Analytical Image Reconstruction Methods for Medical Tomography - Recent Advances and A New Uniqueness Result -

Image reconstruction is a key step in tomographic medical imaging. Roughly speaking, the image reconstruction methods can be classified into analytical methods and iterative (or algebraic) methods. In this presentation, we review advances on the analytical image reconstruction methods since 1990. In particular, we pick up the following two important reconstruction problems. The first topic is the 2-D region of interest (ROI) reconstruction problem in which our aim is to reconstruct an object f(x, y) on a ROI from its projection data p(r, θ) truncated with respect to the radial variable r. The second topic is the cone-beam reconstruction problem in which our aim is to reconstruct a 3-D object f(x, y, z) from a set of cone-beam projections gλ(u, v) measured by moving an x-ray source along some curve ~a(λ); λ ∈ Λ ((u, v) denotes the planar detector coordinates).