Estimating Anomalies from Indirect Observations

Indirect observations often lead to ill-posed inverse problems, where the use of prior information plays a crucial role. When correctly used, informative priors should be based on our belief of what the typical situation looks like, while the aim of the measurement procedure is often to find deviations from the typical. This work proposes a method of implementing priors that on one hand reflects the belief concerning the typical situation and on the other retains sensitivity to anomalies of the prescribed type. Numerical results are based on Bayesian sampling methods.