# Deterministic Sampling of Sparse Trigonometric Polynomials - Mathematics > Numerical Analysis

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Abstract: One can recover sparse multivariate trigonometric polynomials from fewrandomly taken samples with high probability as shown by Kunis and Rauhut. Wegive a deterministic sampling of multivariate trigonometric polynomialsinspired by Weil-s exponential sum. Our sampling can produce a deterministicmatrix satisfying the statistical restricted isometry property, and also nearlyoptimal Grassmannian frames. We show that one can exactly reconstruct every\$M\$-sparse multivariate trigonometric polynomial with fixed degree and oflength \$D\$ from the determinant sampling \$X\$, using the orthogonal matchingpursuit, and \$# X\$ is a prime number greater than \$M\log D^2\$. This result isalmost optimal within the \$\log D^2 \$ factor. The simulations show that thedeterministic sampling can offer reconstruction performance similar to therandom sampling.

Autor: Zhiqiang Xu

Fuente: https://arxiv.org/