Efficient nullspace-constrained modifications of incompletely sampled CT images

摘要

A recurring challenge in many contexts is the reconstruction of incompletely sampled CT images, e.g. due to few projections, limited angular range or truncated projections. From an algebraic point of view, an underdetermined system must be solved. Its solution has many degrees of freedom, which are determined by the nullspace of the system. We propose a method to apply generic modifications to a CT image that are restricted to this nullspace. We constructed a nullspace basis using ART or FBP algorithms and propose an image update with low computing effort using this basis. We used simulation experiments to provide a proof-of-concept for angular undersampled projections. Various nullspace-constrained modifications were applied to unconstrained ART reconstructions. The method provides the flexibility to incorporate prior knowledge after the reconstruction without violating data consistency and enables the use of unconstrained ARTs that are much faster than regularized ARTs. Our proposed method appears to be particularly promising for fast imaging with a low resolution while having certain prior knowledge about the object.