Spotlight inversion by orthogonal projections

Abstract: In inverse problems, the goal is to estimate unknown parameters from indirect noisy observations. It is not uncommon that the forward model assigning the observed variables to given values of the unknowns depend on variables that are not of primary interest, often referred to as nuisance parameters. In this article, we consider linear inverse problems, and propose a novel technique, based on linear algebra and orthogonal projections, to eliminate, or at least mitigate, the contribution of the nuisance parameters on the data. The approach is referred to as spotlight inversion, as it allows to focus on the part of primary interest of the unknown parameter, leaving the uninteresting part in the shadow. The viability of the approach is demonstrated by a computed example of local fanbeam X-ray tomography: the spotlight is on the region of interest that is part of the full target.