Aligning Coupled Manifolds for Face Hallucination

Many learning-based super-resolution methods are based on the manifold assumption, which claims that point-pairs from the low-resolution representation manifold (LRM) and the corresponding high-resolution representation manifold (HRM) possess similar local geometry. However, the manifold assumption does not hold well on the original coupled manifolds (i.e., LRM and HRM) due to the nonisometric one-to-multiple mappings from low-resolution (LR) image patches to high-resolution (HR) ones. To overcome this limitation, we propose a solution from the perspective of manifold alignment. In this context, we perform alignment by learning two explicit mappings which project the point-pairs from the original coupled manifolds into the embeddings of the common manifold (CM). For the task of SR reconstruction, we treat HRM as target manifold and employ the manifold regularization to guarantee that the local geometry of CM is more consistent with that of HRM than LRM is. After alignment, we carry out the SR reconstruction based on neighbor embedding between the new couple of the CM and the target HRM. Besides, we extend our method by aligning the multiple coupled subsets instead of the whole coupled manifolds to address the issue of the global nonlinearity. Experimental results on face image super-resolution verify the effectiveness of our method.