Volume 31, pp. 30-39, 2008.

Stability results for scattered data interpolation on the rotation group

Manuel Gräf and Stefan Kunis

Abstract

Fourier analysis on the rotation group SO(3) expands each function into the orthogonal basis of Wigner-D functions. Recently, fast and reliable algorithms for the evaluation of finite expansion of such type, referred to as nonequispaced FFT on SO(3), have become available. Here, we consider the minimal norm interpolation of given data by Wigner-D functions. We prove bounds on the conditioning of this problem which rely solely on the number of Fourier coefficients and the separation distance of the sampling nodes. The reconstruction of N3 Fourier coefficients from M well separated samples is shown to take only O(N3log2N+M) floating point operations.

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Key words

Scattered data interpolation, iterative methods, FFT.

AMS subject classifications

65T50, 65F10, 43A75, 41A05, 15A60.