41:31Carola Schönlieb explains how mathematical models for image restoration and denoising developed into methods for medical imaging, where algorithms reconstruct images from indirect, noisy measurements such as X-ray projections. She compares interpretable handcrafted methods, including total variation regularization, with deep neural networks, which can perform well on familiar data but may fail when conditions change. She describes ways to combine the two, including learning a small number of parameters for a handcrafted model and adding measurement information to neural-network reconstruction. The talk also covers applications in dynamic medical imaging, forest monitoring, security footage, and virtual restoration of artworks and manuscripts.