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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 2731 (61 self)
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for decomposition have been proposed, including the Method of Frames (MOF), Matching Pursuit (MP), and, for special dictionaries, the Best Orthogonal Basis (BOB). Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having
Basis Pursuit
, 2002
"... This paper presents a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). In the setting of a tensor product reproducing kernel Hilbert space, we decompose the log likelihood into the sum of different functional components suc ..."
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This paper presents a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). In the setting of a tensor product reproducing kernel Hilbert space, we decompose the log likelihood into the sum of different functional components
Probing the Pareto frontier for basis pursuit solutions
, 2008
"... The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit and the ..."
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Cited by 363 (4 self)
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The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit
Nonlinear Basis Pursuit
"... Abstract—In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In ..."
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Abstract—In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit
Greedy Basis Pursuit
, 2006
"... We introduce Greedy Basis Pursuit (GBP), a new algorithm for computing signal representations using overcomplete dictionaries. GBP is rooted in computational geometry and exploits an equivalence between minimizing the ℓ 1norm of the representation coefficients and determining the intersection of th ..."
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Cited by 10 (0 self)
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We introduce Greedy Basis Pursuit (GBP), a new algorithm for computing signal representations using overcomplete dictionaries. GBP is rooted in computational geometry and exploits an equivalence between minimizing the ℓ 1norm of the representation coefficients and determining the intersection
Distributed basis pursuit
 IEEE Trans. Sig. Proc
, 2012
"... Abstract—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the leastnorm solution of the underdetermined linear system and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a s ..."
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Cited by 28 (7 self)
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Abstract—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the leastnorm solution of the underdetermined linear system and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a
DISTRIBUTED ALGORITHMS FOR BASIS PURSUIT
"... The Basis Pursuit (BP) problem consists in finding a least ℓ1 norm solution of the underdetermined linear system Ax = b. It arises in many areas of electrical engineering and applied mathematics. Applications include signal compression and modeling, estimation, fitting, and compressed sensing. In th ..."
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Cited by 6 (4 self)
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The Basis Pursuit (BP) problem consists in finding a least ℓ1 norm solution of the underdetermined linear system Ax = b. It arises in many areas of electrical engineering and applied mathematics. Applications include signal compression and modeling, estimation, fitting, and compressed sensing
BASIS PURSUIT FOR SPECTRUM CARTOGRAPHY∗
"... A nonparametric version of the basis pursuit method is developed for field estimation. The underlying model entails known bases, weighted by generic functions to be estimated from the field’s noisy samples. A novel field estimator is developed based on a regularized variational leastsquares (LS) cr ..."
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A nonparametric version of the basis pursuit method is developed for field estimation. The underlying model entails known bases, weighted by generic functions to be estimated from the field’s noisy samples. A novel field estimator is developed based on a regularized variational leastsquares (LS
BASIS PURSUIT IN SENSOR NETWORKS
"... Basis Pursuit (BP) finds a minimum ℓ1norm vector z that satisfies the underdetermined linear system Mz = b, where the matrix M and vector b are given. Lately, BP has attracted attention because of its application in compressed sensing, where it is used to reconstruct signals by finding the sparsest ..."
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Cited by 12 (4 self)
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Basis Pursuit (BP) finds a minimum ℓ1norm vector z that satisfies the underdetermined linear system Mz = b, where the matrix M and vector b are given. Lately, BP has attracted attention because of its application in compressed sensing, where it is used to reconstruct signals by finding
1 Distributed Basis Pursuit
"... Abstract—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least ℓ1norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform su ..."
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Abstract—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least ℓ1norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform
Results 1  10
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169,439