Return to Answer

Here is a solution using Quantile regression twice: to detect the outliers, and then find quantile regression curves in the data without the outliers.

I am not sure what is called "noise" in the question, from the description, I think it is about removing outliers. This solution uses Quantile regression twice: to detect the outliers, and then to find quantile regression curves in the data without the outliers.

Make another quantile regression computation over the new data. (This time is for to facilitate analysis instead of detecting outliers.)

Make another quantile regression computation over the new data. (This time is to facilitate analysis instead of detecting outliers.)

Adding x-coordinates to the data:

Make another quantile regression over the new data. (This time is for to facilitate analysis instead of detecting outliers.)

Load the package:

Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/QuantileRegression.m"]

Adding x-coordinates to the data:

Make another quantile regression computation over the new data. (This time is for to facilitate analysis instead of detecting outliers.)

Obviously other methods of signal analysis can be applied to the cleaned data. In this particular case, the cleaned data would give better results for the conditional PDF/CDF reconstruction shown in this blog post "Estimation of conditional density distributions".