LpNorm#

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

Bases: Metric

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

Calculates \(L_p(\hat{x},x)\) 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 Jacques et al.[1], 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 \(\ell_2\) spatial norm, min_max normalizes by min and max of each input.

  • center_crop (int, tuple[int], None) – If not None (default), center crop the tensor(s) before computing the metrics. If an int is provided, the cropping is applied equally on all spatial dimensions (by default, all dimensions except the first two). If tuple of int, cropping is performed over the last len(center_crop) dimensions. If positive values are provided, a standard center crop is applied. If negative (or zero) values are passed, cropping will be done by removing center_crop pixels from the borders (useful when tensors vary in size across the dataset).

References:

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