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15,809
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 483 (2 self)
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This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination
Stable recovery of sparse overcomplete representations in the presence of noise
 IEEE TRANS. INFORM. THEORY
, 2006
"... Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes t ..."
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Cited by 460 (22 self)
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Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3393 (12 self)
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The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 513 (17 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.
 IEEE Trans. Pattern Anal. Mach. Intell.
, 1984
"... AbstractWe make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a latticelike physical system. The assignment of an energy function in the physical system determines its Gibbs di ..."
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Cited by 5126 (1 self)
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mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical
Improving generalization with active learning
 Machine Learning
, 1994
"... Abstract. Active learning differs from "learning from examples " in that the learning algorithm assumes at least some control over what part of the input domain it receives information about. In some situations, active learning is provably more powerful than learning from examples ..."
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Cited by 544 (1 self)
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alone, giving better generalization for a fixed number of training examples. In this article, we consider the problem of learning a binary concept in the absence of noise. We describe a formalism for active concept learning called selective sampling and show how it may be approximately implemented by a
Nonlinear Filtering of NonGaussian Noise
, 1997
"... This paper introduces a new nonlinear filter for a discrete time, linear system which is observed in additive nonGaussian measurement noise. The new filter is recursive, computationally efficient and has significantly improved performance over other linear and nonlinear schemes. The problem of na ..."
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Cited by 5 (0 self)
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This paper introduces a new nonlinear filter for a discrete time, linear system which is observed in additive nonGaussian measurement noise. The new filter is recursive, computationally efficient and has significantly improved performance over other linear and nonlinear schemes. The problem
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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, suppose that A is a Gaussian random matrix; then stable recovery occurs for almost all such A's provided that the number of nonzeros of x 0 is of about the same order as the number of observations. As a second instance, suppose one observes few Fourier samples of x 0 ; then stable recovery occurs
Linklevel Measurements from an 802.11b Mesh Network
 In SIGCOMM
, 2004
"... This paper anal yzes the causes of packetl oss in a 38node urban mul tihop 802.11b network. The patterns and causes oflv# are important in the design of routing and errorcorrection proto colv as wel as in networkplqq"(v The paper makes the fol l owing observations. The distribution of intern ..."
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Cited by 567 (11 self)
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This paper anal yzes the causes of packetl oss in a 38node urban mul tihop 802.11b network. The patterns and causes oflv# are important in the design of routing and errorcorrection proto colv as wel as in networkplqq"(v The paper makes the fol l owing observations. The distribution of inter
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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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
Results 1  10
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15,809