generalized_anscombe_transform

deepinv.models.generalized_anscombe_transform(x, gain, sigma)

Generalized Anscombe Transform (GAT)

The transform converts a noisy observation \(y\) from a Poisson-Gaussian distribution with gain \(\gamma\) and Gaussian noise standard deviation \(\sigma\) to an approximately Gaussian distribution with variance \(\gamma\), see Makitalo and Foi[1].

The transform is defined as:

\[h(y) = 2 \sqrt{\gamma x + \frac{3}{8}\gamma^2 + \sigma^2}\]

Note

The formula varies slightly from the one proposed by Makitalo and Foi[1], as the library considers a normalized Poisson-Gaussian noise model, \(y = \gamma \mathcal{P}(x/\gamma) + \epsilon\), whereas the authors consider \(y = \gamma \mathcal{P}(x) + \epsilon\).

Parameters:

• x (torch.Tensor) – tensor corrupted with Poisson-Gaussian noise

• gain (float | torch.Tensor) – Gain of the Poisson distribution \(\gamma\)

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

Return torch.Tensor:

Transformed measurements

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References:

[1] (1,2)

Markku Makitalo and Alessandro Foi. Optimal inversion of the generalized anscombe transformation for poisson-gaussian noise. IEEE transactions on image processing, 22(1):91–103, 2012.

Examples using generalized_anscombe_transform:

Poisson-Gaussian Denoising with the Generalized Anscombe Transform

Poisson-Gaussian Denoising with the Generalized Anscombe Transform