Smoothing noisy increasing measurement/calculation

I have a set of calculated values based on measured data (erosion through a pipe) where decreasing values are physically impossible. I want to smooth out the data and account for the fact that it is impossible to decrease, but don't want my new data to take giant jumps when the noise is significant. Any suggestions would me much appreciated.

Answer 1

[Chad Greene]

A moving average should do it. You'll lose some temporal resolution, but if the noise is gaussian then a moving average will force the noise to asymptote to zero with increasing time window size. There are several moving average functions on the file exchange; I'm not sure which is best.

Alternatively, you could apply a low-pass frequency filter if the lowest frequency of the noise is not below the highest frequency of your erosion signal. If you have the signal processing toolbox, I made this to make frequency filtering a little more intuitive: http://www.mathworks.com/matlabcentral/fileexchange/38584-butterworth-filters

[Mark]

Thanks Chad. For now the moving average looks like it's giving something acceptable (smooth() with a large enough span). I'll do some diving into your frequency filtering. Thanks again.

Answer 2

[John D'Errico]

So use a tool like SLM (download from the file exchange) to fit a monotone increasing spline to the data, smoothing through the noise.

Answer 3

[Image Analyst]

How about just scan the array and compare to the prior value?

for k = 2 : length(erosion)
  if erosion(k) < erosion(k-1)
    erosion(k) = erosion(k-1);
  end
end

Simple, fast, intuitive.

[Mark]

Right right, the only problem is I have giant jumps in noise, so if it reads the apex of the noise, it will not go back down to the realistic values, and I will be getting a flat line for a good amount of time until my calculated values reach a point greater than what the noise said it was.

[Image Analyst]

Even if you do a sliding mean like Chad suggested, you'll still have to do my method (or equivalent) because you said that decreasing values are physically impossible. A sliding mean filter can have values that decrease so you'll have to scan for that and fix it when it occurs.