Source code for pyproximal.projection.AffineSet

from scipy.sparse.linalg import lsqr as sp_lsqr
from scipy.sparse.linalg import cg as sp_cg
from pylops.optimization.basic import cg, lsqr
from pylops.utils.backend import get_array_module, get_module_name

[docs]class AffineSetProj(): r"""Affine set projection. Parameters ---------- Op : :obj:`pylops.LinearOperator` Linear operator b : :obj:`numpy.ndarray` Data vector niter : :obj:`int` Number of iterations of iterative scheme used to compute the projection. Notes ----- Given an Affine set defined as: .. math:: \{ \mathbf{x} : \mathbf{Opx}=\mathbf{b} \} its orthogonal projection is: .. math:: 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 :math:`I_{\{\mathbf{Opx}=\mathbf{b}\}}` """ def __init__(self, Op, b, niter): self.Op = Op self.b = b self.niter = niter def __call__(self, x): if get_module_name(get_array_module(x)) == 'numpy': inv = sp_cg(self.Op * self.Op.H, self.Op * x - self.b, maxiter=self.niter)[0] else: inv = cg(self.Op * self.Op.H, self.Op * x - self.b, niter=self.niter)[0] y = x - self.Op.H * inv.ravel() # currently ravel is added to ensure that the output is always a vector return y