pyproximal.projection.AffineSetProj#
- class pyproximal.projection.AffineSetProj(Op, b, niter)[source]#
Affine set projection.
- Parameters
- Op
pylops.LinearOperator Linear operator
- b
numpy.ndarray Data vector
- niter
int Number of iterations of iterative scheme used to compute the projection.
- Op
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)