MOEILoss

class deepinv.loss.MOEILoss(transform, physics=None, physics_generator=None, metric=torch.nn.MSELoss(), apply_noise=True, weight=1.0, no_grad=False, rng=None)

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:

• transform (deepinv.transform.Transform) – Transform to generate the virtually augmented measurement. It can be any torch-differentiable function (e.g., a torch.nn.Module).

• 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.

• metric (Metric, torch.nn.Module) – Metric used to compute the error between the reconstructed augmented measurement and the reference image.

• apply_noise (bool) – if True, the augmented measurement is computed with the full sensing model \(\sensor{\noise{\forw{\hat{x}}}}\) (i.e., noise and sensor model), otherwise is generated as \(\forw{\hat{x}}\).

• weight (float) – Weight of the loss.

• no_grad (bool) – if True, the gradient does not propagate through \(T_g\). Default: False. This option is useful for super-resolution problems, see https://arxiv.org/abs/2312.11232.

• rng (torch.Generator) – torch randon number generator for randomly selecting from physics list. If using physics generator, rng is ignored.

forward(x_net, physics, model, **kwargs)

Computes the MO-EI loss

Parameters:

• x_net (torch.Tensor) – Reconstructed image \(\inverse{y}\).

• physics (deepinv.physics.Physics) – Forward operator associated with the measurements.

• model (torch.nn.Module) – Reconstruction function.

Returns:

(torch.Tensor) loss.