I have some MRI data collected across time. When the patient moves, this results in a spike in the signal (so I guess it's not really "noise"). I would like to identify and remove these. So far I have been removing based on the local median and it works pretty well for the big spikes, but I'd like to do better.
I noticed that if I measure the signal in 2 places in the image, some of the noise will be correlated between the 2 signals (e.g., at some time point, both signals show an upward spike of about the same size), while some of it does not appear correlated. It would make sense that spikes due to motion would be correlated, because the motion would affect the whole image. Is there a way I can exploit the apparent correlation to remove these points from the signals? I don't know where to start. Thanks for any tips.
An example of the signals:
Yes the topic that you are talking about is in the area of robust statistics. Have a look at my previous answer here. You may want to check robust statistics for correlated data. But it is about the correlation of the data over time. In indeed there is correlation between two signals a short time correlation should tell this.