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4,792
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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, where r is the residual vector y − A˜x and t is a positive scalar. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the true parameter vector x is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large probability
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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? To recover x 0 , we consider the solution x to the 1 regularization problem where is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the vector x 0 is sufficiently sparse, then the solution is within the noise level As a first example
A computational approach to edge detection
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1986
"... This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumpti ..."
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Cited by 4675 (0 self)
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. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals
Northern hemisphere temperatures during the past millennium: Inferences, uncertainties, and limitations
 GEOPHYSICAL RESEARCH LETTERS
, 1999
"... Building on recent studies, we attempt hemispheric temperature reconstructions with proxy data networks for the past millennium. We focus not just on the reconstructions, but the uncertainties therein, and important caveats. Though expanded uncertainties prevent decisive conclusions for the period ..."
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Cited by 302 (13 self)
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Building on recent studies, we attempt hemispheric temperature reconstructions with proxy data networks for the past millennium. We focus not just on the reconstructions, but the uncertainties therein, and important caveats. Though expanded uncertainties prevent decisive conclusions
Mobile Robot Localization and Mapping with Uncertainty using ScaleInvariant Visual Landmarks
, 2002
"... A key component of a mobile robot system is the ability to localize itself accurately and, simultaneously, to build a map of the environment. Most of the existing algorithms are based on laser range finders, sonar sensors or artificial landmarks. In this paper, we describe a visionbased mobile robo ..."
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Cited by 279 (12 self)
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are robustly matched, robot pose is estimated and a consistent threedimensional map is built. As image features are not noisefree, we carry out error analysis for the landmark positions and the robot pose. We use Kalman filters to track these landmarks in a dynamic environment, resulting in a database map
Sure independence screening for ultrahigh dimensional feature space
, 2006
"... Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, ..."
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Cited by 283 (26 self)
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uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method based on a correlation learning, called the Sure Independence Screening (SIS), to reduce dimensionality from high to a moderate scale that is below sample size. In a
Some Fundamental Limits on Cognitive Radio
 in Fortysecond Allerton Conference on Communication, Control, and Computing
, 2004
"... Cognitive radio refers to wireless architectures in which a communication system does not operate in a fixed assigned band, but rather searches and finds an appropriate band in which to operate. In this paper we explore, from first principles, the fundamental requirements for such system that tries ..."
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Cited by 171 (15 self)
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greatly. We further motivate the need for pilot signals by showing that the radiometer is rendered useless by just moderate noise uncertainty. Finally, we show that quantization combined with noise uncertainty can make the detection of signals by any detector absolutely impossible below a certain SNR
Weighing Risk and Uncertainty
, 1995
"... Decision theory distinguishes between risky prospects, where the probabilities associated with the possible outcomes are assumed to be known, and uncertain prospects, where these probabilities are not assumed to be known. Studies of choice between risky prospects have suggested a nonlinear transform ..."
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Cited by 187 (10 self)
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transformation of the probability scale that overweights low probabilities and underweights moderate and high probabilities. The present article extends this notion from risk to uncertainty by invoking the principle of bounded subadditivity: An event has greater impact when it turns impossibility
Analogtodigital converter survey and analysis
 IEEE Journal on Selected Areas in Communications
, 1999
"... Abstract—Analogtodigital converters (ADC’s) are ubiquitous, critical components of software radio and other signal processing systems. This paper surveys the stateoftheart of ADC’s, including experimental converters and commercially available parts. The distribution of resolution versus samplin ..."
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Cited by 263 (0 self)
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sampling rate provides insight into ADC performance limitations. At sampling rates below 2 million samples per second (Ms/s), resolution appears to be limited by thermal noise. At sampling rates ranging from 2 Ms/s to 4 giga samples per second (Gs/s), resolution falls off by 1 bit for every doubling
Bayesian Modeling of Uncertainty in LowLevel Vision
, 1990
"... The need for error modeling, multisensor fusion, and robust algorithms i becoming increasingly recognized in computer vision. Bayesian modeling is a powerful, practical, and general framework for meeting these requirements. This article develops a Bayesian model for describing and manipulating the d ..."
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Cited by 204 (17 self)
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constraints from regularization to define a Markov Random Field. The sensor model describes the behavior and noise characteristics of our measurement system. We develop a number of sensor models for both sparse and dense measurements. The posterior model combines the information from the prior and sensor
Results 1  10
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4,792