A particular directional multilevel transform based method for single-image rain removal

Abstract

In this work, the wavelet based sparse optimization approach is introduced to process rain removal problem from a single image by considering the direction and shape of rain streaks. Firstly, a new kind of wavelet, the uni-directional multilevel system is construct to describe the singularities of noisy in particular direction and scales, like rain streaks and stripes in radar images. Compared with total variation, the uni-directional multilevel transform of rainy images gives the sparse representation of singularities in different scales and frequency bands due to its multiscale structure, which includes more rain details. Secondly, a convex optimization rain removal model is proposed by considering the intrinsic directional and structure information of the rain streak and the background image. The model involves three sparse priors, including the sparse regularizer on rain streaks and two sparse regularizers on the uni-directional multilevel transform of background layer in the rain drop’s direction and the multilevel transform of rain streaks across the rain direction. The split Bregman algorithm is utilized to solve the proposed convex optimization model which ensures the global optimal solution. Thirdly, comparison tests with four stat-of-the-art methods are implemented on synthetic and real rainy images, which suggests that the proposed method is efficient both in rain removal and details preservation of the background layer.