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KarhunenLoeve expansion of stationary random signals with exponentially oscillating covariance function
"... Abstract. The KarhunenLoeve expansion based on the calculation of the eigenvalues and eigenfunctions of the KarhunenLoeve integral equation is known to have certain properties that make it optimal for many signal detection and filtering applications. We propose an analytical solution of the equat ..."
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Abstract. The KarhunenLoeve expansion based on the calculation of the eigenvalues and eigenfunctions of the KarhunenLoeve integral equation is known to have certain properties that make it optimal for many signal detection and filtering applications. We propose an analytical solution
ASYMPTOTIC ESTIMATES OF THE NORMS OF POSITIVE DEFINITE TÖPLITZ MATRICES AND DETECTION OF QUASIPERIODIC COMPONENTS OF STATIONARY RANDOM SIGNALS
, 2005
"... Abstract. Asymptotic forms of the HilbertScmidt and Hilbert norms of positive definite Töplitz matrices QN = (b(j − k)) N−1 j,k=0 as N → ∞ are determined. Here b(j) are consequent trigonometric moments of a generating nonnegative mesure dσ(θ) on [−π, π]. It is proven that σ(θ) is continuous if an ..."
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if and only if any of those contributions is o(N). Analogous criteria are given for positive integral operators with difference kernels. Obtained results are applied to processing of stationary random signals, in particular, neutron signals emitted by boiling water nuclear reactors. 1.
Signal recovery from random measurements via Orthogonal Matching Pursuit
 IEEE TRANS. INFORM. THEORY
, 2007
"... This technical report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous ..."
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Cited by 802 (9 self)
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This technical report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
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Cited by 1397 (38 self)
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Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y
Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information
, 2006
"... This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this pa ..."
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Cited by 2632 (50 self)
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This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result
Minimum energy mobile wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 1999
"... We describe a distributed positionbased network protocol optimized for minimum energy consumption in mobile wireless networks that support peertopeer communications. Given any number of randomly deployed nodes over an area, we illustrate that a simple local optimization scheme executed at each n ..."
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Cited by 749 (0 self)
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We describe a distributed positionbased network protocol optimized for minimum energy consumption in mobile wireless networks that support peertopeer communications. Given any number of randomly deployed nodes over an area, we illustrate that a simple local optimization scheme executed at each
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods
The capacity of wireless networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2000
"... When n identical randomly located nodes, each capable of transmitting at bits per second and using a fixed range, form a wireless network, the throughput @ A obtainable by each node for a randomly chosen destination is 2 bits per second under a noninterference protocol. If the nodes are optimally p ..."
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Cited by 3243 (42 self)
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When n identical randomly located nodes, each capable of transmitting at bits per second and using a fixed range, form a wireless network, the throughput @ A obtainable by each node for a randomly chosen destination is 2 bits per second under a noninterference protocol. If the nodes are optimally
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1791 (69 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
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