Limits on Super-Resolution and How to Break Them

Nearly all super-resolution algorithms are based on the fundamental constraints that the super-resolution image should generate the low resolution input images when appropriately warped and down-sampled to model the image formation process. (These reconstruction constraints are normally combined with some form of smoothness prior to regularize their solution.) In the first part of this paper, we derive a sequence of analytical results which show that the reconstruction constraints provide less and less useful information as the magnification factor increases. We also validate these results empirically and show that for large enough magnification factors any smoothness prior leads to overly smooth results with very little high-frequency content (however many low resolution input images are used.) In the second part of this paper, we propose a super-resolution algorithm that uses a different kind of constraint, in addition to the reconstruction constraints. The algorithm attempts to recognize local features in the low resolution images and then enhances their resolution in an appropriate manner. We call such a super-resolution algorithm a hallucination or recogstruction algorithm. We tried our hallucination algorithm on two different datasets, frontal images of faces and printed Roman text. We obtained significantly better results than existing reconstruction-based algorithms, both qualitatively and in terms of RMS pixel error.