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I've been reading about Super Resolution Image reconstruction (Reconstruction of high resolution image from multiple low resolution aliased images contain sub pixel shifts), and i want to know why SR is possible? this document explains why SR is possible, but i didn't understand completely!

please can you explain more clearly.

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    $\begingroup$ There is no document behind the link (anymore). $\endgroup$
    – Olli Niemitalo
    Jul 12, 2018 at 14:04

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The more independent data you have, the more constrained are the possible solution sets that could produce that data, usually. If any higher frequency content in the possible solution sets is constrained to not be completely arbitrary (which data derived from sub-pixel shifted sampling might so constrain), then the solution sets could possibly becomes sharper due to the steeper edges that can be reproduced using said higher frequency content.

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The fundamental reason this works is because you are using $p$ times as many (hopefully independent) samples as any individual low-resolution image to form the high resolution image.

How you generate the high resolution image is a harder problem. The reason it works is easy.

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  • $\begingroup$ if you use p times as many samples than you can not reconstruct a higher frequency from your low-resolution or am i wrong? I mean you can sample as long as you want and combine them all together. The only resolution you will increase is the resolution below nyquist. But How to increase above nyquist? Therefore you need aliasing right? $\endgroup$
    – Khan
    Apr 11, 2020 at 14:14
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    $\begingroup$ @Khan That depends on where the samples are. If the extra $(p-1) \times N$ samples are between the original $N$ samples, then you can effectively increase the Nyquist frequency. The trick is how to position those extra samples so that is possible. Even if the samples are not uniformly distributed, there are some techniques that allow you to use them. $\endgroup$
    – Peter K. ♦
    Apr 11, 2020 at 17:53
  • $\begingroup$ so thats what you mean with (independent samples in your answer) ok... if you have 3 lowresolution signals wich are sampled on different offsets from the original, then you can reconstruct a higher resolution than nyquist? even without aliasing? or is aliasing necessary for higher resolution? $\endgroup$
    – Khan
    Apr 11, 2020 at 18:24
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    $\begingroup$ @Khan Higher than the original Nyquist rate, yes, but not higher than the new extra-data Nyquist rate. $\endgroup$
    – Peter K. ♦
    Apr 11, 2020 at 23:15
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    $\begingroup$ @khan yes. I’m not sure if the offsets of the new data sets matter (so that the sampling is uniform), but what you wrote is broadly correct. Not sure about your aliasing comment. $\endgroup$
    – Peter K. ♦
    Apr 12, 2020 at 15:07

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