We present an effective semi-supervised learning algorithm for single image dehazing. The proposed algorithm applies a deep Convolutional Neural Network (CNN) containing a supervised learning branch and an unsupervised learning branch. In the supervised branch, the deep neural network is constrained by the supervised loss functions, which are mean squared, perceptual, and adversarial losses. In the unsupervised branch, we exploit the properties of clean images via sparsity of dark channel and gradient priors to constrain the network. We train the proposed network on both the synthetic data and real-world images in an end-to-end manner. Our analysis shows that the proposed semi-supervised learning algorithm is not limited to synthetic training datasets and can be generalized well to real-world images. Extensive experimental results demonstrate that the proposed algorithm performs favorably against the state-of-the-art single image dehazing algorithms on both benchmark datasets and real-world images.

Stripe and random noise are two different degradation phenomena that commonly coexist in optical remote sensing images, and they are often modeled as inverse problems. In model-based inverse problems, analysis and synthesis sparse representations (SSRs) are used as regularization terms to obtain approximate solutions due to their respective merits, i.e., the nonzero coefficients in SSR are usually used to describe an image, while the indexes of zeros in analysis sparse representation (ASR) are used to characterize the stripe. Inspired by these merits, we propose a unified variational framework, called a joint analysis and weighted synthesis (JAWS) sparsity model, to simultaneously separate the clean image and the stripe from a single optical remote sensing image. To solve the JAWS sparsity model efficiently, an alternating minimization optimization strategy is first employed to separate it into two subproblems that are used for different tasks. One called as weighted SSR (WSSR) is the main for optical remote sensing image denoising, which can be effectively solved by employing the weighted singular value thresholding operator, while the other called as ASR is the main approach for optical remote sensing image destriping, which is optimized by adopting the split Bregman iteration. By minimizing the two subproblems alternatively, the proposed JAWS sparsity model is efficiently solved. Finally, both quantitative and qualitative results of experiments on synthetic and real-world optical remote sensing images validate that the proposed approach is effective and even better than the state of the arts.