
The Kaczmarz method, or the algebraic reconstruction technique (ART), is a popular method for solving large-scale overdetermined systems of equations. Recently, Strohmer et al. proposed the ran-domized Kaczmarz algorithm, an improvement that guarantees exponential convergence to the solution. This has spurred much interest in the algorithm and its(More)
In this paper, the problem of informed-transmitter cooperative MIMO communications is addressed. The informed-transmitter link assumes that the distributed transmit nodes have access to channel state information. The channel state information includes the channel between the transmit and receive antenna arrays and a statistical model for interference(More)
The classical uncertainty principle provides a fundamental tradeoff in the localization of a signal in the time and frequency domains. In this paper we describe a similar tradeoff for signals defined on graphs. We describe the notions of " spread " in the graph and spectral domains, using the eigenvectors of the graph Laplacian as a surrogate Fourier basis.(More)
—Distributed detection of information flows spanning many nodes in a wireless sensor network is considered. In such a system, eavesdroppers are deployed near several nodes in the network. As data may be encrypted or padded, the eavesdroppers can only measure packet timestamps. Each eavesdropper, given a sequence of timestamps, must compress the information(More)
—The problem of detecting multi-hop information flows subject to communication constraints is considered. In a distributed detection scheme, eavesdroppers are deployed near nodes in a network, each able to measure the transmission times-tamps of a single node. The eavesdroppers must then compress the information and transmit it to a fusion center, which(More)
We consider the problem of distinguishing between two hypotheses: that a sequence of signals on a large graph consists entirely of noise, or that it contains a realization of a random walk buried in the noise. The problem of computing the error exponent of the optimal detector is simple to formulate, but exhibits deep connections to problems known to be(More)