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Accurate registration is critical to most multi-channel signal processing setups, including image super-resolution. In this paper we use modern sampling theory to propose a new robust registration algorithm that works with arbitrary sampling kernels. The algorithm accurately approximates continuous-time Fourier coefficients from discrete-time samples. These Fourier coefficients can be used to construct an over-complete system, which can be solved to approximate translational motion at around 100-th of a pixel accuracy. The over-completeness of the system provides robustness to noise and other modelling errors. For example we show an image registration result for images that have slightly different backgrounds, due to a viewpoint translation. Our previous registration techniques, based on similar sampling theory, can provide a similar accuracy but not under these more general conditions. Simulation results demonstrate the accuracy and robustness of the approach and demonstrate the potential applications in image super-resolution.