Reconstruction of 3-D Density Functions from Few Projections: Structural Assumptions for Graceful Degradation

We present a spatial-domain method for reconstructing a three-dimensional density distribution from one or more projections (images formed by integration of density along lines of sight) and using the three-dimensional reconstruction to explain features of the two-dimensional images. The advantages of our proposed method are that it degrades gracefully down to a single image, that it uses linear equations and constraints (allowing the use of convex optimization), that it is amenable to three-dimensional structural biases, and that ambiguity can be expressed precisely (it is possible to "know what we don\´t know"). Previously described methods have some, but not all, of these properties.