When doing random sampling, you can get noisy results if you don't use enough samples like in the shadows below.

I know that if you use high frequency noise (aka blue noise), the noise pattern can be high frequency content only, which can then be low pass filtered (aka blur) to remove the high frequencies and leave just the lower frequency content which would be less noisy.

Is denoising ALWAYS about doing a low pass filter / blur? Or are there other ideas and techniques for removing noise?