Total Generalized Variation

Question

While reading the paper Total Generalized Variation, I came across the following formula (Equation 1.5), which describes the regularization term:

Total Generalized Variation formula

While there are a lot of things I don't understand here, my main question is what is the $div^k$ operator. I imagine that it's a generalization of the divergence operator, but how is it defined?

Answer 1

The paper says:

For the definition of the remaining quantities, we ask for the readers’ patience until Section 2.

Looking there I find $\operatorname{div}^k$ to be defined in equation (2.1) which depends on the definition of $\operatorname{tr}^l$ on page 6.

Thus: Be patient and continue reading.