Outdoor imaging often suffers from the negative effects of the rain streaks, which would lead to the distortion of image contents. Most of the existing deraining approaches propose to build prior models to formulate the appearance of rain streaks and image features. However, these works deal with the rain streaks removal on the whole image regions. This may lead to the image regions without rain streaks distorted. In this paper, we proposed a new method for simultaneously investigating the candidates of rain streaks and image restoration. We use the L0 sparsity regularization for rain region estimation , and apply the framelet with L0 norm to protect the sharpen images. Our method only processes the regions with rain streaks and leaves other regions free. Experimental results demonstrate the effectiveness of our approach on rain streak removal and image restoration.
Images are often corrupted by impulse noise due to transmission errors, malfunctioning pixel elements in camera sensors, faulty memory locations in the imaging process. This paper proposes a new method for removing the mixed impulse noise and gaussian noise. The proposed method has two-phase, and the first phase is to identify candidate pixels existing impulse noise by using median filtering. The second phase processes the regions with impulse noise and leaves the others free with a mask generated by the previous phase. In order to protect the sharp image, we propose a L0 regularized framelet with a L1 fidelity term to recover the images. Numerical results demonstrate that the proposed method is a significantly advance over several state-of-the-art techniques on restoration performance.