Utilizing homotopy for single image superresolution

Learning an appropriate dictionary is a critical issue for sparse representation based super-resolution algorithms. A good dictionary can well represent an underlying image. In super-resolution algorithms, classical dictionary learning doesn´t consider the information of test image which contains the information of the reconstructed image. In this paper, the new dictionary is design for image super-resolution, incorporating both training image patches and test image patches for training. It is important for dictionary learning to adaptively choose the training image patches and test image patches which effectively represent the reconstructed image structures. In the new learning strategy, a homotopy method is applied to choose the parameter that yields a proper balance between the use of training image patches and test image patches. The homotopy method is used to track the homotopy path leading to the solution to the desired problem at the terminal point. Compared with other state-of-the-art learning methods, our algorithm learns an over-complete dictionary by exploiting the information of the given test image and training images. The experimental results show that the proposed method is able to achieve better experimental results in terms of both PSNR and visual perception.