Transform-invariant group-sparse regularization with directional total variation is an efficient method to solve the super-resolution problem in the regions with highly structured straight edges which is deformed from the real urban scenes and space scenes. Total variation

however

probably leads to staircase artifacts

which may affect the result of super-resolution to large extent. In this paper

we present a new method by mixing different regularizers

especially by combining wavelet analysis with the Transform invariant directional total variation objective function. This allows us to simultaneously recover textures and local geometry structures

particularly highly structured straight edges. To solve this hybrid regularization problem with different norms

we used the idea of templates for first-order conic solvers

and derived the solution of the whole object function that we proposed. Experiments on same real image collections show that our method is more effective than prior works.