The problem of increasing spatial resolution from Bayer images is considered. It is solved locally at each point of the unknown high-resolution image. In each local neighbourhood, subpixel warp and blur kernel are assumed to be the same, which makes it possible to reduce the computational complexity from (n⁶) to (n²logn). A detailed description of the algorithm and its proof using the apparatus of multilevel matrices are provided. The relation between solutions of the SR problem with different warping parameters is also studied, and it is proven that certain solutions can be derived from solutions with other parameters by using simple transforms. This makes it possible to reduce the amount of memory used for storing filters within a filter bank approach up to 80 times (2× magnification, 3 input frames).