Beta Process Joint Dictionary Learning for Coupled Feature Spaces with Application to Single Image Super-Resolution

This paper addresses the problem of learning over-complete dictionaries for the coupled feature spaces, where the learned dictionaries also reflect the relationship between the two spaces. A Bayesian method using a beta process prior is applied to learn the over-complete dictionaries. Compared to previous couple feature spaces dictionary learning algorithms, our algorithm not only provides dictionaries that customized to each feature space, but also adds more consistent and accurate mapping between the two feature spaces. This is due to the unique property of the beta process model that the sparse representation can be decomposed to values and dictionary atom indicators. The proposed algorithm is able to learn sparse representations that correspond to the same dictionary atoms with the same sparsity but different values in coupled feature spaces, thus bringing consistent and accurate mapping between coupled feature spaces. Another advantage of the proposed method is that the number of dictionary atoms and their relative importance may be inferred non-parametrically. We compare the proposed approach to several state-of-the-art dictionary learning methods by applying this method to single image super-resolution. The experimental results show that dictionaries learned by our method produces the best super-resolution results compared to other state-of-the-art methods.