LpNorm

class deepinv.loss.metric.LpNorm(p=2, onesided=False, **kwargs)[source]

Bases: Metric

\(\ell_p\) metric for \(p>0\).

Calculates the Lp norm \(L_p(\hat{x},x)\) where \(\hat{x}=\inverse{y}\).

If onesided=False then the metric is defined as \(d(x,y)=\|x-y\|_p^p\).

Otherwise, it is the one-sided error https://ieeexplore.ieee.org/abstract/document/6418031/, defined as \(d(x,y)= \|\max(x\circ y) \|_p^p\). where \(\circ\) denotes element-wise multiplication.

Note

By default, no reduction is performed in the batch dimension.

Example:

>>> import torch
>>> from deepinv.loss.metric import LpNorm
>>> m = LpNorm(p=3) # L3 norm
>>> x_net = x = torch.ones(3, 2, 8, 8) # B,C,H,W
>>> m(x_net, x)
tensor([0., 0., 0.])
Parameters:

  • p (int) – order p of the Lp norm

  • onesided (bool) – whether one-sided metric.

  • complex_abs (bool) – perform complex magnitude before passing data to metric function. If True, the data must either be of complex dtype or have size 2 in the channel dimension (usually the second dimension after batch).

  • reduction (str) – a method to reduce metric score over individual batch scores. mean: takes the mean, sum takes the sum, none or None no reduction will be applied (default).

  • norm_inputs (str) – normalize images before passing to metric. l2``normalizes by L2 spatial norm, ``min_max normalizes by min and max of each input.

metric(x_net, x, *args, **kwargs)[source]

Calculate metric on data.

Override this function to implement your own metric. Always include args and kwargs arguments.

Parameters:

  • x_net (torch.Tensor) – Reconstructed image \(\hat{x}=\inverse{y}\) of shape (B, ...) or (B, C, ...).

  • x (torch.Tensor) – Reference image \(x\) (optional) of shape (B, ...) or (B, C, ...).

Return torch.Tensor:

calculated metric, the tensor size might be (1,) or (B,).