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Proceedings Paper

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)
Author(s): Jade Larriva-Latt; Angela Morrison; Alison Radgowski; Joseph Tobin; Mark Iwen; Aditya Viswanathan
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Paper Abstract

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon – with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

Paper Details

Date Published: 24 August 2017
PDF: 8 pages
Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039414 (24 August 2017); doi: 10.1117/12.2271860
Show Author Affiliations
Jade Larriva-Latt, Wellesley College (United States)
Angela Morrison, Albion College (United States)
Alison Radgowski, Goucher College (United States)
Joseph Tobin, Univ. of Virginia (United States)
Mark Iwen, Michigan State Univ. (United States)
Aditya Viswanathan, Univ. of Michigan, Dearborn (United States)

Published in SPIE Proceedings Vol. 10394:
Wavelets and Sparsity XVII
Yue M. Lu; Dimitri Van De Ville; Manos Papadakis, Editor(s)

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