deepinv.optim

This module provides optimization utils for constructing reconstruction models based on optimization algorithms. Please refer to the user guide for more details.

Base Class

User Guide: refer to Optimization for more information.

deepinv.optim.optim_builder	Helper function for building an instance of the BaseOptim() class.
deepinv.optim.BaseOptim	Class for optimization algorithms, consists in iterating a fixed-point operator.

Potentials

User Guide: refer to Potentials for more information.

deepinv.optim.Potential

Base class for a potential \(h : \xset \to \mathbb{R}\) to be used in an optimization problem.

Data Fidelity

User Guide: refer to Data Fidelity for more information.

deepinv.optim.DataFidelity	Base class for the data fidelity term \(\distance{A(x)}{y}\) where \(A\) is the forward operator, \(x\in\xset\) is a variable and \(y\in\yset\) is the data, and where \(d\) is a distance function, from the class deepinv.optim.Distance().
deepinv.optim.L1	\(\ell_1\) data fidelity term.
deepinv.optim.L2	Implementation of the data-fidelity as the normalized \(\ell_2\) norm
deepinv.optim.IndicatorL2	Data-fidelity as the indicator of \(\ell_2\) ball with radius \(r\).
deepinv.optim.PoissonLikelihood	Poisson negative log-likelihood.
deepinv.optim.LogPoissonLikelihood	Log-Poisson negative log-likelihood.
deepinv.optim.AmplitudeLoss	Amplitude loss as the data fidelity term for deepinv.physics.PhaseRetrieval() reconstrunction.

Priors

User Guide: refer to Priors for more information.

deepinv.optim.Prior	Prior term \(\reg{x}\).
deepinv.optim.PnP	Plug-and-play prior \(\operatorname{prox}_{\gamma \regname}(x) = \operatorname{D}_{\sigma}(x)\).
deepinv.optim.RED	Regularization-by-Denoising (RED) prior \(\nabla \reg{x} = x - \operatorname{D}_{\sigma}(x)\).
deepinv.optim.ScorePrior	Score via MMSE denoiser \(\nabla \reg{x}=\left(x-\operatorname{D}_{\sigma}(x)\right)/\sigma^2\).
deepinv.optim.Tikhonov	Tikhonov regularizer \(\reg{x} = \frac{1}{2}\| x \|_2^2\).
deepinv.optim.L1Prior	\(\ell_1\) prior \(\reg{x} = \| x \|_1\).
deepinv.optim.WaveletPrior	Wavelet prior \(\reg{x} = \|\Psi x\|_{p}\).
deepinv.optim.TVPrior	Total variation (TV) prior \(\reg{x} = \| D x \|_{1,2}\).
deepinv.optim.PatchPrior	Patch prior \(g(x) = \sum_i h(P_i x)\) for some prior \(h(x)\) on the space of patches.
deepinv.optim.PatchNR	Patch prior via normalizing flows.
deepinv.optim.L12Prior	\(\ell_{1,2}\) prior \(\reg{x} = \sum_i\| x_i \|_2\).

Predefined models

User Guide: refer to Predefined Iterative Algorithms for more information.

deepinv.optim.DPIR	Deep Plug-and-Play (DPIR) algorithm for image restoration.
deepinv.optim.EPLL	Expected Patch Log Likelihood reconstruction method.

Bregman

User Guide: refer to Bregman for more information.

deepinv.optim.Bregman	Module for the Bregman framework with convex Bregman potential \(\phi\).
deepinv.optim.BregmanL2	Module for the L2 norm as Bregman potential \(\phi(x) = \frac{1}{2} \|x\|_2^2\).
deepinv.optim.BurgEntropy	Module for the using Burg's entropy as Bregman potential \(\phi(x) = - \sum_i \log x_i\).
deepinv.optim.NegEntropy	Module for the using negative entropy as Bregman potential \(\phi(x) = \sum_i x_i \log x_i\).
deepinv.optim.Bregman_ICNN	Module for the using a deep ICNN as Bregman potential.

Distance

User Guide: refer to Potentials for more information.

deepinv.optim.Distance	Distance \(\distance{x}{y}\).
deepinv.optim.L2Distance	Implementation of \(\distancename\) as the normalized \(\ell_2\) norm
deepinv.optim.IndicatorL2Distance	Indicator of \(\ell_2\) ball with radius \(r\).
deepinv.optim.PoissonLikelihoodDistance	(Negative) Log-likelihood of the Poisson distribution.
deepinv.optim.L1Distance	\(\ell_1\) distance
deepinv.optim.AmplitudeLossDistance	Amplitude loss for deepinv.physics.PhaseRetrieval() reconstrunction, defined as
deepinv.optim.LogPoissonLikelihoodDistance	Log-Poisson negative log-likelihood.

Iterators

User Guide: refer to Iterators for more information.

deepinv.optim.FixedPoint	Fixed-point iterations module.
deepinv.optim.OptimIterator	Base class for all Optim() iterators.
deepinv.optim.optim_iterators.fStep	Module for the single iteration steps on the data-fidelity term \(f\).
deepinv.optim.optim_iterators.gStep	Module for the single iteration steps on the prior term \(\lambda \regname\).
deepinv.optim.optim_iterators.GDIteration	Iterator for Gradient Descent.
deepinv.optim.optim_iterators.PGDIteration	Iterator for proximal gradient descent.
deepinv.optim.optim_iterators.FISTAIteration	Iterator for fast iterative soft-thresholding (FISTA).
deepinv.optim.optim_iterators.CPIteration	Iterator for Chambolle-Pock.
deepinv.optim.optim_iterators.ADMMIteration	Iterator for alternating direction method of multipliers.
deepinv.optim.optim_iterators.DRSIteration	Iterator for Douglas-Rachford Splitting.
deepinv.optim.optim_iterators.HQSIteration	Single iteration of half-quadratic splitting.
deepinv.optim.optim_iterators.MDIteration	Iterator for Mirror Descent.
deepinv.optim.optim_iterators.SMIteration	Iterator for Spectral Methods for deepinv.physics.PhaseRetrieval().

Utils

User Guide: refer to Utils for more information.

deepinv.optim.utils.conjugate_gradient	Standard conjugate gradient algorithm.
deepinv.optim.utils.gradient_descent	Standard gradient descent algorithm`.
deepinv.optim.utils.GaussianMixtureModel	Gaussian mixture model including parameter estimation.