It is difficult to design an effective image super-resolution model and algorithm that can preserve the geometric structures and texture.Two incoherent geometry and texture sub-dictionaries are constructed

which can provide sparse representations of geometry and texture structures respectively.Thus

a multi-morphology sparse representation model is established.Furthermore

a convex variational model is proposed for multi-frame image super-resolution with multi-morphology sparsity regularization.The regularization term constrains the underlying image to have a sparse representation in a multi-component dictionary.The fidelity term restricts the consistency with the measured image in terms of the data degradation model.An alternate minimization iteration algorithm is proposed to solve it numerically and proximal forward-backward operator splitting method is adopted for each sub-problem.Numerical experiments for optics and infrared images are presented and the experimental results demonstrate that our super-resolution model and numerical algorithm are both effective.