ABSTRACT

This chapter considers the general reconstruction problem with total variation (TV). It addresses the problem of computing the proximity operator of the discrete TV and describes a few elementary imaging applications. The chapter describes the parametric maximum approach for computing the proximity operator of the discrete TV. It describes a parametric network flow based approach for minimizing discrete total variations with separable convex data fidelity terms. The chapter explains the presentation of some numerical experiments in image processing. It considers anistropic total variations defined on the 8 nearest neighbors: the weights on the 4 nearest ones (i.e., left, right, top, and bottom) are set to 1, while the weights for the 4 diagonal interactions are set to 1/2. It considers the optimization of DTV energies with nonseparable data fidelities. The speed of the proximal splitting algorithm can be improved using acceleration techniques.