Image super-resolution via sparse representation

This thesis presents a new approach to single-image super-resolution (SR), based on sparse signal recovery. Research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary. Inspired by this observation, we seek a sparse representation for each patch of the low-resolution input, and then use the coefficients of this representation to generate the high-resolution output. Theoretical results from compressed sensing suggest that under mild conditions, the sparse representation can be correctly recovered from the downsampled signals. By jointly training two dictionaries for the low- and high-resolution image patches, we can enforce the similarity of sparse representations between the low- and high-resolution image patch pairs with respect to their own dictionaries. Therefore, the sparse representation of a low-resolution image patch can be applied with the dictionary of high-resolution image patches to generate a high-resolution image patch. Compared to previous approaches, which simply sample a large amount of raw image patch pairs, the learned dictionary pair is a more compact representation of the patch pairs, and, therefore, reduces the computation cost substantially. The effectiveness of such a sparsity prior is demonstrated on both general image super-resolution and the special case of face hallucination. In both cases, our algorithm can generate high-resolution images that are competitive or superior in quality to images produced by other similar SR methods, but with much faster processing speed