Transductive Regression with Local and Global Consistency for Image Super-Resolution

In this paper, we propose a novel image super-resolution algorithm, referred to as interpolation based on transductive regression with local and global consistency (TRLGC). Our algorithm first constructs a set of local interpolation models which can predict the intensity labels of all image samples, and a loss term will be minimized to keep the predicted labels of available low-resolution (LR) samples sufficiently close to the original ones. Then, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples. Furthermore, a graph-Laplacian based manifold regularization term is incorporated to penalize the global smoothness of intensity labels, such smoothing can alleviate the insufficient training of the local models and make them more robust. Finally, we construct a unified objective function to combine together the accumulated loss of the locally linear regression, square error of prediction bias on the available LR samples and the manifold regularization term, which could be solved with a closed-form solution as a convex optimization problem. In this way, a transductive regression algorithm with local and global consistency is developed. Experimental results on benchmark test images demonstrate that the proposed image super-resolution method achieves very competitive performance with the state-of-the-art algorithms.