An Information Field Theory Approach to Regularized Inverse Problems

Speaker: Alex Albert (Purdue)
Dates: 2024/11/08
Location: zoom
Abstract: Inverse problems in infinite dimensions are ubiquitously encountered across the scientific disciplines. These problems are defined by the need to reconstruct continuous fields from incomplete, noisy measurements, which oftentimes leads to ill-posed problems. Almost universally, the solutions to these problems are constructed in a Bayesian framework. However, in the infinite-dimensional setting, the theory is largely restricted to the Gaussian case, and the treatment of prior physical knowledge is lacking. We develop a new framework of Bayesian field reconstruction which encodes our physical knowledge directly into the prior, while remaining in the function space setting.