The problem of computing a single super-resolved image from multiple shifted images of the same scene has been addressed in several ways in the literature, with different levels of assumptions on the image to reconstruct, but a frequent core step is the resolution of the linear system derived from the image formation model. We here propose a detailed description of a direct (non-iterative) algorithm that computes the least-squares solution of the super-resolution problem in the general case of possibly non-integer super-resolution factors. We also provide a detailed analysis of the reconstruction error, both in the image and Fourier domains. In order to handle potential outliers, we build a robust (L1) variant of the algorithm, and illustrate its efficiency on synthetic and real data. We finally show how this linear and well-controlled process can be supplemented with a simple (still linear) spectral enhancement filter in order to better reveal super-resolved details without creating artifacts.