We propose and state a novel scheme for image magnification. It is formulated as a minimization problem which incorporates a data fidelity and a regularization term. Data fidelity is modeled using a wavelet transformation operator while the Total Generalized Variation functional of second order is applied for regularization. Well-posedness is obtained in a function space setting and an efficient numerical algorithm is developed. Numerical experiments confirm a high quality of the magnified images. In particular, with an appropriate choice of wavelets, geometrical information is preserved.