I have read your CSD tutorial, where you explain that the stiffness and lambda2 parameters affect the smoothness and flexibility of the spline.
After some reading and research (e.g.,this article), it seems that stiffness controls the sensitivity of the spherical spline to distances between electrodes (impact on smoothness/spatial definition) and that increasing stiffness increases the spatial resolution of EEG data, but this can amplify noise. We can observe this phenomenon in your example (illustration below).
Why does some research that applies CSD to improve local spatial resolution use a stiffness = 4 (default), and others a stiffness = 3 to be more precise? And if the results differ between the two stiffnesses, how do you explain this, and what do you think is the most appropriate parameter?
I know that my question isn’t simple and that there isn’t necessarily a clear answer,
Good questions: CSD computes the spatial derivative of the voltage which is classically explained as showing sources and sinks of dipoles. I think that’s fairly clear but it’s also pretty technical, sorry probably for a more accessible version I’d read those papers you cited.
To my knowledge, there isn’t a theoretical reason for selecting stiffness values: the researchers just picked what they thought looked good. That’s a good place to start but it’s not really best practice, someone needs to take the time to check many parameter combinations on many datasets with a known ground truth to make better recommendations for the field. To my knowlege it hasn’t happened yet, no one has taken the time (other than the recommendations in the original papers which focus on the math description and not wide ranging empirical results).
