That is clearly not the case, as the article repeatedly shows. By the time you have a digital signal, it’s too late. Any noise above the nyquist frequency has already been mixed into the noise below it and they cannot be separated.
This is what we do in high-quality computer graphics rendering.
Suppose you are want to reconstruct a signal, showing only the frequencies < N hz.
With an analog filter, you filter out everything above N hz. Then you can sample at the nyquist frequency of 2N hz, and then perfectly reconstruct the filtered signal.
Alternatively, without the analog filter, you can take some number of samples M >= 2N. The samples are randomly placed/timed. You accumulate the samples at the 2N locations, but you weight the sample when you accumulate it with some filter function. This effectively convolves and filters the signal with a low-pass filter.
Because of the random sample placement/timing, high frequencies get converted to noise instead of causing aliasing.
Admittedly you are taking more than 2N samples, however you don't have to do any analog filtering, and you can still reconstruct he bandlimited signal. Your reconstruction will have some noise, but the noise will decrease as you take more samples (e.g. as M increases).
I think you’re thinking of stochastic sampling. This still requires additional samples in the time domain and only works for relatively static signals over those increased number of samples.
If you have enough samples, then of course you can do it. The article is all about someone claiming they can do it without taking more samples. Given that was the topic at hand, I kind of assumed that was what you meant.
My spidey sense tingled on the sentence just previous:
"Filtering means removing the high frequency components from the signal"
Sure, it can mean that. To claim it always and only means that, even in the context of periodic waveforms, makes me question the authors understanding of the subject.
