Like non-uniform sampling? https://en.wikipedia.org/wiki/Nonuniform_sampling

There is no Nyquist frequency limitation there. But the spectral signal is much more noisy.

Long time ago I was in this field! Dear @Vladimir, I will atach a fine article of an expert in this field speaking about Sampling: What Nyquist Didn’t Say, and What to Do About It! "The Nyquist-Shannon sampling theorem is useful, but often misused when engineers establish sampling rates or design anti-aliasing filters. This article explains how sampling affects a signal, and how to use this information to design a sampling system with known performance." It may be helpful!

http://www.wescottdesign.com/articles/Sampling/sampling.pdf

Dear Vladimir Farber, the answers given suggest that there are, broadly speaking, two types of sampling criteria.

If you wish to extract meaningful parameters from an analogically scanned pattern, weighting them correctly, or to fit a curve starting from observational data, you have recourse to regression analysis.

If you want to recover coded data, or data in a known time/frequency range from unwanted signals (noise), you apply some method related to Nyquist and Shannon theories.

Both approaches usually rely on statistics. In addition, some of the recently developed approaches endeavor to deal with non-uniform statistics. However, it should be checked if statistics can be applied to the data at all. In fact, the data sets may evolve during acquisition or the chosen sample may not reflect the whole population. Besides that, if you don't know prof. Leonid Yaroslavsky, I suggest to take a look at his papers.

Hi  Vladimir

Two quick points:

First as an engineer I learned early on  that when dealing with experimental data it is always good to over sample.  In fact doubling the number of points you think you need is a pretty good rule of thumb..

Second there are several regular/uniform sampling generalisations.  I am thinking here of "Ding Sampling" as it applies in the case of the 1D Separable Linear Canonical Transform (of which the FT is a special case).  You can look up our recent papers in Appl. Optics and  J Opt Soc Am A.

I hope this comment provides slightly more help than it causes confusion.

JTS

 Hi Vladimir,

Delta-dense is a way of implementing non-uniform sampling and there are a few papers that establish the theoretical basis for that as well numerical implementation.

You might want to take a look at these.

Best,

Sumeet

Conference Paper Stable arrangements of mobile sensors for sampling physical fields

Article Non-uniform sampling and reconstruction in shift-invariant spaces