# Noise from irregular sampling pattern

In this paper the author says

By using an irregular sampling pattern and filtering the irregular samples to create the pixels, featureless noise is produced from such high frequencies rather than false patterns.

A similar argument is outlined in here without explanation

If we make the samples irregular, in a controlled fashion, then these higher frequencies would appear in the image as noise rather than aliases.

I am writing a little report investigating stochastic sampling as a second-year undergraduate student. I would be grateful if someone could explain this in more detail. Thanks!! Other resource recommendation and guidance are also appreciated!

UPDATE: I have found this paper which says that because stochastic sampling break the periodicity of aliasing artefacts as a result of randomness, it creates noise instead. To my understanding, this is saying that noise is a form of artefact such as "aliasing" but less concentrate. However this contradicts with its definition as wikipedia says it

is random variation of brightness or color information in images

Thanks!

The core is the sentence directly before the one you cited from the second link:

The coherence of the samples interferes with the coherence of the image to produce errors called aliasing.

The coherence is the key here. The human eye-brain signal processing chain is highly focused on pattern recognition, and aliasing produces coherent errors which the eye basically jumps to, because they form a pattern. Non-coherent errors, your "classic" noise is perceived as much less annoying.

By using irregular sampling, you ditch the coherence of the error you produce. Aliasing is transformed to broadband random noise.

Mind, this is no "magic trick". The energy of the error is just as high with irregular sampling. But the perception thresholds of the human brain are very different for the kinds of errors produced by the two methods.

• Irregular sampling is basically a method to avoid proper pre-filtering, at the cost of increased pseudo-noise, right? If Nyquist can be economically satisfied (either by lowpass filtering or by having a high sample rate), then irregular sampling seems pointless. Commented Dec 16, 2021 at 9:01
• Yes. If proper preconditioning of the signal is possible, irregular samping is mostly pointless. But in some cases where p/c is impossible or not wanted for some reason, irregular sampling can push the error signal below the perception threshold. Or, precisely, push the perception threshold above the error signal.
– Max
Commented Dec 16, 2021 at 9:13
• Thank you so much for the clarification. I just noticed that aliasing is also "variation of brightness or color information in images" since the pixels have changed. Commented Dec 16, 2021 at 17:08
• Yeah, that is a very complicated way of saying "error". :-D
– Max
Commented Dec 17, 2021 at 7:20