Direct Energy Minimization for Super-Resolution on Nonlinear Manifolds

We address the problem of single image super-resolution by exploring the manifold properties. Given a set of low resolution image patches and their corresponding high resolution patches, we assume they respectively reside on two non-linear manifolds that have similar locally-linear structure. This manifold correlation can be realized by a three-layer Markov network that connects performing super-resolution with energy minimization. The main advantage of our approach is that by working directly with the network model, there is no need to actually construct the mappings for the underlying manifolds. To achieve such efficiency, we establish an energy minimization model for the network that directly accounts for the expected property entailed by the manifold assumption. The resulting energy function has two nice properties for super-resolution. First, the function is convex so that the optimization can be efficiently done. Second, it can be shown to be an upper bound of the reconstruction error by our algorithm. Thus, minimizing the energy function automatically guarantees a lower reconstruction error— an important characteristic for promising stable super-resolution results.