Fast reconstruction from non-uniform samples in shift-invariant spaces

We propose a new approach for signal reconstruction from non-uniform samples, without constraints on their locations. We look for a function that belongs to a linear shift-invariant space and minimizes a variational criterion that is a weighted sum of a least-squares data term and a quadratic term penalizing the lack of smoothness. This leads to a resolution-dependent solution, that can be computed exactly by a fast non-iterative algorithm.