Inverse problems are a vibrant research field in the intersection of pure and applied mathematics. The goal in inverse problems is to recover information from indirect and noisy observations. The problems arise in practical situations such as medical imaging, exploration geophysics, and non-destructive testing where measurements made in the exterior of a body are used to deduce properties of the unaccessible interior. In order to do this we measure the response of the medium probed with different kinds of waves, including X-rays, sound waves, electromagnetic waves, etc. The mathematical research on inverse problems is under a significant change: The earlier studies have mostly concerned linear models. Recently, non-linear models have become the focus of interest. We combine the novel methods that use the non-linearity as a beneficial tool in imaging and the manifold learning methods to create new type of imaging methods.

2019

2023