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86,451
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
"... ..."
The Convex Geometry of Linear Inverse Problems
, 2010
"... In applications throughout science and engineering one is often faced with the challenge of solving an illposed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constr ..."
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Cited by 189 (20 self)
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are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems
Aggregation for Linear Inverse Problems
, 2014
"... In the framework of inverse problems, we consider the question of aggregating estimators taken from a given collection. Extending usual results for the direct case, we propose a new penalty to achieve the best aggregation. An oracle inequality provides the asymptotic behavior of this estimator. We i ..."
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In the framework of inverse problems, we consider the question of aggregating estimators taken from a given collection. Extending usual results for the direct case, we propose a new penalty to achieve the best aggregation. An oracle inequality provides the asymptotic behavior of this estimator. We
IllPosed and Linear Inverse Problems
, 2015
"... Abstract. In this paper illposed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is ..."
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Abstract. In this paper illposed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization
ROBUST CENSORING FOR LINEAR INVERSE PROBLEMS
"... Existing methods for smart data reduction are typically sensitive to outlier data that do not follow postulated data models. We propose robust censoring as a joint approach unifying the concepts of robust learning and data censoring. We focus on linear inverse problems and formulate robust censor ..."
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Cited by 1 (0 self)
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Existing methods for smart data reduction are typically sensitive to outlier data that do not follow postulated data models. We propose robust censoring as a joint approach unifying the concepts of robust learning and data censoring. We focus on linear inverse problems and formulate robust
Nonlinear solution of linear inverse problems by waveletvaguelette decomposition
, 1992
"... We describe the WaveletVaguelette Decomposition (WVD) of a linear inverse problem. It is a substitute for the singular value decomposition (SVD) of an inverse problem, and it exists for a class of special inverse problems of homogeneous type { such asnumerical di erentiation, inversion of Abeltype ..."
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Cited by 251 (12 self)
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We describe the WaveletVaguelette Decomposition (WVD) of a linear inverse problem. It is a substitute for the singular value decomposition (SVD) of an inverse problem, and it exists for a class of special inverse problems of homogeneous type { such asnumerical di erentiation, inversion of Abel
Nonlinear estimation for linear inverse problems with error in the operator
 Annals of Statistics
"... We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove t ..."
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Cited by 30 (2 self)
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We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove
Computational methods for sparse solution of linear inverse problems
, 2009
"... The goal of sparse approximation problems is to represent a target signal approximately as a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, ..."
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Cited by 167 (0 self)
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The goal of sparse approximation problems is to represent a target signal approximately as a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues
Sparse solutions to linear inverse problems with multiple measurement vectors
 IEEE Trans. Signal Processing
, 2005
"... Abstractâ€”We address the problem of finding sparse solutions to an underdetermined system of equations when there are multiple measurement vectors having the same, but unknown, sparsity structure. The single measurement sparse solution problem has been extensively studied in the past. Although known ..."
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Cited by 272 (22 self)
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Abstractâ€”We address the problem of finding sparse solutions to an underdetermined system of equations when there are multiple measurement vectors having the same, but unknown, sparsity structure. The single measurement sparse solution problem has been extensively studied in the past. Although known
Results 1  10
of
86,451