spyrit.core.recon.Tikhonov.forward

Tikhonov.forward(y: tensor, gamma: tensor) → tensor

Reconstructs the signal from measurements and noise covariance.

The Tikhonov solution is computed as

\[\hat{x} = B^\top (C + \Gamma)^{-1} y\]

with \(B = \Sigma A^\top\) and \(C = A \Sigma A^\top\). When self.approx is True, it is approximated as

\[\hat{x} = B^\top \frac{y}{\text{diag}(C + \Gamma)}\]

Args:

y (torch.tensor): A batch of measurement vectors \(y\)

gamma (torch.tensor): A batch of noise covariance \(\Gamma\)

Shape:

y (torch.tensor): \((*, M)\)

gamma (torch.tensor): \((*, M, M)\)

Output (torch.tensor): \((*, N)\)