AbstractID: 8961 Title: Tomographic Reconstructions from Incomplete Data
By demonstrating a direct equivalence between tomographic imaging and classical electromagnetic field theory, a new method for the
reconstruction of objects from measurements of their projections has been derived. In the specific application of computed
tomography (CT), sinogram data is first transformed as a weighted integral along the trajectory of a spatial point into a two
dimensional (2D) scalar potential in the image domain, and then Green’s theorem is used (in the form of a convolution operation) to
generate a three dimensional (3D) potential volume. 2D-image slices are shown to represent a solution of Poisson’s equation operating
on this potential, analogous to problems in electrostatic field theory. This method is analytical, has computational complexity
comparable to filtered back projection (FBP), and provides profound insight into the tomographic reconstruction process. With this
approach, the long-standing challenge of CT reconstruction from incomplete data (e.g., presence of opaque metal, objects extending
outside the detector field of view, etc.) is addressed through the use of mathematical tools developed for electromagnetism.
Specifically, missing measurement data is treated as an instance of an anisotropic Green’s function, allowing the estimation of the
original object in closed form. The relationship of this method to existing CT reconstruction techniques (e.g., FBP, local tomography,
algebraic reconstruction) will be explained, and applications in clinical CT as well as other tomographic imaging tasks (tomosynthesis,
cone beam reconstruction) will be discussed.