  Recently, it has been observed that a sparse trigonometric polynomial, i.e.
having only a small number of non-zero coefficients, can be reconstructed
exactly from a small number of random samples using Basis Pursuit (BP) or
Orthogonal Matching Pursuit (OMP). In the present article it is shown that
recovery by a BP variant is stable under perturbation of the samples values by
noise. A similar partial result for OMP is provided. For BP in addition, the
stability result is extended to (non-sparse) trigonometric polynomials that can
be well-approximated by sparse ones. The theoretical findings are illustrated
by numerical experiments.
