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 ConfocalBlurGenerator3D gaussian_blur, sinc_filter bilinear_filter, bicubic_filter
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 & Multispectral	deepinv.physics.Pansharpen deepinv.physics.HyperSpectralUnmixing deepinv.physics.CompressiveSpectralImaging
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 Ptychography PtychographyLinearOperator	build_probe generate_shifts

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	$y=\gamma z+ϵ$, $z\sim \mathcal{P}(\frac{z}{\gamma })$, $ϵ\sim \mathcal{N}(0,I{\sigma }^2)$
deepinv.physics.LogPoissonNoise	$y=\frac{1}{\mu }\log (\frac{\mathcal{P}(\exp (-\mu z)N_0)}{N_0})$
deepinv.physics.UniformNoise	$y\sim \mathcal{U}(z-a,z+b)$