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In 1949 Shannon [55] proved a theorem which is now commonly known as the Shannon sampling theorem, however it was quite well-known long before as a rule of thumb [39]. This theorem states that a signal which is band-limited and which was sampled with a frequency at least twice its highest frequency is completely determined by its samples. It can be reconstructed by convolution with the sinc function.
Although the theory sounds nice there are several problems with this fact in practice. Most notably, the sinc function has infinite spatial extend and therefore cannot be used in practice. Also the computational complexity is an important point here. So many researchers in many different fields like signal processing, image processing and (especially important for our purposes) more recently in volume visualization investigated the problem of practical function reconstruction, i.e., interpolating between sampling points.