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Polynomial interpolation and approximation methods on sampling points along Lissajous curves using Chebyshev series is an effective way for a fast image reconstruction in Magnetic Particle Imaging (MPI). We introduce Lissajous sampling and classical filtering techniques in one and several dimensions. We then present an adaptive spectral filtering process for the reduction of the Gibbs phenomenon and for an improved approximation of the underlying function or image. In this adaptive filtering technique, the spectral filter depends on the distance of a spatial point to the nearest discontinuity. We show the effectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging.
This presentation is part of Minisymposium “MS2 - Interpolation and Approximation Methods in Imaging (4 parts)”
organized by: Alessandra De Rossi (University of Torino) , Costanza Conti (University of Firenze) , Francesco Dell'Accio (University of Calabria) .