It is widely acknowledged that single image super resolution(SISR) methods play a critical role in recovering the missing high-frequencies in an input low-resolution (LR) image.As SISR is severely ill-conditioned, image priors are necessary to regularize the solution spaces and generate the corresponding high-resolution (HR) image. In this paper, we propose an effective SISR framework based on the enhanced non-local similarity modeling and learning-based multi-directional feature prediction(ENLTV-MDFP). Since both the modeled and learned priors are exploited, the proposed ENLTV-MDFP method benefits from the complementary properties of the reconstruction-based and learning-based SISR approaches. Specifically, for the nonlocal similarity based modeled prior (enhanced non-local total variation, ENLTV), it is characterized via the decaying kernel(DK) and stable group similarity reliability (SGSR) schemes.For the learned prior (multi-directional feature prediction prior,MDFP), it is learned via the deep convolutional neural network(CNN). The modeled prior performs well in enhancing edges and suppressing visual artifacts, while the learned prior is effective in hallucinating details from external images. Combining these two complementary priors in the MAP framework, a combined SR cost function is proposed. Finally, the combined SR problem is solved via the split Bregman iteration (SBI) algorithm.Based on the extensive experiments, the proposed ENLTV-MDFP method outperforms many state-of-the-art algorithms visually and quantitatively.
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