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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/







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