Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Sampling of Sparse Trigonometric Polynomials   We study the problem of reconstructing a multivariate trigonometric
polynomial having only few non-zero coefficients from few random samples.
Inspired by recent work of Candes, Romberg and Tao we propose to recover the
polynomial by Basis Pursuit, i.e., by $\ell^1$-minimization. Numerical
experiments show that in many cases the trigonometric polynomial can be
recovered exactly provided the number $N$ of samples is high enough compared to
the ``sparsity'' -- the number of non-vanishing coefficients. However, $N$ can
be chosen small compared to the assumed maximal degree of the trigonometric
polynomial. Hence, the proposed scheme may overcome the Nyquist rate. We
present two theorems that explain this observation. Unexpectly, they establish
a connection to an interesting combinatorial problem concerning set partitions,
which seemingly has not yet been considered before.

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The categories of this paper are: eess
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex