Single image super resolution by ℓ₂ approximation with random sampled dictionary

In this paper, we propose an example-based single image super resolution (SR) method by ℓ₂ approximation with self-sampled image patches. Example-based super resolution methods can reconstruct high resolution image patches by a linear combination of atoms in an overcomplete dictionary. This reconstruction requires a pair of two dictionaries created by tremendous low and high resolution image pairs from the prepared image databases. In our method, we introduce the dictionary by random sampling patches from just an input image and eliminate its training process. This dictionary exploits the self-similarity of images and it will no more depend on external image sets, which consern the storage space or the accuracy of referred image sets. In addition, we modified the approximation of input image to an ℓ₂-norm minimization problem, instead of commonly used sparse approximation such as.1-norm regularization. The ℓ₂ approximation has an advantage of computational cost by only solving an inverse problem. Through some experiments, the proposed method drastically reduces the computational time for the SR, and it provides a comparable performance to the conventional example-based SR methods with an.1 approximation and dictionary training.