Learning Regularizers for Inverse Problems in Imaging, Erich Kobler
Sprache des Titels:
Numerous problems in computer vision and medical imaging can be cast as inverse problems. The variational approach robustly estimates solutions of an inverse problem by minimizing an energy composed of a data fidelity term and a regularizer. While the data fidelity term is utilized to incorporate knowledge about the underlying physical process of the inverse problem, the regularizer typically encodes a-priori statistical properties of the desired solutions. Classically, handcrafted regularizers motivated by first-order statistics of images are used, which are frequently outperformed by state-of-the-art purely data-driven deep learning models. In this talk, we develop novel methods combining variational methods and deep learning that lead to state-of-the-art results on various imaging tasks and allow a rigorous mathematical analysis. In detail, we further investigate the effect that in variational methods the best image quality is frequently observed when the associated gradient flow is stopped before converging to a stationary point. We argue that this phenomenon originates from a tradeoff between optimization and modeling errors and remains valid even if highly expressive deep learning-based regularizers are employed. We analyze this paradox by considering a variational method featuring a parametric regularizer and by introducing an optimal stopping time in the corresponding gradient flow. ....