ИСТИНА

The assumption of uniform motion and blur kernel in multi-frame L2-L2 super-resolution (SR) leads to special structure matrices in problem formulation. This structure allows us to reduce the original SR problem to several simpler problems. Detailed proofs are provided for 1D and 2D case. Explicit formulae of transforms are also given. Results are extended to the super-resolution problem from Bayer images (joint demosaicing and super-resolution). Proofs are carried out in the unified manner based on properties of multi-level matrices. Obtained results allow to solve SR problem with complexity $\mathcal{O}\left(n^2s^4\right) + \mathcal{O}\left(n^2\log n\right)$ instead of $\mathcal{O}\left(n^6\right)$ (for magnification factor $s$ and output images of size $n\times n$). Also the special structure of matrices allows us to reduce the solution of a certain set of problems to the solution of the only one problem. Such relations between problems are also considered in this article.