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 deepinv.optim.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.StackedPhysicsDataFidelity	Stacked data fidelity term \(\datafid{x}{y} = \sum_i d_i(A_i(x),y_i)\).
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.
deepinv.optim.ZeroFidelity	Zero data fidelity term \(\datafid{x}{y} = 0\).

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 reconstruction, defined as
deepinv.optim.LogPoissonLikelihoodDistance	Log-Poisson negative log-likelihood.
deepinv.optim.ZeroDistance	Zero distance \(\distance{z}{y} = 0\).

Iterators

User Guide: refer to Iterators for more information.

deepinv.optim.FixedPoint	Fixed-point iterations module.
deepinv.optim.OptimIterator	Base class for optimization 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.least_squares	Solves \(\min_x \|Ax-y\|^2 + \frac{1}{\gamma}\|x-z\|^2\) using the specified solver.
deepinv.optim.utils.least_squares_implicit_backward	Least squares solver with O(1) memory backward propagation using implicit differentiation.
deepinv.optim.utils.lsqr	LSQR algorithm for solving linear systems.
deepinv.optim.utils.bicgstab	Biconjugate gradient stabilized algorithm.
deepinv.optim.utils.minres	Minimal Residual Method for solving symmetric equations.
deepinv.optim.utils.conjugate_gradient	Standard conjugate gradient algorithm.
deepinv.optim.utils.gradient_descent	Standard gradient descent algorithm`.
deepinv.optim.phase_retrieval.correct_global_phase	Corrects the global phase of the reconstructed image.
deepinv.optim.phase_retrieval.spectral_methods	Utility function for spectral methods.

deepinv.optim.utils.GaussianMixtureModel

Gaussian mixture model including parameter estimation.