This project focuses on improving methods to solve inverse problems, which are essential in fields like medical imaging and seismic exploration. In an inverse problem, we work backward from measurements to determine hidden information, such as identifying tumors from X-ray CT data or underground structures from seismic waves. Traditional methods rely on reconstructing detailed images, which can be inefficient and prone to errors when data is limited. Our approach directly targets the most important details, called Quantities of Interest, using advanced mathematical tools to work efficiently with sparse data. This means fewer measurements are needed, reducing costs, radiation exposure in medical imaging, and environmental impacts in seismic studies. By creating user-friendly software and validating the method with real-world examples, this project aims to make cutting-edge mathematics accessible and impactful in medicine, engineering, and geosciences.

2025

2029