Second-order total Generalized Variation constraint

This paper proposes to use the Total Generalized Variation (TGV) of second order in a constrained form for image processing, which we call the TGV constraint. The main contribution is twofold: i) we present a general form of convex optimization problems with the TGV constraint, which is, to the best of our knowledge, the first attempt to use TGV as a constraint and covers a wide range of problem formulations sufficient for image processing applications; and ii) a computationally-efficient algorithmic solution to the problem is provided, where we mobilize several recently-developed proximal splitting techniques to handle the complicated structured set, i.e., the TGV constraint. Experimental results illustrate the potential applicability and utility of the TGV constraint.