Time-dependent inverse problems are experiencing a concerted increase in research effort. The simplest example is video reconstruction while more advanced problems include industrial and other process monitoring, such as the flow of a fluid in a tube to detect impurities. Efficient computational tools for the solution of dynamic inverse problems are, however, largely non-existent: the problems are dynamic, but the algorithms are not. They need to be run offline after taking taking measurements for a long time interval. There is therefore an urgent need to develop “online” algorithms that can in real-time process newly arriving data---and to understand what these algorithms solve. We propose to do exactly these two things.

2021

2025