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	deepinv.physics.Denoising deepinv.physics.Inpainting deepinv.physics.Demosaicing deepinv.physics.Decolorize	BernoulliSplittingMaskGenerator GaussianSplittingMaskGenerator Phase2PhaseSplittingMaskGenerator Artifact2ArtifactSplittingMaskGenerator
Blur & Super-Resolution	deepinv.physics.Blur deepinv.physics.BlurFFT deepinv.physics.SpaceVaryingBlur deepinv.physics.Downsampling	MotionBlurGenerator DiffractionBlurGenerator ProductConvolutionBlurGenerator
Magnetic Resonance Imaging (MRI)	deepinv.physics.MRIMixin deepinv.physics.MRI deepinv.physics.MultiCoilMRI deepinv.physics.DynamicMRI deepinv.physics.SequentialMRI The above all also natively support 3D MRI.	GaussianMaskGenerator RandomMaskGenerator EquispacedMaskGenerator The above all also support k+t dynamic sampling.
Tomography	deepinv.physics.Tomography
Remote Sensing	deepinv.physics.Pansharpen
Compressive	deepinv.physics.CompressedSensing deepinv.physics.StructuredRandom deepinv.physics.SinglePixelCamera
Radio Interferometric Imaging	deepinv.physics.RadioInterferometry
Single-Photon Lidar	deepinv.physics.SinglePhotonLidar
Dehazing	deepinv.physics.Haze
Phase Retrieval	deepinv.physics.PhaseRetrieval RandomPhaseRetrieval StructuredRandomPhaseRetrieval

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