harmonica
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Add a finite-difference upward derivative
The upward_derivative function gains a method argument that defaults to finite-diff. The way this works is by upward and downward continuing the grid by half of the average grid spacing and then calculating a central difference approximation for the derivative. An advantage of this method is a lower sensitivity to noise than the FFT-based one. Even though the continuation is FFT-based, it's not very sensitive to high-frequency noise.
Trying this out. We've had good experiences with it in our magnetic microscopy paper. This was much better than the FFT-based one, particularly for Euler Deconvolution where the quality of the upward derivative is very important.
Implemented a test but it's still failing. Need to see if this is something I'm doing wrong in the code of if the results aren't as good as I thought.
@leouieda I think this PR just needs some little work to be ready, and I think it would be great to have it in the next release of Harmonica. Is that possible? What do you think?
@santisoler not sure I'll be able to finish this in time. I'll try but don't let this be a bottleneck for a release.
In the paper we were writing, it was the difference between getting completely wrong depth from Euler deconvolution and getting the correct ones. But now that I think about it, our data didn't have a lot of high frequency noise so maybe that's what's making it not so good in this case.
Closing this. We've been experimenting with this and it doesn't really make as large of a difference as we thought. Plus, I couldn't get it to work reliably in Harmonica so maybe it was a fluke in our original microscopy code.