Inverse problems are widespread in many varied fields such as medical and satellite imaging, biology, astronomy, geophysics, environmental sciences, computer vision, energy, finance, and defence. These problems are inverse in the sense that they arise from seeking to use a mathematical or physical model “backwards” to indirectly determine a quantity of interest from the effect that this quantity causes on some observed data. A main challenge resulting from using models “backwards” to measure causes from their effects is that solutions are often not well posed, i.e., not unique and/or unstable with respect to small perturbations in the data. This difficulty has stimulated an important amount of research and innovation at the interface of applied mathematics, statistics, engineering, physics, and other fields, leading to great social and economic benefit through impact on science, medicine, and engineering.
Topics: applied mathematics, statistics, machine learning, engineering, physics, inverse problems, theory, methodology, computational algorithms, and applications,