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The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions. We assume that the reconstruction subspace reproduces polynomials up to a certain degree. We then derive a lower bound on the sum of supports of its generators. Finally, we illustrate the tightness of our bound with some examples.
Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos
Xavier Fernandez-Real Girona, Riccardo Tione