Smooth Joint TV implementation

[epapoutsellis]

This is a draft implementation for Smooth Joint TV that was used in the Fully3D meeting.

• [ ] No unittest atm.
• [ ] As we do for the TotalVariation function, we have to extract the domain from a DataContainer and then use it for the GradientOperator. This is not correct. See my comment

• A convex combination for the regularisation parameter lambda_par is used, i.e., \lambda\nabla u, (1-lambda)\nabla v.
• There is no proximal method implementation. This will be in another class, the non-smooth case. This follows the same ideas as the MixedL21Norm and the SmoothMixedL21Norm.

Note We can have different definitions for the JTV. Generally, we can have three parameters: one outside JTV and two in front of the two gradients:

$alpha_{1} \sum_{\sqrt{ \alpha_{2}\nabla u + \alpha_{3}\nabla v}}$

[paskino]

• As we do for the TotalVariation function, we have to extract the domain from a DataContainer and then use it for the GradientOperator. This is not correct. See my comment

Why you say it's not correct? In the design of the Function class there is no domain, though sometimes it may turn useful. Like here, where we need the domain because this function uses an operator inside which requires the domain. The current workaround solution is not too bad, IMO.