Gabor Analysis and Algorithms: Theory and Applications
Gabor Analysis and Algorithms: Theory and Applications
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Foundations of Computational Mathematics
Combinatorial Sublinear-Time Fourier Algorithms
Foundations of Computational Mathematics
Lower bounds on the maximum cross correlation of signals (Corresp.)
IEEE Transactions on Information Theory
Bounds on crosscorrelation and autocorrelation of sequences (Corresp.)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
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One can recover sparse multivariate trigonometric polynomials from a 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 with |X| a prime number greater than (MlogD)^2. This result is optimal within the (logD)^2 factor. The simulations show that the deterministic sampling can offer reconstruction performance similar to the random sampling.