Geometry constrained sparse coding for single image super-resolution

The choice of the over-complete dictionary that sparsely represents data is of prime importance for sparse coding-based image super-resolution. Sparse coding is a typical unsupervised learning method to generate an over-complete dictionary. However, most of the sparse coding methods for image super-resolution fail to simultaneously consider the geometrical structure of the dictionary and corresponding coefficients, which may result in noticeable super-resolution reconstruction artifacts. In this paper, a novel sparse coding method is proposed to preserve the geometrical structure of the dictionary and the sparse coefficients of the data. Moreover, the proposed method can preserve the incoherence of dictionary entries, which is critical for sparse representation. Inspired by the development on non-local self-similarity and manifold learning, the proposed sparse coding method can provide the sparse coefficients and learned dictionary from a new perspective, which have both reconstruction and discrimination properties to enhance the learning performance. Extensive experimental results on image super-resolution have demonstrated the effectiveness of the proposed method.