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Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1371 (16 self)
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fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced
Compressed sensing
, 2004
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
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Cited by 3557 (22 self)
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number of pixels, and yet be accurately reconstructed. The samples are nonadaptive and measure ‘random’ linear combinations of the transform coefficients. Approximate reconstruction is obtained by solving for the transform coefficients consistent with measured data and having the smallest possible `1
Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm
 Machine Learning
, 1988
"... learning Boolean functions, linearthreshold algorithms Abstract. Valiant (1984) and others have studied the problem of learning various classes of Boolean functions from examples. Here we discuss incremental learning of these functions. We consider a setting in which the learner responds to each ex ..."
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Cited by 766 (5 self)
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learning Boolean functions, linearthreshold algorithms Abstract. Valiant (1984) and others have studied the problem of learning various classes of Boolean functions from examples. Here we discuss incremental learning of these functions. We consider a setting in which the learner responds to each
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 551 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
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 772 (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
Ideal spatial adaptation by wavelet shrinkage
 Biometrika
, 1994
"... With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic ad ..."
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Cited by 1244 (5 self)
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advantages over traditional linear estimation by nonadaptive kernels � however, it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone. We describe a new principle for spatiallyadaptive estimation: selective wavelet reconstruction. Weshowthatvariableknot
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 1484 (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
An Empirical Study of Smoothing Techniques for Language Modeling
, 1998
"... We present an extensive empirical comparison of several smoothing techniques in the domain of language modeling, including those described by Jelinek and Mercer (1980), Katz (1987), and Church and Gale (1991). We investigate for the first time how factors such as training data size, corpus (e.g., Br ..."
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Cited by 1190 (21 self)
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.g., Brown versus Wall Street Journal), and ngram order (bigram versus trigram) affect the relative performance of these methods, which we measure through the crossentropy of test data. In addition, we introduce two novel smoothing techniques, one a variation of JelinekMercer smoothing and one a very
Investigating the Energy Consumption of a Wireless Network Interface in an Ad Hoc Networking Environment
 In IEEE Infocom
, 2001
"... Energyaware design and evaluation of network protocols requires knowledge of the energy consumption behavior of actual wireless interfaces. But little practical information is available about the energy consumption behavior of wellknown wireless network interfaces and device specifications do not ..."
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Cited by 650 (3 self)
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not provide information in a form that is helpful to protocol developers. This paper describes a series of experiments which obtained detailed measurements of the energy consumption of an IEEE 802.11 wireless network interface operating in an ad hoc networking environment. The data is presented as a
Detection and Tracking of Point Features
 International Journal of Computer Vision
, 1991
"... The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade i ..."
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Cited by 622 (2 self)
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in 1981. The method defines the measure of match between fixedsize feature windows in the past and current frame as the sum of squared intensity differences over the windows. The displacement is then defined as the one that minimizes this sum. For small motions, a linearization of the image intensities
Results 1  10
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2,139,435