Multidimensional image reconstruction in astronomy

A unified approach based on the assumption of additive Gaussian noise and regularization theory that illustrates the flavor of multidimensional image reconstruction problems and the associated challenges, is presented. In such image formation scenarios involving multiple sensors or perspectives, the relationship between the set of observations and the unknown field can often be adequately characterized by a linear observation model. The response function is typically determined from the characteristics of the electromagnetic radiation propagating between the source and the detector. A common challenge in practical astronomical inverse imaging problems is that the resulting linear systems are typically of enormous dimension, requiring special considerations for obtaining feasible solutions. Variational and statistical formulation of the associated inverse problems address the incomplete data aspect of the problem, while a statespace formulation offers spatial-temporal estimation of nonstationary images.