Optimization Algorithms for Bilevel Learning with Applications to Imaging

Many imaging problems, such as denoising or inpainting, can be expressed as variational regularization problems. These are optimization problems for which many suitable algorithms exist. We consider the problem of learning suitable regularizers for imaging problems from example (training) data, which can be formulated as a large-scale bilevel optimization problem. In this talk, I will introduce new deterministic and stochastic algorithms for bilevel optimization, which require no or minimal hyperparameter tuning while retaining convergence guarantees. This is joint work with Mohammad Sadegh Salehi and Matthias Ehrhardt (University of Bath), and Subhadip Mukherjee (IIT Kharagpur).