# Multi-channel filter for correlated noise suppression

### Short question

We need to cancel the correlated noise from recorded datasets, as shown in the figure below, coming from arrays of charge sensitive sensors.
I would like to ask to this community to point me to the relevant literature about correlated noise suppression. In addition, I would like to know if there exists some code and/or algorithms, and a base textbook that can serve as reference in the future for offline signal processing (I believe it is referred as DSP).

Example showing 36 out of 64 total channels of a triggered event where charge signal is present. The upper pad shows the single channels where the amplitude of the waveforms are shown represented by the color scale. This view shows evidence for a correlated noise across chanels as vertical runninbg "valleys" and "cliffs". The lower pad shows the waveforms of the same channels overlapped and plotted with a different color each. The strong pulses correspond to electrons "collected" at our anode electrode (pixels) and are our "signal".

### The longer story

I am analysing digitised data from several charge sensitive amplifiers (here a link) of a particle detector, consisting in a liquid argon time projection chamber (LArTPC). As shown, the recorded waveforms are strongly affected by correlated noise/disturbances. I believe that this noise is due to some ground loop that we will identify and remove in some future setups of our detector (still in R&D stage) and to some EMI of nearby power electronic (and a train station closeby our laboratory).
In order to get some accuracy from the analysis of the charge (taken from the hight of pulses), we need to figure out how to filter out the correlated part of the noise among the channels. At the moment, we are subtracting from each channel either the mean or the median waveform calculated using all the channels. Both methods work not too bad when the SNR of the pulses is high as in the shown example. However, when the SNR is lower the performance really drops making the analysis almost impossible. Being able to study also small signal events is fundamental for us, as we need to investigate the evolution of the liquid argon purity achieved over time.
What I would like to develop is a filter based on the waveforms in the "No signal region" (see the figure), where no signal can fall, and apply it to the middle region where charge signals can occur.
I have digged quite a lot into the literature, but it was almost a random walk as I am not expert of signal processing/conditioning. Thus, I am not sure that I could find (or understand) what I was looking for. The only things I could find (and understand) are the following 3 papers: Trojanoski et al., Wang et al., Ozbek. It seems that the first two references propose to estimate the Green function (in frequency domain) between two channels (R$$_{ij}$$) averaging noise only (seismic) waveforms over several acquisitions. This has the advantage of cancelling the uncorrelated noise for getting a good estimation of the correlated one. If I am right, this is not really applicable to our case as the ground loop and EMI induced noise is not really stationary across several events. The third link proposes an adaptive filter (in time domain) and assumes non stationary correlated noise. However, the credentials of my institution don't allow me to get that paper and thus I do not know whether it is relevant for our needs.
At the moment, I am mainly looking for filters that minimize the RMS (Wiener etc.) as I can better understand the math and what they do. It seems that adaptive filters also are interesting especially if the noise is not stationary. However, once we have managed to implement in our analysis a better filter, it would be good to make a next step trying to develop and implement a filter with minimum or very controlled signal distortion.