  We introduce a novel deep-learning architecture for image upscaling by large
factors (e.g. 4x, 8x) based on examples of pristine high-resolution images. Our
target is to reconstruct high-resolution images from their downscale versions.
The proposed system performs a multi-level progressive upscaling, starting from
small factors (2x) and updating for higher factors (4x and 8x). The system is
recursive as it repeats the same procedure at each level. It is also residual
since we use the network to update the outputs of a classic upscaler. The
network residuals are improved by Iterative Back-Projections (IBP) computed in
the features of a convolutional network. To work in multiple levels we extend
the standard back-projection algorithm using a recursion analogous to
Multi-Grid algorithms commonly used as solvers of large systems of linear
equations. We finally show how the network can be interpreted as a standard
upsampling-and-filter upscaler with a space-variant filter that adapts to the
geometry. This approach allows us to visualize how the network learns to
upscale. Finally, our system reaches state of the art quality for models with
relatively few number of parameters.
