L12Prior

class deepinv.optim.L12Prior(*args, l2_axis=-1, **kwargs)

Bases: Prior

\(\ell_{1,2}\) prior \(\reg{x} = \sum_i\| x_i \|_2\).

The \(\ell_2\) norm is computed over a tensor axis that can be defined by the user. By default, l2_axis=-1.

Parameters:

l2_axis (int) – dimension in which the \(\ell_2\) norm is computed.

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Examples:

>>> import torch
>>> from deepinv.optim import L12Prior
>>> seed = torch.manual_seed(0) # Random seed for reproducibility
>>> x = torch.randn(2, 1, 3, 3) # Define random 3x3 image
>>> prior = L12Prior()
>>> prior.fn(x)
tensor([5.4949, 4.3881])
>>> prior.prox(x)
tensor([[[[-0.4666, -0.4776,  0.2348],
          [ 0.3636,  0.2744, -0.7125],
          [-0.1655,  0.8986,  0.2270]]],


        [[[-0.0000, -0.0000,  0.0000],
          [ 0.7883,  0.9000,  0.5369],
          [-0.3695,  0.4081,  0.5513]]]])

fn(x, *args, **kwargs)

Computes the regularizer \(\reg{x} = \sum_i\| x_i \|_2\).

Parameters:

x (torch.Tensor) – Variable \(x\) at which the prior is computed.

Returns:

(torch.Tensor) prior \(\reg{x}\).

prox(x, *args, gamma=1.0, **kwargs)

Calculates the proximity operator of the \(\ell_{1,2}\) function at \(x\).

More precisely, it computes

\[\operatorname{prox}_{\gamma g}(x) = (1 - \frac{\gamma}{max{\Vert x \Vert_2,\gamma}}) x\]

where \(\gamma\) is a stepsize.

Parameters:

• x (torch.Tensor) – Variable \(x\) at which the proximity operator is computed.

• gamma (float) – stepsize of the proximity operator.

• l2_axis (int) – axis in which the l2 norm is computed.

Return torch.Tensor:

proximity operator at \(x\).