[Hendrik-code]

What

RandomGaussianNoiseGPU takes relative (default False). When set, std is read as a fraction of each sample's own std in that channel, not in absolute intensity units:

"RandomGaussianNoiseGPU": { "p": 0.1, "std": 0.2, "relative": true }

Why

The std is drawn from U(0, std) in absolute units, so one config is a different augmentation on every intensity scale. Measured on 128³ training patches, image std is about 0.9 on z-scored Dixon MR, 0.17 on CT under nnU-Net's CT normalisation, and 0.16-0.20 on a [0, 1] SynthSeg synthesis. The paper config's std: 1.0 therefore means:

• noise up to about the image's own spread on MR;
• up to about six times it on CT and on synthetic samples.

For scale, nnU-Net's default noise std is at most 0.1 on z-scored data (from memory of batchgenerators' noise_variance=(0, 0.1), which it uses as the std).

Behaviour

• The relative scale is applied after both random draws, so the noise field is the absolute one rescaled per sample (tested). mean stays absolute.
• The absolute path is arithmetically unchanged: the batch-shared std now broadcasts through the same reshape as the per-sample one, which multiplies by the same value (tested bit-exact against the old formula).
• Also fixes the docstring, which gave the default std as 0.1. It is 1.0.

Tests

unit_tests/test_gaussian_noise_relative.py:

• the absolute form is bit-identical to the old arithmetic;
• the relative form is scale-equivariant;
• it equals the absolute draw × the sample std;
• the registry accepts the key.

Full suite: 477 passed, 13 skipped. mypy smauglab/ clean, pre-commit passes.

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