This aim is to introduce basic notions from machine learning. We will quickly focus on supervised learning in the purely data driven setting, i.e., there are no physics driven mechanistic models for how training data is generated. The aim is to survey some of the results and open problems associated with developing a mathematical and computational theory for deep learning in this setting.
Focus here is on applying machine learning to solve ill-posed inverse problems, i.e., to recover an operator that maps the data to signal. The starting point is to very briefly survey current regularization schemes emphasizing on the ability to account for a priori information. Next, is to outline challenges associated with using machine learning for solving ill-posed inverse problems followed by a survey on early attempts that are based on using it as a post- processing step. We conclude with outlining the limitations with this latter approach.
This lecture introduces specific deep neural networks for solving ill-posed inverse problems that account for the a priori information contained in a forward model. We outline the current approaches, point to open problems, and conclude with showing examples of their performance illustrated in tomographic image reconstruction.