Denoising Data with ICA

ICA classification methods like tedana will produce two important outputs: component time series and component classifications. The component classifications will indicate whether each component is “good” (accepted) or “bad” (rejected). To remove noise from your data, you can regress the “bad” components out of it, though there are multiple methods to accomplish this.

Let’s start by loading the necessary data.

Python

import numpy as np
import pandas as pd
from nilearn import masking

# For this, you need the mixing matrix, the data you're denoising,
# a brain mask, and an index of "bad" components
data_file = "preprocessed_data.nii.gz"
mixing_file = "mixing.tsv"
mask_file = "mask.nii.gz"
den_idx = np.array([0, 1, 2, 3, 4, 5])

# Load the mixing matrix
mixing_df = pd.read_table(mixing_file, index_col="component")
mixing = mixing_df.data

# Apply the mask to the data image to get a 2d array
data = masking.apply_mask(data_file, mask_file)

# Transpose to voxels-by-time
data = data.T

# The first dimension should be time
assert data.shape[1] == mixing.shape[0]

FSL

data_file=preprocessed_data.nii.gz
mixing_file=mixing.tsv
mask_file=mask.nii.gz
den_idx=(0, 1, 2, 3, 4, 5)

AFNI

data_file=preprocessed_data.nii.gz
mixing_file=mixing.tsv
mask_file=mask.nii.gz
den_idx=(0, 1, 2, 3, 4, 5)

Aggressive Denoising

If you regress just nuisance regressors (i.e., rejected components) out of your data, then retain the residuals for further analysis, you are doing aggressive denoising.

Python

# Fit GLM to bad components only
betas = np.linalg.lstsq(motion_components, data, rcond=None)[0]

# Denoise the data with the bad components
pred_data = np.dot(motion_components, betas)
data_denoised = data - pred_data

# Save to file
img_denoised = masking.unmask(data_denoised.T, mask_file)
img_denoised.to_filename("denoised.nii.gz")

FSL

3dcalc --input stuff

AFNI

3dcalc --input stuff

Non-Aggressive Denoising

If you include both nuisance regressors and regressors of interest in your regression, you are doing nonaggressive denoising.

Python

# Fit GLM to all components
betas = np.linalg.lstsq(mixing, data, rcond=None)[0]

# Denoise the data using the betas from just the bad components
pred_data = np.dot(motion_components, betas[den_idx, :])
data_denoised = data - pred_data

# Save to file
img_denoised = masking.unmask(data_denoised.T, mask_file)
img_denoised.to_filename("denoised.nii.gz")

FSL

3dcalc --input stuff

AFNI

3dcalc --input stuff

Component orthogonalization

Independent component analysis decomposes the data into independent components, obviously. Unlike principal components analysis, the components from ICA are not orthogonal, so they may explain shared variance. If you want to ensure that variance shared between the accepted and rejected components does not contaminate the denoised data, you may wish to orthogonalize the rejected components with respect to the accepted components. This way, you can regress the rejected components out of the data in the form of, what we call, “pure evil” components.

Python

good_idx = np.setdiff1d(np.arange(mixing.shape[1]), den_idx)

# Separate the mixing matrix into "good" and "bad" components
bad_mixing = mixing[:, den_idx]
good_mixing = mixing[:, good_idx]

# Regress the good components out of the bad ones
betas = np.linalg.lstsq(good_mixing, bad_mixing, rcond=None)[0]
pred_bad_mixing = np.dot(good_mixing, betas)
orth_motion_components = bad_mixing - pred_bad_mixing

# Replace the old component time series in the mixing matrix with the new ones
mixing[:, den_idx] = orth_motion_components

FSL

3dcalc --input stuff

AFNI

3dcalc --input stuff

Once you have these “pure evil” components, you can perform aggressive denoising on the data.

Python

# Fit GLM to bad components only
betas = np.linalg.lstsq(orth_motion_components, data, rcond=None)[0]

# Denoise the data with the bad components
pred_data = np.dot(orth_motion_components, betas)
data_denoised = data - pred_data

# Save to file
img_denoised = masking.unmask(data_denoised.T, mask_file)
img_denoised.to_filename("denoised.nii.gz")

FSL

3dcalc --input stuff

AFNI

3dcalc --input stuff