AnscombeDenoiser

class deepinv.models.AnscombeDenoiser(denoiser, *args, **kwargs)

Bases: Denoiser

Wraps a Gaussian denoiser into a Poisson-Gaussian denoiser using the Generalized Anscombe Transform (GAT) and its inverse.

Given a noisy observation \(y\) corrupted by Poisson-Gaussian noise with gain \(\gamma\) and Gaussian standard deviation \(\sigma\), the wrapper:

1. Applies the GAT to stabilize the variance to approximately \(\gamma^2\):

\[z = 2 \sqrt{\gamma y + \frac{3}{8}\gamma^2 + \sigma^2}\]

2. Applies the wrapped Gaussian denoiser \(\denoisername\) at noise level \(\gamma\) (which matches the standard deviation of the GAT output):

\[\hat{z} = \denoisername(z,\; \sigma=\gamma)\]

3. Applies the inverse GAT to return to the original domain. Setting \(u = \hat{z}/\gamma\):

\[\hat{y} = \gamma\left(\frac{1}{4}u^2 + \frac{1}{4}\sqrt{\frac{3}{2}}\,u^{-1} - \frac{11}{8}u^{-2} + \frac{5}{8}\sqrt{\frac{3}{2}}\,u^{-3} - \frac{1}{8} + \frac{\sigma^2}{\gamma^2}\right), \qquad u = \frac{\hat{z}}{\gamma}\]

Note

When gain = None the noise is purely Gaussian and the GAT/IGAT are bypassed: the wrapped denoiser is called directly as \(\denoisername(y, \sigma)\).

Parameters:

denoiser (deepinv.models.Denoiser) – Gaussian denoiser \(\denoisername\) to wrap.

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Examples:

>>> import deepinv as dinv
>>> import torch
>>> from deepinv.models import AnscombeDenoiser, DRUNet
>>> denoiser = DRUNet(pretrained="download")
>>> anscombe_denoiser = AnscombeDenoiser(denoiser)
>>> x = dinv.utils.load_example('butterfly.png')
>>> y = dinv.physics.Denoising(dinv.physics.PoissonNoise(gain=.2))(x)
>>> with torch.no_grad():
...     y_denoised = anscombe_denoiser(y, sigma=0., gain=0.2)
>>> dinv.utils.plot([x, y, y_denoised], ["ground-truth", "noisy", "denoised"])

forward(y, sigma, gain=None, *args, **kwargs)

Applies the Poisson-Gaussian denoiser via the Anscombe transform.

Parameters:

• y (torch.Tensor) – Noisy measurements corrupted by Poisson-Gaussian noise.

• sigma (float | torch.Tensor) – Standard deviation of the Gaussian noise \(\sigma\).

• gain (float | torch.Tensor | None) – Gain of the Poisson distribution \(\gamma\).

• args – Additional positional arguments passed to the wrapped denoiser.

• kwargs – Additional keyword arguments passed to the wrapped denoiser.

Return torch.Tensor:

Denoised measurements in the original domain.

Return type:

Tensor

Examples using AnscombeDenoiser:

Poisson-Gaussian Denoising with the Generalized Anscombe Transform

Poisson-Gaussian Denoising with the Generalized Anscombe Transform