Single image super resolution based on sparse representation via structurally directional dictionaries

ABSTRACT: In this thesis, we propose an algorithm of sparse representation using structurally directional dictionaries to super resolve a single low resolution input image. We have focused on the designing structured dictionaries for different clusters of patches instead of a global dictionary for all the patches. Due to highly directional nature of image content, designing structurally directional dictionaries promises to better capture the intrinsic image characteristics. Furthermore, designing multiple dictionaries with smaller sizes leads to less computational complexity. The proposed algorithm is based on dictionary learning in the spatial domain. In order to design dictionaries the K-SVD algorithm is used and for this purpose for each of the structured dictionaries a structured training set is prepared. In order to classify the patches into different data sets, a set of templates are designed and each patch is clustered using template matching. Each and every of the templates is modeled according to a specific direction. Then using a similarity measurement, the HR patches and the corresponding features (LR patches) are clustered into directional clusters. Then structurally directional dictionaries are learned by employing the structured training clusters via the K-SVD algorithm. For every cluster two dictionaries are designed: one for the HR patches and the other one for the features. In the reconstruction part, a LR input image comes in and all the features are coded sparsely with the most suitable directional LR dictionary; and the sparse coding coefficients are then used together with the corresponding HR dictionary to reconstruct the HR patch. In order to choose the best dictionary in sense of direction, a dictionary selection model is needed. Many approaches are tried to find the best dictionary selection method which are mostly error based. But it is not an easy issue while the LR patches (features) are the main criteria to select the most appropriate HR dictionary; it does not always yield to correct selection. However the core idea of the proposed method, designing structurally directional dictionaries, is demonstrated to have superior results compared to the state-of-the-art algorithm proposed by R. Zeyde et.al [23], both visually and quantitatively with an average of 0.2 dB improvements in PSNR over Kodak set and some bench mark images. Keywords: super resolution, sparse representation, structurally directional dictionary. …………………………………………………………………………………………………………………………