Editing Super-resolution imaging (section)

==Aliasing==
Geometrical SR reconstruction [[algorithm]]s are possible if and only if the input low resolution images have been under-sampled and therefore contain [[aliasing]]. Because of this aliasing, the high-frequency content of the desired reconstruction image is embedded in the low-frequency content of each of the observed images. Given a sufficient number of observation images, and if the set of observations vary in their phase (i.e. if the images of the scene are shifted by a sub-pixel amount), then the phase information can be used to separate the aliased high-frequency content from the true low-frequency content, and the full-resolution image can be accurately reconstructed.<ref>J. Simpkins, R.L. Stevenson, "An Introduction to Super-Resolution Imaging."[http://www.crcpress.com/product/isbn/9781439869604 '' Mathematical Optics: Classical, Quantum, and Computational Methods''], Ed. V. Lakshminarayanan, M. Calvo, and T. Alieva. CRC Press, 2012. 539-564.</ref>

In practice, this frequency-based approach is not used for reconstruction, but even in the case of spatial approaches (e.g. shift-add fusion<ref name="users.soe.ucsc.edu">S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, [http://users.soe.ucsc.edu/~milanfar/publications/journal/SRfinal.pdf "Fast and Robust Multi-frame Super-resolution"], IEEE Transactions on Image Processing, vol. 13, no. 10, pp. 1327–1344, October 2004.</ref>), the presence of aliasing is still a necessary condition for SR reconstruction.