Abstract
This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. Finally, we provide preliminary results from employing spectral re-projection methods in the reconstruction.
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In memory of David Gottlieb, beloved teacher, scholar, and friend. His pioneering work in spectral methods and in particular in resolving the Gibbs phenomenon has had a profound influence on this research.
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Viswanathan, A., Gelb, A., Cochran, D. et al. On Reconstruction from Non-uniform Spectral Data. J Sci Comput 45, 487–513 (2010). https://doi.org/10.1007/s10915-010-9364-3
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DOI: https://doi.org/10.1007/s10915-010-9364-3