Denoise and INU correct anatomical images post-merge

[effigies]

Is your feature request related to a problem? Please describe.

In cases where we run DenoiseImage and N4BiasFieldCorrection on multiple images, we're almost certainly wasting effort. DenoiseImage estimates and removes Gaussian or Rician noise. The sum of Gaussians is Gaussian and the sum of Ricians is Rician, so there is no advantage to running DenoiseImage prior to merge unless the noise present in the image damages the ability to align and merge the images.

Similarly, N4BiasFieldCorrection estimates bias fields at a particular spatial frequency. Summing the bias fields of two images should not generate a bias field of a higher spatial frequency. It should be safe to perform this after the fact.

Describe the solution you'd like
Instead of:

graph LR;
    img1 -- Denoise --> denoised1 -- N4 --> corrected1;
    img2 -- Denoise --> denoised2 -- N4 --> corrected2;
    img3 -- Denoise --> denoised3 -- N4 --> corrected3;
    corrected1 & corrected2 & corrected3 --> merged;

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Do

graph LR;
    img1 & img2 & img3 --> merged -- Denoise --> denoised -- N4 --> corrected

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A dataset with 3 or more T1w or T2w images would make a decent test to verify that the combined process is not measurably worse. Using a canonical FAST or Atropos segmentation, we could estimate the mean and variance within each tissue class in each image to have a quantitative estimate.

Describe alternatives you've considered

The status quo.

[effigies]

Reading up, it's not clear that the sum of Rician variates produce a Rician distribution.

• https://doi.org/10.1049/el:20057727
• https://doi.org/10.1109/LSP.2008.2012223