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I have been trying to understand what super-resolution is, in the context of DSP/DIP. What criteria is being maximized/minimized, and why?

Most of my online searches yield super-res techniques from the optical physics stand point, however I know anecdotally that they have been used in image processing, and in some doppler-radar processing as well.

One particular instance of Super-Res I remember seeing was in the design of a windowing function, where the main lobe was the same width as that of a boxcar, while simultaneously having very low and fast degrading side lobes, similar to a hamming window. In this sense, the 'super-res' came from the fact that frequencies very close to one another were able to be resolved due to the low main lobe width, and a very high dynamic range. Is this what super-res really amounts to?

Is there an explanation that, (perhaps), likens it to a form of de-noising, or sparsity pursuit? Or is it a different animal altogether?

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  • $\begingroup$ Aren't both optimization criteria a result of inherent physical structure of the signal? I.e., one can search for a sparse solution only if the physical phenomena has a good sparse representation? All SR techniques must assume a physical model that relates the data that is used to enhance the signal. $\endgroup$ – nimrodm Aug 2 '12 at 5:24
  • $\begingroup$ @nimrodm I just remembered another example of 'super-res', I have added to the question. $\endgroup$ – Spacey Aug 2 '12 at 13:31
  • $\begingroup$ I don't want to argue but in general, without additional information there is no way to increase the resolution of the signal in the general case. E.g. if a bandlimited signal is sampled below the Nyquist rate, there is no way to reconstruct it unless some more information is known. So for me, SR means MAP estimation of the original noiseless signal using a prior (for example due to the underlying physical phenomena) or additional sampled data. $\endgroup$ – nimrodm Aug 2 '12 at 13:58
  • $\begingroup$ @nimrodm The way I am currently thinking about it, in the case of no apriori information, there are different windowing functions one can use to trade frequency-resolution with dynamic range. Under this constraint of no apriori knowledge, is there such a thing as super-resolution? Maybe, maybe not, I do not know. In contrast, perhaps super-res is only applicable if aprior knowledge is known? Then as you mentioned, MAP estimation can be used. But again I do not know, this is part of the confusion I have. $\endgroup$ – Spacey Aug 2 '12 at 14:25
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The term super-resolution is used very loosely nowadays. But I think the following problem was the original idea, or at least, the one that made the term famous.

Suppose you have a scene and several observations of that scene, i.e. several frames of a video with slight camera motion between them. Super-resolution algorithms combine those several observation into one highly resolved image. This is possible because each observation might contain unique information not present in the others.

If you consider a certain frame as the key frame, this process can be interpreted as a MAP estimation since a priori (or extra) information is present in others frames.

Additionally, we can use natural image statistics as extra information to regularize the solution. Total variation regularization is a broadly used technique.

I suggest the paper by Park 2003.

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  • $\begingroup$ Thanks Daniel - I wonder if such techniques might be readily extendible to, say, Doppler radar imagery? $\endgroup$ – Spacey Aug 3 '12 at 22:41
  • $\begingroup$ Probably so. But for Doppler radar, I think SAR (synthetic aperture radar) and/or communication techniques (MIMO, SIMO, etc) are more appropriate approaches to enhance resolution. $\endgroup$ – Daniel R. Pipa Aug 4 '12 at 20:52

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