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REDUCED CONSISTENCY SAMPLING IN HILBERT SPACES

We present a new approach for the problem of reconstructing an element of a Hilbert space in an arbitrary reconstruction basis given its measurements with respect to certain sampling vectors. This procedure differs from more standard techniques in that it is not consistent: the samples of the reconstructed function are not equal to those of the original function. However, by dropping this requirement, we are able to obtain a method that is both numerically stable and which provides a reconstruction that is closer to optimal. Keywords— Sampling theory, Riesz bases, finite sections