Deterministic Sampling of Sparse Trigonometric Polynomials

Details Deterministic Sampling of Sparse Trigonometric Polynomials Deterministic Sampling of Sparse Trigonometric Polynomials

2010-06-11

arxiv.org/abs/1006.2221v2

Mathematics

Numerical Analysis

9 pages

Scientific paper

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 $(M\log D)^2$. This result is almost optimal within the $(\log D)^2 $ factor. The simulations show that the deterministic sampling can offer reconstruction performance similar to the random sampling.

Affiliated with

Also associated with

No associations

Rating

Deterministic Sampling of Sparse Trigonometric Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deterministic Sampling of Sparse Trigonometric Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deterministic Sampling of Sparse Trigonometric Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-77071