Recovery

The recovery module provides an implementation of state-of-the-art recovery algorithms widely used in image restoration on inverse problems.

\[\textbf{x}^{*} \in \underset{\textbf{x}}{ \argmin } \; f(\mathbf{x})+ \lambda g(\mathbf{x})\]

where \(f(\mathbf{x})\) is the fidelity term ( e.g., \(\Vert \textbf{y} - \textbf{H}(\textbf{x}) \Vert_2^2\) ) and \(g(\mathbf{x})\) is the prior term.

List of Algorithms

`colibri.recovery.fista.Fista`	Fast Iterative Shrinkage-Thresholding Algorithm (FISTA)
`colibri.recovery.pnp.PnP_ADMM`	Plug-and-Play (PnP) algorithm with Alternating Direction Method of Multipliers (ADMM) formulation.

List of Solvers

`colibri.recovery.solvers.core.L2L2Solver`	Base class for linear solvers.
`colibri.recovery.solvers.spc.L2L2SolverSPC`	Solver for the SPC acquisition model.

Fidelity Terms

The module contains differents fidelity terms \(f(\mathbf{x})\) that can be used in the recovery algorithms.

`colibri.recovery.terms.fidelity.L2`	L2 fidelity
`colibri.recovery.terms.fidelity.L1`	L1 fidelity

Prior Terms

The module contains differents prior terms \(g(\mathbf{x})\) that can be used in the recovery algorithms.

colibri.recovery.terms.prior.Sparsity

Sparsity prior

Transormation

The module contains differents signal transforms that can be used in the recovery algorithms.

colibri.recovery.terms.transforms.DCT2D

2D Discrete Cosine Transform