Operators & Noise#

Operators#

Operators describe the forward model \(z = A(x,\theta)\), where \(x\) is the input image and \(\theta\) are the parameters of the operator. The parameters \(\theta\) can be sampled using random generators, which are available for some specific classes.

Table 1 Operators, Definitions, and Generators#

Family

Operators

Generators

Pixelwise

Blur & Super-Resolution

Magnetic Resonance Imaging (MRI)

The above all also support k+t dynamic sampling.

Tomography

Remote Sensing & Multispectral

Compressive

Radio Interferometric Imaging

Single-Photon Lidar

Dehazing

Phase Retrieval

Noise distributions#

Noise distributions describe the noise model \(N\), where \(y = N(z)\) with \(z=A(x)\). The noise models can be assigned to any operator in the list above, by setting the set_noise_model attribute at initialization.

Table 2 Noise Distributions and Their Probability Distributions#

Noise

\(y|z\)

deepinv.physics.GaussianNoise

\(y\sim \mathcal{N}(z, I\sigma^2)\)

deepinv.physics.PoissonNoise

\(y \sim \mathcal{P}(z/\gamma)\)

deepinv.physics.PoissonGaussianNoise

\(y = \gamma z + \epsilon\), \(z\sim\mathcal{P}(\frac{z}{\gamma})\), \(\epsilon\sim\mathcal{N}(0, I \sigma^2)\)

deepinv.physics.LogPoissonNoise

\(y = \frac{1}{\mu} \log(\frac{\mathcal{P}(\exp(-\mu z) N_0)}{N_0})\)

deepinv.physics.UniformNoise

\(y\sim \mathcal{U}(z-a, z+b)\)