0000000000217067

AUTHOR

Stefano De Marchi

0000-0002-2832-8476

showing 2 related works from this author

Polynomial mapped bases: theory and applications

2022

Abstract In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.

Settore MAT/08 - Analisi Numericafake nodes Gibbs phenomenon mapped basis Runge's phenomenonmapped basisGibbs phenomenonRunge’s phenomenonfake nodesApplied MathematicsFOS: MathematicsMathematicsofComputing_NUMERICALANALYSISNumerical Analysis (math.NA)Mathematics - Numerical AnalysisIndustrial and Manufacturing Engineering
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Fake Nodes approximation for Magnetic Particle Imaging

2020

Accurately reconstructing functions with discontinuities is the key tool in many bio-imaging applications as, for instance, in Magnetic Particle Imaging (MPI). In this paper, we apply a method for scattered data interpolation, named mapped bases or Fake Nodes approach, which incorporates discontinuities via a suitable mapping function. This technique naturally mitigates the Gibbs phenomenon, as numerical evidence for reconstructing MPI images confirms.

Computer scienceComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONradial basis functionsFunction (mathematics)Magnetic Particle ImagingClassification of discontinuitieskernelsinterpolationGibbs phenomenonSettore MAT/08 - Analisi Numericasymbols.namesakeMagnetic particle imagingsymbolsKey (cryptography)Radial basis functioninterpolation; kernels; Magnetic Particle Imaging; radial basis functionsGFadial basis functionAlgorithmComputingMethodologies_COMPUTERGRAPHICSInterpolation2020 IEEE 20th Mediterranean Electrotechnical Conference ( MELECON)
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