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Efficient Calculations of 3-D FFTs on Spiral Contours

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Abstract

This paper proposes a fast algorithm, called the SpiralFFT, that computes samples of the 3-D discrete Fourier transform of an object of interest along spiral contours in frequency space. This type of sampling geometry is prevalent in 3-D magnetic resonance imaging, as spiral sampling patterns allow for rapid, uninterrupted scanning over a large range of frequencies. We show that parameterizing the spiral contours in a certain way allows us to decompose the computation into a series of 1-D transforms, meaning that the 3-D transform is effectively separable, while still yielding spiral sampling patterns that are geometrically faithful and provide dense coverage of 3-D frequency space. We present a number of simulations which demonstrate that the SpiralFFT compares favorably to a state-of-the-art algorithm for computing general non-uniform discrete Fourier transforms.

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Correspondence to Christopher K. Turnes.

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This work was partially supported by a Packard Fellowship.

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Turnes, C.K., Romberg, J. Efficient Calculations of 3-D FFTs on Spiral Contours. J Sci Comput 50, 610–628 (2012). https://doi.org/10.1007/s10915-011-9534-y

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  • DOI: https://doi.org/10.1007/s10915-011-9534-y

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