Results 1 - 10 of 4,205

Greed is Good: Algorithmic Results for Sparse Approximation

by Joel A. Tropp , 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
Abstract - Cited by 916 (9 self) - Add to MetaCart
This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal

Sparse Approximations

by Thomas Blumensath, Mike E. Davies
"... Early version, also known as pre-print ..."
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Early version, also known as pre-print

Applications of sparse approximation in communications

by A. C. Gilbert - in IEEE Int. Symp. Inf. Theory, 2005
"... Abstract—Sparse approximation problems abound in many ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Abstract—Sparse approximation problems abound in many

Parallel Preconditioning with Sparse Approximate Inverses

by Marcus J. Grote, Thomas Huckle - SIAM J. Sci. Comput , 1996
"... A parallel preconditioner is presented for the solution of general sparse linear systems of equations. A sparse approximate inverse is computed explicitly, and then applied as a preconditioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application o ..."
Abstract - Cited by 226 (10 self) - Add to MetaCart
A parallel preconditioner is presented for the solution of general sparse linear systems of equations. A sparse approximate inverse is computed explicitly, and then applied as a preconditioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application

Algorithms for simultaneous sparse approximation. Part II: Convex relaxation

by Joel A. Tropp, Anna C. Gilbert, Martin, J. Strauss, J. A. Tropp, A. C. Gilbert, M. J. Strauss , 2004
"... Abstract. A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals th ..."
Abstract - Cited by 366 (5 self) - Add to MetaCart
Abstract. A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals

An equivalence between sparse approximation and Support Vector Machines

by Federico Girosi - A.I. Memo 1606, MIT Arti cial Intelligence Laboratory , 1997
"... This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: ai-publications/1500-1999/AIM-1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995), ..."
Abstract - Cited by 243 (7 self) - Add to MetaCart
), and a sparse approximation scheme that resembles the Basis Pursuit De-Noising algorithm (Chen, 1995 � Chen, Donoho and Saunders, 1995). SVM is a technique which can be derived from the Structural Risk Minimization Principle (Vapnik, 1982) and can be used to estimate the parameters of several di erent

Shearlets and Optimally Sparse Approximations

by Gitta Kutyniok, Jakob Lemvig, Wang-q Lim, Gitta Kutyniok
"... Abstract Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient anal-ysis is the provision of optimally sparse approxim ..."
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provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representa-tion systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an in

Shearlets and Optimally Sparse Approximations∗

by unknown authors , 2013
"... Abstract: Multivariate functions are typically governed by aniso-tropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the pur-pose of compression as well as for an efficient analysis is the pro-vision of optimally sparse appro ..."
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provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other di-rectional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this opti-mality benchmark. This chapter shall serve

Sparse Approximations for Quaternionic Signals

by Quentin Barthélemy, Anthony Larue, Jérôme I. Mars , 2013
"... Abstract. In this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. Due to quaternions noncommutativity, two quaternionic extensions are presented: the right-multipli ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Abstract. In this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. Due to quaternions noncommutativity, two quaternionic extensions are presented: the right

Quaternionic sparse approximation

by Anthony Larue, Jérôme I. Mars - In Conf. on Applied Geometric Algebras in Computer Science and Engineering AGACSE , 2012
"... Abstract In this paper, we introduce a new processing procedure for quater-nionic signals through consideration of the well-known orthogonal matching pur-suit (OMP), which provides sparse approximation. We present a quaternionic ex-tension, the quaternionic OMP, that can be used to process a right-m ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Abstract In this paper, we introduce a new processing procedure for quater-nionic signals through consideration of the well-known orthogonal matching pur-suit (OMP), which provides sparse approximation. We present a quaternionic ex-tension, the quaternionic OMP, that can be used to process a right
Results 1 - 10 of 4,205