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
2013
Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging
Talmon R, Shkolnisky Y, Coifman R. Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging. Lecture Notes In Computer Science 2013, 8085: 441-448. DOI: 10.1007/978-3-642-40020-9_48.Peer-Reviewed Original ResearchNonlinear filtering problemInformation geometryFiltering problemDifferential geometryNonlinear filteringIntrinsic modelingIntrinsic geometryBayesian frameworkStatistical modelRandom observationsNonlinear modelingInstrumental modalitiesInferred modelGeometryNoise resilientReal signalsInvariantsModelingPhoton counterModelBiomedical imagingFilteringApplicationsProblem
2006
Fast and accurate Polar Fourier transform
Averbuch A, Coifman R, Donoho D, Elad M, Israeli M. Fast and accurate Polar Fourier transform. Applied And Computational Harmonic Analysis 2006, 21: 145-167. DOI: 10.1016/j.acha.2005.11.003.Peer-Reviewed Original ResearchPolar coordinatesFourier transformContinuous formulationApplied problemsCartesian gridTwo-dimensional signalsInitial gridSize n×nContinuum ideasInterpolation operationError analysisAlgorithm complexityFFT methodConversion processPolar Fourier transformInverse transformPolar systemsFFTGridCentral toolCoordinatesInterpolationTransformProblemN×n
1995
Local discriminant bases and their applications
Saito N, Coifman R. Local discriminant bases and their applications. Journal Of Mathematical Imaging And Vision 1995, 5: 337-358. DOI: 10.1007/bf01250288.Peer-Reviewed Original ResearchOrthonormal basisStatistical methodsClassification problemSignificant coordinatesBasis functionsSignal classification problemsTrigonometric basisLocal trigonometric basesLinear discriminant analysisInput signalDirect applicationRegression treesProblemBest basis algorithmAlgorithmTime-frequency planeSignal componentsFurther applicationCoordinatesDimensionalityImage classification problemsApplicationsSmall numberTexture classification problemOn local orthonormal bases for classification and regression
Saito N, Coifman R. On local orthonormal bases for classification and regression. 2013 IEEE International Conference On Acoustics, Speech And Signal Processing 1995, 3: 1529-1532 vol.3. DOI: 10.1109/icassp.1995.479852.Peer-Reviewed Original ResearchOrthonormal basisRegression problemsLocal orthonormal basisRelative entropyRegression errorsStatistical methodsSynthetic examplesSignificant coordinatesBasis functionsLinear discriminant analysisRegression methodEnergy distributionRegression treesProblemClassification problemTime-frequency planeSignal classificationEntropyTraditional methodsCoordinatesDimensionalityTime-frequency energy distributionSmall number
1994
Selection of best bases for classification and regression
Coifman R, Saito N. Selection of best bases for classification and regression. 1994, 51. DOI: 10.1109/wits.1994.513882.Peer-Reviewed Original Research
1993
The Inverse Spectral Method on the Plane
Coifman R, Fokas A. The Inverse Spectral Method on the Plane. Springer Series In Nonlinear Dynamics 1993, 58-85. DOI: 10.1007/978-3-642-58045-1_5.Peer-Reviewed Original ResearchThe fast multipole method for electromagnetic scattering calculations
Coifman R, Rokhlin V, Wandzura S. The fast multipole method for electromagnetic scattering calculations. 1993, 48-51 vol.1. DOI: 10.1109/aps.1993.385405.Peer-Reviewed Original ResearchFast multipole methodMultipole methodDense impedance matrixThree-dimensional electromagnetic problemsBoundary integral equationsAccurate numerical modelingMethod of momentsIntegral equationsElectromagnetic problemsElectromagnetic scattering calculationsRadiation problemsElementary derivationPhysical interpretationImpedance matrixComputational complexityElectromagnetic scatteringScattering calculationsNumerical modelingSparse decompositionEquationsProblemDerivationMomentModelingCalculations
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
1989
Linear spectral problems, non-linear equations and the δ-method
Beals R, Coifman R. Linear spectral problems, non-linear equations and the δ-method. Inverse Problems 1989, 5: 87. DOI: 10.1088/0266-5611/5/2/002.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
1986
The D-bar approach to inverse scattering and nonlinear evolutions
Beals R, Coifman R. The D-bar approach to inverse scattering and nonlinear evolutions. Physica D Nonlinear Phenomena 1986, 18: 242-249. DOI: 10.1016/0167-2789(86)90184-3.Peer-Reviewed Original ResearchSelf-dual Yang-Mills equationsComplex differential equationsYang-Mills equationsInverse scattering methodDavey–StewartsonDifferential equationsNonlinear equationsSchrödinger equationAssociated hierarchyInverse scatteringNonlinear evolutionEquationsMultidimensional problemsScattering methodInversionProblemR3Scattering