# Tikhonov

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

Bases: [`Prior`](https://deepinv.org/api/stubs/deepinv.optim.Prior.html.md#deepinv.optim.Prior)

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

#### fn(x, \*args, \*\*kwargs)

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

* **Parameters:**
  **x** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Variable $x$ at which the prior is computed.
* **Returns:**
  ([`torch.Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) prior $\reg{x}$.
* **Return type:**
  [*Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)

#### grad(x, \*args, \*\*kwargs)

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

* **Parameters:**
  **x** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Variable $x$ at which the gradient is computed.
* **Returns:**
  ([`torch.Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) gradient at $x$.
* **Return type:**
  [*Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)

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

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

* **Parameters:**
  * **x** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Variable $x$ at which the proximity operator is computed.
  * **gamma** ([*float*](https://docs.python.org/3.12/library/functions.html#float)) – stepsize of the proximity operator.
* **Returns:**
  ([`torch.Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) proximity operator at $x$.
* **Return type:**
  [*Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)