Superfast superresolution

We propose a fast algorithm for solving the inverse problem of resolution enhancement (superresolution). Robustness is achieved by a non-linear regularizer and a method based on variable splitting is used to obtain an equivalent linear formulation. Special attention is paid to fast implementation using the Fourier transform. In particular, we show that a degradation operator (downsampling) can be implemented in the frequency domain and that all computations can be performed very efficiently without losing robustness. To our knowledge, this is the first attempt towards a very fast SR algorithm, which retains favorable edge-preserving properties of non-linear regularizers.