Title: Recent advances in using machine learning for image reconstruction
The talk will outline recent approaches for using (deep) convolutional neural networks to solve a wide range of inverse problems, such as image reconstruction in tomography. A key element is to use a neural network architecture for reconstruction that includes physics-based models that describe how data is generated as well as its statistical properties Another is the possibility to integrate complex task related a priori information and elements of decision making into the reconstruction procedure. The resulting approach outperforms current state-of-the-art in terms of ‘quality’, computational speed and there is no need to manually set parameters as with variational methods. Furthermore, the amount of training data and network size can be kept surprisingly small. The talk will also touch upon further developments based on using generative adversarial networks for uncertainty quantification.
Our seminar focuses on efficient computational methods for numerical problems, mostly phrased in a mathematical language, arising in areas of science throughout the Institute and beyond. Topics include signal processing and data analysis (spike sorting of neural recordings, cryo-EM for protein imaging, audio representation); computational statistics (with applications such as the ocean microbiome); PDEs (fluid flow, waves), integral equations, spectral methods, “fast” algorithms (i.e., close to optimal complexity); software libraries and programming. We discuss research topics as well as review classical topics in numerical analysis.