Tikhonov

class deepinv.optim.Tikhonov(*args, **kwargs)

Bases: Prior

Tikhonov regularizer \(\reg{x} = \frac{1}{2}\| x \|_2^2\).

g(x, *args, **kwargs)

Computes the Tikhonov regularizer \(\reg{x} = \frac{1}{2}\| x \|_2^2\).

Parameters:

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

Returns:

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

grad(x, *args, **kwargs)

Calculates the gradient of the Tikhonov regularization term \(\regname\) at \(x\).

Parameters:

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

Returns:

(torch.Tensor) gradient at \(x\).

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

Calculates the proximity operator of the Tikhonov regularization term \(\gamma g\) at \(x\).

Parameters:

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

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

Returns:

(torch.Tensor) proximity operator at \(x\).