Minimax sampling with arbitrary spaces [signal sampling and reconstruction]

We consider non-ideal sampling and reconstruction schemes in which the sampling and reconstruction spaces as well as the input signal can be arbitrary. To obtain a good reconstruction of the signal in the reconstruction space, from arbitrary samples, we suggest processing the samples prior to reconstruction with a linear transformation that is designed to minimize the worst-case squared-norm error between the reconstructed signal, and the best possible (but usually unattainable) approximation of the signal in the reconstruction space. We show both theoretically and through a simulation that if the input signal does not lie in the reconstruction space, then this method can outperform the consistent reconstruction method previously proposed for this problem.