remove noise while preserving peak

Question

I have a data (see this link) which has some wiggles at both end.

I tried to apply different filters to smooth the data, like this

ListLinePlot[{data, MeanFilter[data, 2]}]

The wiggles are perfectly smooth. However, the problem is that the main peak is also severely drop down(show in green circle) which is not what I want. I also tried other filter like LowpassFilter, GaussianFilter, all suffers this problem.

So how to remove small wiggles and preserve main peak of a data? Splitting data to piecewise may not be a good idea, because I have dozens of data to smooth, their main peaks are not at the same locations.

Answer 1

You need a nonlinear filter like MeanShiftFilter to do that. MeanShiftFilter asks for a radius and a threshold, which have to be set according to the noise in your data. MeanShiftFilter[data, 10, 50] gives this result:

The peak value is preserved:

Max /@ {MeanShiftFilter[data, 10, 50], data}
{802.993, 802.993}