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
2003
Accurate and Fast Discrete Polar Fourier Transform
Averbuch A, Coifman R, Donoho D, Elad M, Israeli M. Accurate and Fast Discrete Polar Fourier Transform. 2003, 2: 1933-1937. DOI: 10.1109/acssc.2003.1292319.Peer-Reviewed Original Research