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Hi FSL experts (perhaps specifically Dr. Christian F. Beckmann),

I'm working on adding ICA_AROMA functionality to another software tool (fmriprep): https://github.com/poldracklab/fmriprep/pull/539

where I'm having trouble: 
I'm attempting to recreate the fsl_regfilt partial regression equation, but instead of the output being the denoised data, I want a matrix of confounds where each column is a noise component, and the rows are the length of the time series.

I see fsl_regfilt's partial regression explained here: https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind1307&L=fsl&D=0&P=288785

My thought process right now is to:

1)  regress the image data against the entire melodic_mix: 
data_hat = B0 + B1*melodic_mix
residual_data = data - data_hat

2) regress the noise_components against the signal_components and the residual_data
noise_components_hat = B0 + B1*signal_components + B2*residual_data
residual_noise_components = noise_components - noise_components_hat

The residual_noise_components are the partially regressed noise components and if given to fsl_glm as a design matrix would give the same result as using fsl_regfilt with the filter and melodic_mix. 

Is my reasoning sound? Can anyone help with how I can conceptualize making this regression? 

Thank you so much!
James