Deterministic Sampling of Sparse Trigonometric Polynomials
نویسنده
چکیده
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 M -sparse multivariate trigonometric polynomial with fixed degree and of length D from the determinant sampling X, using the orthogonal matching pursuit, and |X| is a prime number greater than (M logD). This result is optimal within the (logD) factor. The simulations show that the deterministic sampling can offer reconstruction performance similar to the random sampling.
منابع مشابه
Reconstruction of sparse Legendre and Gegenbauer expansions
Recently the reconstruction of sparse trigonometric polynomials has attained much attention. There exist recovery methods based on random sampling related to compressed sensing (see e.g. [17, 10, 5, 4] and the references therein) and methods based on deterministic sampling related to Prony–like methods (see e.g. [15] and the references therein). Both methods are already generalized to other pol...
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عنوان ژورنال:
- J. Complexity
دوره 27 شماره
صفحات -
تاریخ انتشار 2011