In this paper, we present a new method for signal reconstruction from multiple sets of samples with unknown offsets which can be written as a set of polynomial equations in both the unknown signal coefficients and the offsets. The solution can then be computed using Groebner bases. In any practical setting, the samples are corrupted by noise, and then there is no algebraic solution. Thus, the next step is to address this noisy version of the problem, and to show how a good approximation can be obtained from multiple Groebner bases for subsets of samples. This provides us with an elegant solution method for the initial nonlinear problem. We show two examples for the reconstruction of polynomial signals and Fourier series.
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