62 research outputs found
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
Explicit universal sampling sets in finite vector spaces
In this paper we construct explicit sampling sets and present reconstruction
algorithms for Fourier signals on finite vector spaces , with for
a suitable prime . The two sets have sizes of order and
respectively, where 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 non-zero Fourier
coefficients. The fastest of the algorithms has complexity
Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform
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
Publication in the conference proceedings of SampTA, Bremen, Germany, 201
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