Is wavelet noise reduction just removing the higher frequency coefficients?

Question

I read some tutorials in noise reduction using wavelets, and they seem to be too simple.

With Fourier transforms, there is a distinction between types of noise, and some attempts to estimate the noise present on the data (White noise, shot noise, etc).

Wavelet methods seem to just remove the high frequency data, without considering that they may encode useful information.

So, there is more complexity than that on wavelet methods? what are the most common of those methods?

Answer 1

I see I am quite late for answering. I hope someone still may find it useful.

1. The most primitive just throw away high pass bands, this usually results in blurry signals/images a bit akin to low-pass (for example Gaussian) filtering of signal /image.
2. Some little bit more advanced set some noise threshold and keep everything above the noise threshold. This is also called hard thresholding.
3. Famous concept is soft thresholding techniques. Instead of a hard threshold we use wavelet coefficient magnitudes for some kind of certainty measure. We keep larger percent of the coefficients the more confident or certain we are that they are not noise.
4. More sophisticated denoisers run some kind of quantization scheme on them. At this level we are in practice almost building a primitive codec.