pyproximal.projection.AffineSetProj

class pyproximal.projection.AffineSetProj(Op: LinearOperator, b: ndarray[tuple[Any, ...], dtype[_ScalarT]], niter: int)

Affine set projection.

Parameters:

Oppylops.LinearOperator

Linear operator

bnumpy.ndarray

Data vector

niterint

Number of iterations of iterative scheme used to compute the projection.

Notes

Given an Affine set defined as:

\[\{ \mathbf{x} : \mathbf{Opx}=\mathbf{b} \}\]

its orthogonal projection is:

\[P_{\{\mathbf{y}:\mathbf{Opy}=\mathbf{b}\}} (\mathbf{x}) = \mathbf{x} - \mathbf{Op}^H(\mathbf{Op}\mathbf{Op}^H)^{-1}(\mathbf{Opx}-\mathbf{b})\]

Note the this is the proximal operator of the corresponding indicator function \(I_{\{\mathbf{Opx}=\mathbf{b}\}}\)

Methods

__init__(Op, b, niter)