Information Theoretic Limit of Single-Frame Super-Resolution

We elucidate the potential limit of single-frame super-resolution by information theory. Though various algorithms for super-resolution have been proposed, there exist only few works that evaluate the performance of super-resolution to our knowledge. Our key idea is that "single-frame super-resolution task can be regarded as channel coding in information theory." Based on this recognition, we can apply some techniques of information theory to the analysis of single-frame super-resolution. As its first step, we clarify the potential limit of single-frame super-resolution. For this purpose, we use a model of Yang et al. (2008) as a statistical model of natural images. As a result, we elucidate the condition that" arbitrary high-resolution natural image can be potentially recovered with arbitrarily small error by single-frame super-resolution." This condition depends on S/N ratio and blurring parameter. We investigate numerically whether this condition is satisfied or not for several situations.