We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the Landweber-Richardson method are proposed, that determine the ``optimal'' reconstruction level a posteriori from quantities that arise during the numerical calculations. As an important example we discuss the reconstruction of band-limited signals from irregularly spaced noisy samples, when the actual bandwidth of the signal is not available. Numerical examples show the usefulness of the proposed algorithms.
Keywords: algorithms, irregular sampling, numerical work, moment
problems, frames, regularization
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