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Deterministic Sampling of Sparse Trigonometric Polynomials
One can recover sparse multivariate trigonometric polynomials from few
randomly taken samples with high probability (as shown by Kunis and Rauhut). We
give a deterministic sampling of multivariate trigonometric polynomials
inspired by Weil's exponential sum. Our sampling can produce a deterministic
matrix satisfying the statistical restricted isometry property, and also nearly
optimal Grassmannian frames. We show that one can exactly reconstruct every
-sparse multivariate trigonometric polynomial with fixed degree and of
length from the determinant sampling , using the orthogonal matching
pursuit, and # X is a prime number greater than . This result is
almost optimal within the factor. The simulations show that the
deterministic sampling can offer reconstruction performance similar to the
random sampling.Comment: 9 page
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