Mixed-Derivative Total Variation
Vincent Patrick Lawrence Guillemet, Doctoral Student at EPFL

Meeting • 2025-09-26

Abstract
The formulation of norms on continuous-domain Banach spaces with exact pixel-based discretization is advan- tageous for solving inverse problems (IPs). In this paper, we investigate a new regularization that is a convex combination of a TV term and the M(\R^2) norm of mixed derivatives. We show that the extreme points of the corresponding unit ball are indicator functions of polygons whose edges are aligned with either the x1- or x2-axis. We then apply this result to construct a new regularization for IPs, which can be discretized exactly by tensor products of first-order B-splines, or equivalently, pixels. Furthermore, we exactly discretize the loss of the denoising problem on its canonical pixel basis and prove that it admits a unique solution, which is also a solution to the underlying continuous-domain IP.