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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 560 (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
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Robust Monte Carlo Localization for Mobile Robots
, 2001
"... Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), whi ..."
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Cited by 826 (88 self)
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), which approximate the posterior under a common Bayesian formulation of the localization problem. Building on the basic MCL algorithm, this article develops a more robust algorithm called MixtureMCL, which integrates two complimentary ways of generating samples in the estimation. To apply this algorithm
EigenTracking: Robust Matching and Tracking of Articulated Objects Using a ViewBased Representation
 International Journal of Computer Vision
, 1998
"... This paper describes an approach for tracking rigid and articulated objects using a viewbased representation. The approach builds on and extends work on eigenspace representations, robust estimation techniques, and parameterized optical flow estimation. First, we note that the leastsquares image r ..."
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Cited by 656 (16 self)
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reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation. Second we define a "subspace constancy assumption" that allows us to exploit techniques for parameterized optical flow estimation to solve for both
Random key predistribution schemes for sensor networks
 IN PROCEEDINGS OF THE 2003 IEEE SYMPOSIUM ON SECURITY AND PRIVACY
, 2003
"... Key establishment in sensor networks is a challenging problem because asymmetric key cryptosystems are unsuitable for use in resource constrained sensor nodes, and also because the nodes could be physically compromised by an adversary. We present three new mechanisms for key establishment using the ..."
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Cited by 813 (14 self)
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the framework of predistributing a random set of keys to each node. First, in the qcomposite keys scheme, we trade off the unlikeliness of a largescale network attack in order to significantly strengthen random key predistribution’s strength against smallerscale attacks. Second, in the multipath
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
"... ..."
Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 619 (14 self)
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based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown
Results 1  10
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277,141