Polynomial interpolation and approximation methods on sampling points along Lissajous curves using Chebyshev series is an e-ffective way for a fast image reconstruc-tion in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discon-tinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the approximating polynomial. In this work, after a description of the Gibbs phenomenon and classical filtering techniques in one and several dimensions, we present an adaptive spectral filtering process for the resolution of this 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 e-ffectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging.

Spectral filtering for the resolution of the Gibbs phenomenon in MPI applications by Lissajous sampling

Marchetti, Francesco
2016/2017

Abstract

Polynomial interpolation and approximation methods on sampling points along Lissajous curves using Chebyshev series is an e-ffective way for a fast image reconstruc-tion in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discon-tinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the approximating polynomial. In this work, after a description of the Gibbs phenomenon and classical filtering techniques in one and several dimensions, we present an adaptive spectral filtering process for the resolution of this 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 e-ffectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging.
2016-10-14
71
Gibbs phenomenon, MPI, Lissajous sampling, Magnetic Particle Imaging
File in questo prodotto:
File Dimensione Formato  
tesiMarchetti.pdf

accesso aperto

Dimensione 2.61 MB
Formato Adobe PDF
2.61 MB Adobe PDF Visualizza/Apri

The text of this website © Università degli studi di Padova. Full Text are published under a non-exclusive license. Metadata are under a CC0 License

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/24678