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Deterministic Sampling of Sparse Trigonometric Polynomials

Abstract

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 MM-sparse multivariate trigonometric polynomial with fixed degree and of length DD from the determinant sampling XX, using the orthogonal matching pursuit, and # X is a prime number greater than (MlogD)2(M\log D)^2. This result is almost optimal within the (logD)2(\log D)^2 factor. The simulations show that the deterministic sampling can offer reconstruction performance similar to the random sampling.Comment: 9 page

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