Discrete Total Variation Flows Without Regularization
This work addresses the need for accurate numerical solutions of total variation flows without regularization, benefiting practitioners in image processing and inverse problems who rely on TV-based models.
The authors propose a regularization-free algorithm for solving the L2-subgradient flow of the total variation functional, ensuring convergence and preserving key features. Numerical experiments demonstrate the method's effectiveness and compare favorably with regularized approaches.
We propose and analyze an algorithm for the solution of the $L^2$-subgradient flow of the total variation functional. The algorithm involves no regularization, thus the numerical solution preserves the main features that motivate practitioners to consider this type of energy. We propose an iterative scheme for the solution of the arising problems, show that the iterations converge, and develop a stopping criterion for them. We present numerical experiments which illustrate the power of the method, explore the solution behavior, and compare with regularized flows.