2013
Multiscale data sampling and function extension
Bermanis A, Averbuch A, Coifman R. Multiscale data sampling and function extension. Applied And Computational Harmonic Analysis 2013, 34: 15-29. DOI: 10.1016/j.acha.2012.03.002.Peer-Reviewed Original ResearchSequence of approximationsGaussian kernel matrixData pointsAdaptive gridSpecial decompositionMultiscale schemeKernel matrixMultiscale decompositionGaussian kernelInterpolation methodMutual distanceData samplingFine hierarchyExtension methodEmpirical functionHierarchical procedureFunction extensionApproximationExtensionDecompositionPointKernelSchemeSubsamplingGrid
2008
A Framework for Discrete Integral Transformations IThe Pseudopolar Fourier Transform
Averbuch A, Coifman R, Donoho D, Israeli M, Shkolnisky Y. A Framework for Discrete Integral Transformations IThe Pseudopolar Fourier Transform. SIAM Journal On Scientific Computing 2008, 30: 764-784. DOI: 10.1137/060650283.Peer-Reviewed Original ResearchSame complexity orderDirect inversion algorithmFrequency gridGram operatorOne-dimensional operationsDiscrete gridDiscrete caseFrequency domain structureComplexity orderContinuous functionsIterative algorithmExact analogueFast algorithmPolar coordinatesInversion algorithmPseudopolar gridApproximate interpolationAnalogous toolsContinuum phenomenaRadial densityPseudopolar Fourier transformDifferent raysAlgorithmGridDiscrete Fourier transform
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