GaussianNoise#

class deepinv.physics.GaussianNoise(sigma=0.1, rng=None)[source]#

Bases: NoiseModel

Gaussian noise \(y=z+\epsilon\) where \(\epsilon\sim \mathcal{N}(0,I\sigma^2)\).

Parameters:

sigma (Union[float, torch.Tensor]) – Standard deviation of the noise.
rng (torch.Generator, None) – (optional) a pseudorandom random number generator for the parameter generation.

Examples:

Adding gaussian noise to a physics operator by setting the noise_model attribute of the physics operator:

>>> from deepinv.physics import Denoising, GaussianNoise
>>> import torch
>>> physics = Denoising()
>>> physics.noise_model = GaussianNoise()
>>> x = torch.rand(3, 1, 2, 2)
>>> y = physics(x)

We can sum 2 GaussianNoise instances:

>>> gaussian_noise_1 = GaussianNoise(sigma=3.0)
>>> gaussian_noise_2 = GaussianNoise(sigma=4.0)
>>> gaussian_noise = gaussian_noise_1 + gaussian_noise_2
>>> y = gaussian_noise(x)
>>> gaussian_noise.sigma.item()
5.0

We can also multiply a GaussianNoise by a float:

\(scaled\_gaussian\_noise(x) = \lambda \times gaussian\_noise(x)\)

>>> scaled_gaussian_noise = 3.0 * gaussian_noise
>>> y = scaled_gaussian_noise(x)
>>> scaled_gaussian_noise.sigma.item()
15.0

We can also create a batch of GaussianNoise with different standard deviations:

\(x=[x_1, ..., x_b]\)
\(t=[[[[\lambda_1]]], ..., [[[\lambda_b]]]]\) a batch of scaling factors.
\([t \times gaussian](x) = [\lambda_1 \times gaussian(x_1), ..., \lambda_b \times gaussian(x_b)]\)

>>> t = torch.rand((x.size(0),) + (1,) * (x.dim() - 1)) # if x.shape = (b, 3, 32, 32) then t.shape = (b, 1, 1, 1)
>>> batch_gaussian_noise = t * gaussian_noise
>>> y = batch_gaussian_noise(x)
>>> assert (t[0]*gaussian_noise).sigma.item() == batch_gaussian_noise.sigma[0].item(), "Wrong standard deviation value for the first GaussianNoise."

Used in benchmarks:

__add__(other)[source]#

Sum of 2 gaussian noises via + operator.

\(\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}\)

Parameters:: other (deepinv.physics.GaussianNoise) – Gaussian with standard deviation \(\sigma\)
Returns:: (deepinv.physics.GaussianNoise) – Gaussian noise with the sum of the linear operators.

__mul__(other)[source]#

Element-wise multiplication of a GaussianNoise via * operator.

If other is a NoiseModel, then applies the multiplication from NoiseModel.
If other is a float, then the standard deviation of the GaussianNoise is multiplied by other.

\(x=[x_1, ..., x_b]\) a batch of images.

\(\lambda\) a float.

\(\sigma = [\lambda \times \sigma_1, ..., \lambda \times \sigma_b]\)
If other is a torch.Tensor, then the standard deviation of the GaussianNoise is multiplied by other.

\(x=[x_1, ..., x_b]\) a batch of images.

\(other=[[[[\lambda_1]]], ..., [[[\lambda_b]]]]\) a batch of scaling factors.

\(\sigma = [\lambda \times \sigma_1, ..., \lambda \times \sigma_b]\)

Parameters:: other (float or torch.Tensor) – Scaling factor for the GaussianNoise’s standard deviation.
Returns:: (deepinv.physics.GaussianNoise) – A new GaussianNoise with the new standard deviation.

forward(x, sigma=None, seed=None, **kwargs)[source]#

Adds the noise to measurements x

Parameters:

x (torch.Tensor) – measurements
sigma (float, torch.Tensor) – standard deviation of the noise. If not None, it will overwrite the current noise level.
seed (int) – the seed for the random number generator, if rng is provided.

Returns: