We obtain new quasi-interpolators for continuous reconstruction of sampled images by minimizing a new objective function that takes into account the approximation error over the full Nyquist interval. To achieve this goal, we optimize with respect to all possible degrees of freedom in the approximation scheme. We consider three study cases offering different trade-offs between quality and computational cost: a linear, a quadratic, and a cubic scheme. Experiments with compounded rotations and translations confirm that our new quasi-interpolators perform better than the state-of-the-art for a similar computational cost.