Bregman Itoh–Abe Methods for Sparse Optimisation

• DOI: 10.1007/s10851-020-00944-x
• Publication Date: 2020-02-03T05:03:27Z
• Authors: Martin Benning; Erlend Skaldehaug...; Carola-Bibiane Sc...
• Keywords: Bregman divergence; Balanced flow

In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse generalises flows by incorporating a generalised Bregman distance as underlying metric. Its discrete-time counterparts, iterations and linearised iterations, are popular schemes that incorporate priori information without loss of contrast. Discrete tools from geometric numerical integration preserving energy dissipation dissipative differential systems. The resultant unconditionally dissipative, achieve rapid convergence rates exploiting structures problem such sparsity. Building previous work gradients non-smooth, non-convex optimisation, prove guarantees these in Clarke subdifferential framework. Numerical results convex examples presented.