How to fit n gaussians/peaks

Hi! I need to fit Gaussian like curves with up to 100 peaks. So far, for less than 8 peaks, I have been using the matlab curve fitting tool box and its gaussian fit algorithm, but it seems like you can only fit 8 gaussians at the most to your curve. Is there a simple way or another function to fit about 100 peaks?

Thanks a lot knut

[Knut Tutgut]

actually, it does not necessarily need to be gaussians. what I need to do, is fit curves with 10-1000 gaussian-like peaks, like in the attached example file. I will then include the fitting function into a script so I can analyze a time series of up to 1000 frames.

thanks for your help!!

[Star Strider]

You have to fit all the peaks simultaneously, because they overlap, and the overlap has to be considered in estimating the parameters of each one. I also count at least 14, and there could be more (for instance there could be one ‘hidden’ in the upslope of the peak at about 75, and there could be smaller ones at about 120, 140, and 175), so this is not a trivial task.

I have no recent experience with wavelets, but I would be tempted to experiment with a wavelet decomposition to distinguish genuine peaks from noise. That would make the subsequent parameter estimation considerably easier.

[Knut Tutgut]

Okay, I think in my case the data isn't actually too complex and there should not be any "hidden" peaks. I think I have made the task harder than it actually is, by saying I need to fit multiple gaussians. my images look like this (here only 12 obvious peaks):

now, I merely need to fit a curve to these peaks and then find parameters like the centers of the fitted peaks, etc. perhaps there is a better function than fitting gaussians? sorry, I am new to matlab and I would think this should be a pretty simple task?

[Image Analyst]

If you don't have the stats toolbox, and if you can post your data, I can try fitgmdist() on it to see if it works.

[Knut Tutgut]

thanks for that offer! I found this: http://terpconnect.umd.edu/~toh/spectrum/InteractivePeakFitter.htm#ipf_instructions

That actually seems to work quite well! If it's too complex after all, I will get back to your offer!

Answer 1

[Image Analyst]

How about if you locate each peak with findpeaks(), then at each peak location, "fall down" the slopes on each side and extract just that one peak? Then fit that peak to a Gaussian. Repeat for all peaks found.

[Knut Tutgut]

So in principle, that would mean splitting the data into n parts (where n is the number of peaks) and fit single gaussians to each part, respectively, right? Shouldn't there exist some way to first fit the curve and the use findpeaks() on the fit? I would assume that other people have written such function to fit multiple peaks? I couldn't really find anything like that on the internet though.. :( Thanks for your help!

[Image Analyst]

Well if you have the Statistics and Machine Learning Toolbox, you can try using

GMModel = fitgmdist(X, 100)

to use a Gaussian Mixture Model, though I don't know how well it will handle 100 ill-defined peaks.