2015
Manifold Learning for Latent Variable Inference in Dynamical Systems
Talmon R, Mallat S, Zaveri H, Coifman R. Manifold Learning for Latent Variable Inference in Dynamical Systems. IEEE Transactions On Signal Processing 2015, 63: 3843-3856. DOI: 10.1109/tsp.2015.2432731.Peer-Reviewed Original ResearchDynamical systemsLatent variable inferenceOutput signal measurementsNonlinear observerEigenvector problemLaplace operatorSignal geometryIntrinsic distanceSignal measurementsAccurate recoveryIntrinsic variablesLatent variablesObserverInferenceMeasurement deviceManifoldOperatorsVariablesGeometryIntracranial electroencephalography signalsKernelDynamicsPropertiesProblemSolution
2011
Harmonic Analysis of Digital Data Bases
Coifman R, Gavish M. Harmonic Analysis of Digital Data Bases. Applied And Numerical Harmonic Analysis 2011, 161-197. DOI: 10.1007/978-0-8176-8095-4_9.Peer-Reviewed Original ResearchSpace of matricesData matrixData pointsEntropy conditionTensor productLaplacian eigenvectorsPotential operatorsDistribution geometryIterative procedureHarmonic analysisGraph oneAffinity graphLocal geometryEfficient reconstructionEigenvectorsGeometryData analysis methodsOperatorsGraphHaar-like basesMatrixAnalysis methodPartition treeExpansion coefficientVertices
2006
Diffusion wavelet packets
Bremer J, Coifman R, Maggioni M, Szlam A. Diffusion wavelet packets. Applied And Computational Harmonic Analysis 2006, 21: 95-112. DOI: 10.1016/j.acha.2006.04.005.Peer-Reviewed Original ResearchDiffusion waveletsWavelet packetEfficient algorithmImage denoisingSame algorithmMultiscale representationPacketsSignal processingWaveletsAlgorithmDenoisingGraphLower dimensionHigher dimensionsApplicationsTime-frequency basisComputationTaskCompressionAnisotropic settingProcessingRepresentationExampleOperatorsTool
2000
Challenges in Analysis
Coifman R. Challenges in Analysis. Modern Birkhäuser Classics 2000, 471-480. DOI: 10.1007/978-3-0346-0425-3_2.Peer-Reviewed Original Research
1993
Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
Alpert B, Beylkin G, Coifman R, Rokhlin V. Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations. SIAM Journal On Scientific Computing 1993, 14: 159-184. DOI: 10.1137/0914010.Peer-Reviewed Original ResearchIntegral equationsSecond kind integral equationsKind integral equationsWavelet-like basisVector space basisIntegral operatorsNumerical solutionNumber of pointsFinite numberFast solutionSparse matricesNumerical resultsDiscretizationEquationsOperatorsSparse representationSingularitySolutionGeneralization
1991
Fast wavelet transforms and numerical algorithms I
Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I. Communications On Pure And Applied Mathematics 1991, 44: 141-183. DOI: 10.1002/cpa.3160440202.Peer-Reviewed Original ResearchPseudo-differential operatorsClass of algorithmsLinear operatorsTheory of waveletsN matrixNumerical experimentsArbitrary vectorOrder ONumerical applicationsNarrow classAlgorithm IOperatorsDetailed analytical informationIntractable problemClassAlgorithmMatrixAnalytical informationVectorTheorySchemeO operationsProblemWavelets
1990
Wavelets for the Fast Solution of Second-Kind Integral Equations
Alpert B, Beylkin G, Coifman R, Rokhlin V. Wavelets for the Fast Solution of Second-Kind Integral Equations. 1990 DOI: 10.21236/ada233650.Peer-Reviewed Original ResearchIntegral equationsSecond kind integral equationsKind integral equationsNon-oscillatory kernelsVector space basisIntegral operatorsNumerical solutionNumber of pointsFinite numberFast solutionSparse matricesNumerical resultsDiscretizationEquationsOperatorsSparse representationSingularitySolutionGeneralizationKernelMultiresolution Analysis in Non-Homogeneous Media
Coifman R. Multiresolution Analysis in Non-Homogeneous Media. Inverse Problems And Theoretical Imaging 1990, 259-262. DOI: 10.1007/978-3-642-75988-8_25.Peer-Reviewed Original Research
1989
Multiresolution Analysis in Non-Homogeneous Media
Coifman R. Multiresolution Analysis in Non-Homogeneous Media. Inverse Problems And Theoretical Imaging 1989, 259-262. DOI: 10.1007/978-3-642-97177-8_25.Peer-Reviewed Original ResearchMultiresolution analysis in non-homogeneous media
Coifman R. Multiresolution analysis in non-homogeneous media. 1989, 107. DOI: 10.1109/mdsp.1989.97059.Peer-Reviewed Original ResearchPartial differential operatorsNon-homogeneous mediaDifferential operatorsVariable coefficientsMultiresolution analysisNumerical algorithmInvariant settingImage processing contextNonhomogeneous mediaEdge detection problemDetection problemVariable geometryProcessing contextTime-frequency analysisOperatorsWavelet analysisGeometryFrequency analysisAlgorithmSpaceSummary formProblemWavelets