  Sparse representation with training-based dictionary has been shown
successful on super resolution(SR) but still have some limitations. Based on
the idea of making the magnification of function curve without losing its
fidelity, we proposed a function based dictionary on sparse representation for
super resolution, called hybrid function sparse representation (HFSR). The
dictionary we designed is directly generated by preset hybrid functions without
additional training, which can be scaled to any size as is required due to its
scalable property. We mixed approximated Heaviside function (AHF), sine
function and DCT function as the dictionary. Multi-scale refinement is then
proposed to utilize the scalable property of the dictionary to improve the
results. In addition, a reconstruct strategy is adopted to deal with the
overlaps. The experiments on Set14 SR dataset show that our method has an
excellent performance particularly with regards to images containing rich
details and contexts compared with non-learning based state-of-the art methods.
