Abstract:We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere S d−1 using a near-optimal number of function evaluations. We show that for any f ∈ L 2 (S d−1 ), the number of evaluations of f needed to recover its degree-q spherical harmonic expansion equals the dimension of the space of spherical harmonics of degree at most q up to a logarithmic factor. Moreover, we develop a simple yet efficient algorithm to recover degree-q expansion of … Show more
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