Analysis of spatial-temporal regularization methods for linear inverse problems from a common statistical framework

In some medical imaging problems, the quantity to image is time-varying but related to the measurements by spatial dynamics only. Traditional methods solve the associated inverse problem separately at each time instant. Several recent reports take advantage of prior knowledge and/or measurement temporal behavior to solve jointly in space and time. In this paper we discuss three such approaches, which have been introduced in distinct mathematical contexts, from a common statistical regularization framework, and illuminate their relationships, advantages and disadvantages.