Journal article
Optimized Least-Square Nonuniform Fast Fourier Transform
IEEE transactions on signal processing, Vol.57(6), pp.2165-2177
2009
DOI: 10.1109/TSP.2009.2014809
Abstract
The main focus of this paper is to derive a memory efficient approximation to the nonuniform Fourier transform of a support limited sequence. We show that the standard nonuniform fast Fourier transform (NUFFT) scheme is a shift invariant approximation of the exact Fourier transform. Based on the theory of shift-invariant representations, we derive an exact expression for the worst-case mean square approximation error. Using this metric, we evaluate the optimal scale-factors and the interpolator that provides the least approximation error. We also derive the upper-bound for the error component due to the lookup tablebased evaluation of the interpolator; we use this metric to ensure that this component is not the dominant one. Theoretical and experimental comparisons with standard NUFFT schemes clearly demonstrate the significant improvement in accuracy over conventional schemes, especially when the size of the uniform fast Fourier transform (FFT) is small. Since the memory requirement of the algorithm is dependent on the size of the uniform FFT, the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands.
Details
- Title: Subtitle
- Optimized Least-Square Nonuniform Fast Fourier Transform
- Creators
- Mathews JACOB - Department of Biomedical Engineering, University of Rochester, NY 14622, United States
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on signal processing, Vol.57(6), pp.2165-2177
- Publisher
- Institute of Electrical and Electronics Engineers; New York, NY
- DOI
- 10.1109/TSP.2009.2014809
- ISSN
- 1053-587X
- eISSN
- 1941-0476
- Language
- English
- Date published
- 2009
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Electrical and Computer Engineering; Radiology; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070410402771
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