I have data sets in which important information is allocated in the edges, which are also very sensitive to inaccuracies. I would like to find a regression model based on edge recognition that brings my data closer to the expected avoiding overfitting. Here is an example:
Please note that although I could simulate the data behavior for this very specific case, in reality, I do not have prior knowledge or known model of the data.
Several edge-detection algorithms are based on derivative computations, however for such scarce (and frequently noisy) data, derivatives are not a very robust solution. So far, the closest I have got with derivatives is performing y-y'' transformation. Therefore, I am looking in the direction of regression models with machine learning methods, however I have very little experience on that.
Is there any regression model which is suitable for edge detection and enhancement?
I also provide a link with the corresponding data. Any idea/suggestion/help would be very appreciated, I am currently working on Matlab and Python.
Thanks in advance! .imgur.com/vfqv0.png