Multi-directional rain streak removal based on infimal convolution of oscillation TGV

Image deraining is essential in both image processing and computer vision. However it is still challenging to remove rain streaks, due to the fact that they are complex and usually have multiple directions. In this paper, we propose a novel infimal convolution type functional based model to remove multi-directional rain streaks. Specifically, we employ total generalized variation (TGV) to represent the rain-free background and m-fold infimal convolution of oscillation TGV (ICTGVmosci) to capture the rain streaks with m different directions. The existence of solutions to the proposed model is proved. We also design an algorithm using the classical first-order Primal–Dual method for solving the proposed model. Numerical experiments on both synthetic and real images demonstrate that the proposed model outperforms the state-of-the-art methods quantitatively and qualitatively.