2015
Intrinsic modeling of stochastic dynamical systems using empirical geometry
Talmon R, Coifman R. Intrinsic modeling of stochastic dynamical systems using empirical geometry. Applied And Computational Harmonic Analysis 2015, 39: 138-160. DOI: 10.1016/j.acha.2014.08.006.Peer-Reviewed Original ResearchLow-dimensional manifoldDynamical systemsEmpirical geometryReal-world dynamical systemsStochastic dynamical systemsNon-Gaussian tracking problemsNonlinear filtering applicationsNonlinear differential equationsIntrinsic Riemannian metricMarkov chain schemeEmpirical probability densityLocal tangent spaceIntrinsic modelDifferential equationsIntrinsic modelingKnowledge of modelsTangent spaceProbability densityMathematical calibrationTracking problemInverse problemRiemannian metricLaplace operatorRandom measurementsSmall perturbations
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