On Reconstruction from Non-uniform Spectral Data

Authors:
Adityavikram Viswanathan;Anne Gelb;Douglas Cochran;Rosemary Renaut
Affiliations:
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, USA 85287-5706;School of Mathematical and Statistical Sciences, Arizona State University, Tempe, USA 85287-1804;School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, USA 85287-5706;School of Mathematical and Statistical Sciences, Arizona State University, Tempe, USA 85287-1804
Venue:
Journal of Scientific Computing
Year:
2010

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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.