pyproximal.ProxOperator

class pyproximal.ProxOperator(Op: LinearOperator | None = None, hasgrad: bool = False, sigmame: float = 1.0)

Common interface for proximal operators of a function.

This class defines the overarching structure of any proximal operator. It contains two main methods, prox and dualprox which are both implemented by means of the Moreau decomposition assuming explicit knowledge of the other method. For this reason any proximal operators that subclasses the ProxOperator class needs at least one of these two methods to be implemented directly.

Moreover, the method grad is also defined to compute the gradient of the Moreau envelope of the function. This function is only called if the user does not provide a gradient function when creating the proximal operator. The variable hasgrad is used to indicate if the function has a gradient or not (and thus if the grad method computes the gradient of the actual function or of its Moreau envelope).

Note

End users of PyProximal should not use this class directly but simply use operators that are already implemented. This class is meant for developers and it has to be used as the parent class of any new operator developed within PyProximal. Find more details regarding implementation of new operators at Implementing new operators.

Parameters:

Oppylops.LinearOperator, optional

Linear operator used by the Proximal operator

hasgradbool, optional

Flag to indicate if the function is differentiable, i.e., has a uniquely defined gradient (True) or not (False).

sigmamefloat, optional

Relaxation parameter of the Moreau envelope (when sigmame tends to infinity the gradient of the Moreau envelope tends to the gradient of the function itself). Refer to the docstring of the grad method for more details.

Notes

The proximal operator of a function f is defined as:

\[prox_{\tau f} (\mathbf{x}) = \argmin_{\mathbf{y}} f(\mathbf{y}) + \frac{1}{2 \tau}||\mathbf{y} - \mathbf{x}||^2_2\]

Methods

__init__([Op, hasgrad, sigmame])
affine_addition(v)	Affine addition
chain(g)	Chain
grad(x)	Gradient of the Moreau envelope of the function.
postcomposition(sigma)	Postcomposition
precomposition(a, b)	Precomposition
prox(**kwargs)
proxdual(**kwargs)

Examples using pyproximal.ProxOperator

Concave penalties

Concave penalties

Dykstra’s algorithms

Dykstra's algorithms

Indicators

Indicators

Norms

Norms

Quadratic

Quadratic

Adaptive Primal-Dual

Adaptive Primal-Dual

Basis Pursuit

Basis Pursuit

Deblending

Deblending

Denoising

Denoising

Group sparsity

Group sparsity

Hankel matrix estimation

Hankel matrix estimation

IHT, ISTA, FISTA, AA-ISTA, and TWIST for Compressive sensing

IHT, ISTA, FISTA, AA-ISTA, and TWIST for Compressive sensing

Low-Rank completion via Matrix factorization

Low-Rank completion via Matrix factorization

Low-Rank completion via SVD

Low-Rank completion via SVD

MRI Imaging and Segmentation of Brain

MRI Imaging and Segmentation of Brain

Non-rigid structure-from-motion (NRSfM)

Non-rigid structure-from-motion (NRSfM)

Nonlinear inversion with box constraints

Nonlinear inversion with box constraints

Plug and Play Priors

Plug and Play Priors

Quadratic program with box constraints

Quadratic program with box constraints

Relaxed Mumford-Shah regularization

Relaxed Mumford-Shah regularization