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• W1939462249 abstract "We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available." @default.
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• W1939462249 date "2015-12-01" @default.
• W1939462249 modified "2023-10-02" @default.
• W1939462249 title "A Novel Sampling Theorem on the Rotation Group" @default.
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• W1939462249 doi "https://doi.org/10.1109/lsp.2015.2490676" @default.
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