The image as a database containing echoes of itself.
Abstract:
Methods for super-resolution (SR) can be broadly classified into two families of methods: (i) The classical multi-image super-resolution (combining images obtained at subpixel misalignments), and (ii) Example-Based super-resolution (learning correspondence between low and high resolution image patches from a database). In this paper we propose a unified framework for combining these two families of methods. We further show how this combined approach can be applied to obtain super resolution from as little as a single image (with no database or prior examples).[…] Our approach is based on the observation that patches in a natural image tend to redundantly recur many times inside the image, both within the same scale, as well as across different scales. Recurrence of patches within the same image scale (at subpixel misalignments) gives rise to the classical super-resolution, whereas recurrence of patches across different scales of the same image gives rise to example-based super-resolution. Our approach attempts to recover at each pixel its best possible resolution increase based on its patch redundancy within and across scales. […]
Source:
Super-Resolution From a Single Image
Daniel Glasner, Shai Bagon, Michal Irani
http://www.wisdom.weizmann.ac.il/~vision/SingleImageSR.html
Significantly, the final illustration in this research paper is a drawing by M.C. Escher, the Dutch graphic artist who’s work (typically popular with mathematicians and engineers) explored the idea of self-similarity, fractals, and (often impossible) repetitions.