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arXiv · 1411.5610

Nonuniform Sampling and Recovery of Bandlimited Functions in Higher Dimensions

Keaton Hamm
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Abstract

We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider interpolation of functions whose Fourier transform is supported in some small ball in $\mathbb{R}^d$ at scattered points $(x_j)_{j\in\mathbb{N}}$ such that the complex exponentials $\left(e^{-i\langle x_j,\cdot\rangle}\right)_{j\in\mathbb{N}}$ form a Riesz basis for the $L_2$ space of a convex body containing the ball. Recovery results as well as corresponding approximation orders in terms of the parameter $\alpha$ are obtained.

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Keaton Hamm. 2014-11-20. Nonuniform Sampling and Recovery of Bandlimited Functions in Higher Dimensions. https://doi.org/10.1016/j.jmaa.2017.01.099

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