62 research outputs found

    Deterministic Sampling of Sparse Trigonometric Polynomials

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    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

    Explicit universal sampling sets in finite vector spaces

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    In this paper we construct explicit sampling sets and present reconstruction algorithms for Fourier signals on finite vector spaces GG, with G=pr|G|=p^r for a suitable prime pp. The two sets have sizes of order O(pt2r2)O(pt^2r^2) and O(pt2r3log(p))O(pt^2r^3\log(p)) respectively, where tt is the number of large coefficients in the Fourier transform. The algorithms approximate the function up to a small constant of the best possible approximation with tt non-zero Fourier coefficients. The fastest of the algorithms has complexity O(p2t2r3log(p))O(p^2t^2r^3\log(p))

    Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform

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    Sketching via hashing is a popular and useful method for processing large data sets. Its basic idea is as follows. Suppose that we have a large multi-set of elements S=[formula], and we would like to identify the elements that occur “frequently" in S. The algorithm starts by selecting a hash function h that maps the elements into an array c[1…m]. The array entries are initialized to 0. Then, for each element a ∈ S, the algorithm increments c[h(a)]. At the end of the process, each array entry c[j] contains the count of all data elements a ∈ S mapped to j

    Sparse 2D Fast Fourier Transform

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    Publication in the conference proceedings of SampTA, Bremen, Germany, 201
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