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Despite the fact that great progress has been made on single image deraining tasks, it is still challenging for existing models to produce satisfactory results directly, and it often requires a single or multiple refinement stages to gradually improve the quality. However, in this paper, we demonstrate that existing image-level refinement with a stage-independent learning design is problematic with the side effect of over/under-deraining. To resolve this issue, we for the first time propose the mechanism of learning to carry out refinement on the unsatisfactory features, and propose a novel attentive feature refinement (AFR) module. Specifically, AFR is designed as a two-branched network for simultaneous rain-distribution-aware attention map learning and attention guided hierarchy-preserving feature refinement. Guided by task-specific attention, coarse features are progressively refined to better model the diversified rainy effects. By using a separable convolution as the basic component, our AFR module introduces little computation overhead and can be readily integrated into most rainy-to-clean image translation networks for achieving better deraining results. By incorporating a series of AFR modules into a general encoder-decoder network, AFR-Net is constructed for deraining and it achieves new state-of-the-art results on both synthetic and real images. Furthermore, by using AFR-Net as a teacher model, we explore the use of knowledge distillation to successfully learn a student model that is also able to achieve state-of-the-art results but with a much faster inference speed (i.e., it only takes 0.08 second to process a $512\times 512$ rainy image). Code and pre-trained models are available at $\langle $ https://github.com/RobinCSIRO/AFR-Net $\rangle $. [ABSTRACT FROM AUTHOR]

A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved analytically in term of their canonical dual solutions. The existence and uniqueness of these analytical solutions are proved. NP-hardness of the knapsack problems is discussed. A powerful CDT algorithm combined with an alternative iteration and a volume reduction method is proposed for solving the NP-hard bilevel knapsack problems. Application is illustrated by benchmark problems in optimal topology design. The performance and novelty of the proposed method are compared with the popular commercial codes. [ABSTRACT FROM AUTHOR]