MOEILoss

class deepinv.loss.MOEILoss(*args, physics: list[Physics] | Physics | None = None, physics_generator: PhysicsGenerator | None = None, **kwargs)[source]

Bases: EILoss, MOILoss

Multi-operator equivariant imaging.

This loss extends the equivariant loss deepinv.loss.EILoss, where the signals are not only assumed to be invariant to a group of transformations, but also observed via multiple (possibly incomplete) forward operators \(\{A_s\}_{s=1}^{S}\), i.e., \(y_i = A_{s_i}x_i\) where \(s_i\in \{1,\dots,S\}\).

The multi-operator equivariance loss is defined as

\[\| T_g \hat{x} - \inverse{A_2 T_g \hat{x}, A_2}\|^2\]

where \(\hat{x}=\inverse{y,A_1}\) is a reconstructed signal (observed via operator \(A_1\)), \(A_2\) is a forward operator sampled at random from a set \(\{A_2\}_{s=1}^{S}\) and \(T_g\) is a transformation sampled at random from a group \(g\sim\group\).

By default, the error is computed using the MSE metric, however any other metric (e.g., \(\ell_1\)) can be used as well.

The operators can be passed as a list of physics or as a single physics with a random physics generator.

See deepinv.loss.EILoss for all parameter details for EI.

Parameters:

  • physics (list[Physics], Physics) – list of physics containing the \(G\) different forward operators associated with the measurements, or single physics, or None. If single physics or None, physics generator must be used. If None, physics taken during forward.

  • physics_generator (PhysicsGenerator) – random physics generator that generates new params, if physics is not a list.

forward(x_net, physics, model, **kwargs)[source]

Computes the MO-EI loss

Parameters:
Returns:

(torch.Tensor) loss.