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arXiv · 1507.06849

Explicit universal sampling sets in finite vector spaces

Lucia Morotti
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Abstract

In this paper we construct explicit sampling sets and present reconstruction algorithms for Fourier signals on finite vector spaces $G$, with $|G|=p^r$ for a suitable prime $p$. The two sets have sizes of order $O(pt^2r^2)$ and $O(pt^2r^3\log(p))$ respectively, where $t$ is the number of large coefficients in the Fourier transform. The algorithms approximate the function up to a small constant of the best possible approximation with $t$ non-zero Fourier coefficients. The fastest of the algorithms has complexity $O(p^2t^2r^3\log(p))$.

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Lucia Morotti. 2016-05-18. Explicit universal sampling sets in finite vector spaces. https://doi.org/10.1016/j.acha.2016.06.001

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