Recovering Exponential Accuracy from Non-harmonic Fourier Data Through Spectral Reprojection
| Autor: | Taylor Hines, Anne Gelb |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Applied Mathematics Mathematical analysis General Engineering Reprojection error Harmonic (mathematics) Function (mathematics) Theoretical Computer Science Exponential function Gibbs phenomenon Computational Mathematics symbols.namesake Quality (physics) Fourier transform Computational Theory and Mathematics Sampling (signal processing) symbols Algorithm Software Mathematics |
| Zdroj: | Journal of Scientific Computing. 51:158-182 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-011-9502-6 |
| Popis: | Spectral reprojection techniques make possible the recovery of exponential accuracy from the partial Fourier sum of a piecewise-analytic function, essentially conquering the Gibbs phenomenon for this class of functions. This paper extends this result to non-harmonic partial sums, proving that spectral reprojection can reduce the Gibbs phenomenon in non-harmonic reconstruction as well as remove reconstruction artifacts due to erratic sampling. We are particularly interested in the case where the Fourier samples form a frame. These techniques are motivated by a desire to improve the quality of images reconstructed from non-uniform Fourier data, such as magnetic resonance (MR) images. |
| Databáze: | OpenAIRE |
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