Georgia Institute of Technology College of Sciences

In this talk, we will discuss some advantages of using non-convex penalty functions in variational regularization problems and how to handle them using the so-called Convex-Nonconvex approach. In particular, TV-like non-convex penalty terms will be presented for the problems in segmentation and additive decomposition of scalar functions defined over a 2-manifold embedded in \R^3. The parametrized regularization terms are equipped by a free scalar parameter that allows to tune their degree of non-convexity. Appropriate numerical schemes based on the Alternating Directions Methods of Multipliers procedure are proposed to solve the optimization problems.